Implement Bernstein's breakdown for the perturbed potential energy

docs/tex/recon/references.bib

@@ -0,0 +1,58 @@
+@techreport{chance1992mhd,
+  author       = {Chance, M. S. and Jardin, S. C. and Kessel, C. E. and Okabayashi, M. and others},
+  title        = {Mhd stability of tokamak plasmas},
+  institution = {Princeton Univ., NJ (United States). Plasma Physics Lab},
+  year        = {1992},
+  type        = {Technical Report}
+}
+@article{RevModPhys.76.1071,
+  title = {Physics of magnetically confined plasmas},
+  author = {Boozer, Allen H.},
+  journal = {Rev. Mod. Phys.},
+  volume = {76},
+  issue = {4},
+  pages = {1071--1141},
+  numpages = {0},
+  year = {2005},
+  month = {Jan},
+  publisher = {American Physical Society},
+  doi = {10.1103/RevModPhys.76.1071},
+  url = {https://link.aps.org/doi/10.1103/RevModPhys.76.1071}
+}
+@phdthesis{Park2009Ideal,
+  author       = {Park, Jong-Kyu},
+  title        = {Ideal Perturbed Equilibria in Tokamaks},
+  school       = {Princeton University},
+  year         = {2009},
+  month        = {June},
+  address      = {Princeton, NJ},
+  note         = {Advisers: Jonathan E. Menard and Allen H. Boozer},
+  department   = {Department of Astrophysical Sciences, Program in Plasma Physics}
+}
+@incollection{Bernstein1983,
+  author    = {Bernstein, I. B.},
+  title     = {Basic Plasma Physics I},
+  booktitle = {Handbook of Plasma Physics, Volume 1},
+  editor    = {A. A. Galeev and R. N. Sudan},
+  publisher = {North-Holland},
+  address   = {Amsterdam},
+  year      = {1983},
+  pages     = {421}
+}
+@article{10.1063/1.4958328,
+  author = {Glasser, A. H.},
+  title = {The direct criterion of Newcomb for the ideal MHD stability of an axisymmetric toroidal plasma},
+  journal = {Physics of Plasmas},
+  volume = {23},
+  number = {7},
+  pages = {072505},
+  year = {2016},
+  month = {07},
+  abstract = {A method is presented for determining the ideal magnetohydrodynamic stability of an axisymmetric toroidal plasma, based on a toroidal generalization of the method developed by Newcomb for fixed-boundary modes in a cylindrical plasma. For toroidal mode number n≠0, the stability problem is reduced to the numerical integration of a high-order complex system of ordinary differential equations, the Euler-Lagrange equation for extremizing the potential energy, for the coupled amplitudes of poloidal harmonics m as a function of the radial coordinate ψ in a straight-fieldline flux coordinate system. Unlike the cylindrical case, different poloidal harmonics couple to each other, which introduces coupling between adjacent singular intervals. A boundary condition is used at each singular surface, where m = nq and q(ψ) is the safety factor, to cross the singular surface and continue the solutions beyond it. Fixed-boundary instability is indicated by the vanishing of a real determinant of a Hermitian complex matrix constructed from the fundamental matrix of solutions, the generalization of Newcomb's crossing criterion. In the absence of fixed-boundary instabilities, an M × M plasma response matrix WP, with M the number of poloidal harmonics used, is constructed from the Euler-Lagrange solutions at the plasma-vacuum boundary. This is added to a vacuum response matrix WV to form a total response matrix WT. The existence of negative eigenvalues of WT indicates the presence of free-boundary instabilities. The method is implemented in the fast and accurate DCON code.},
+  issn = {1070-664X},
+  doi = {10.1063/1.4958328},
+  url = {https://doi.org/10.1063/1.4958328},
+  eprint = {https://pubs.aip.org/aip/pop/article-pdf/doi/10.1063/1.4958328/14131506/072505_1_online.pdf},
+}
+
+

gpec/gpec.f

@@ -39,7 +39,7 @@ PROGRAM gpec_main
      $     arbsurf_flag,angles_flag,surfmode_flag,rzpgrid_flag,
      $     singcurs_flag,m3d_flag,cas3d_flag,test_flag,nrzeq_flag,
      $     arzphifun_flag,xbrzphifun_flag,pmodbmn_flag,xclebsch_flag,
-     $     filter_flag,gal_flag,delpsi_flag,use_res_spot,
+     $     filter_flag,gal_flag,delpsi_flag,recon_flag,use_res_spot,
      $     singthresh_callen_flag,singthresh_slayer_flag,singthresh_flag
       LOGICAL, DIMENSION(100) :: ss_flag
       COMPLEX(r8), DIMENSION(:), POINTER :: finmn,foutmn,xspmn,
@@ -73,7 +73,9 @@ PROGRAM gpec_main
      $     xclebsch_flag,pbrzphi_flag,verbose,max_linesout,filter_flag,
      $     netcdf_flag,ascii_flag,singthresh_flag,
      $     singthresh_callen_flag,singthresh_slayer_flag,
-     $     singthresh_slayer_inpr,singthresh_slayer_inpr_prof
+     $     singthresh_slayer_inpr,singthresh_slayer_inpr_prof,
+     $     recon_flag,recon_int,cveri_flag,recon_out,
+     $     recon_flag2,recon_flag3
       NAMELIST/gpec_diagnose/singcurs_flag,xbcontra_flag,
      $     xbnobo_flag,d3_flag,div_flag,xbst_flag,jacfac_flag,
      $     pmodbmn_flag,rzphibx_flag,radvar_flag,eigen_flag,magpot_flag,
@@ -199,6 +201,12 @@ PROGRAM gpec_main
       test_flag=.FALSE.
       eigm_flag=.FALSE.
       mutual_test_flag=.FALSE.
+      recon_flag=.FALSE.
+      recon_flag2=.FALSE.
+      recon_flag3=.FALSE.
+      recon_int="spline"
+      cveri_flag=.FALSE.
+      recon_out=.TRUE.
 
       majr=10.0
       minr=1.0
@@ -229,6 +237,12 @@ PROGRAM gpec_main
       READ(in_unit,NML=gpec_output)
       READ(in_unit,NML=gpec_diagnose)
       CALL ascii_close(in_unit)
+      SELECT CASE(TRIM(recon_int))
+      CASE("spline","trapezoid")
+      CASE DEFAULT
+         CALL gpec_stop("gpec_output recon_int must be spline or "//
+     $        "trapezoid")
+      END SELECT
       galsol%gal_flag=gal_flag
       IF(timeit) CALL gpec_timer(0)
 c-----------------------------------------------------------------------
@@ -619,7 +633,15 @@ PROGRAM gpec_main
       IF (arzphifun_flag) THEN
          CALL gpout_arzphifun(mode,xspmn)
       ENDIF
-
+      IF (recon_flag) THEN
+         CALL gpout_recon(mode,xspmn)
+      ENDIF
+      IF (recon_flag2) THEN
+         CALL gpout_recon2(mode,xspmn)
+      ENDIF
+      IF (recon_flag3) THEN
+         CALL gpout_recon3(mode,xspmn)
+      ENDIF
 c-----------------------------------------------------------------------
 c     diagnose.
 c-----------------------------------------------------------------------
@@ -775,4 +797,3 @@ PROGRAM gpec_main
       CALL gpec_dealloc
       CALL gpec_stop("Normal termination.")
       END PROGRAM gpec_main
-