chipf(1) is never set

[CharlesCNorton]

add_fluxes.f90 fills chipf on the interior and at the edge only:

! add_fluxes.f90:66-67
  chipf(2:ns1) = (chips(2:ns1) + chips(3:ns1+1))/2.0_dp
  chipf(ns)    = 2.0_dp*chips(ns)-chips(ns1)

chipf(1) keeps its allocation value and is written as -0.0 (wrout.f90:738), while iotaf(1) and phipf(1) are both extrapolated to the axis (add_fluxes.f90:70, eqfor.f90:148). chipf/phipf reproduces iotaf on every other surface and is 0 at the axis; q = phipf/chipf is infinite there.

Hirshman fixed both ends of this profile in 2016. PARVMEC add_fluxes.f90:153-155:

      chipf(1)     = c1p5*chips(2) - p5*chips(3)                       !SPH ADDED THIS 4-8-16
      chipf(2:ns1) = (chips(2:ns1) + chips(3:ns1+1))/2
      chipf(ns)    = c1p5*chips(ns)- p5*chips(ns1)                     !SPH FIXED THIS 4-8-16

The 2017 STELLOPT copy of VMEC2000 8.52 that this repository started from has neither line (VMEC2000/Sources/General/add_fluxes.f90:62-63 in the history), so the missing axis value and the 2*chips(ns) - chips(ns1) edge rule are both inherited. The 1.5/-0.5 rule already used for iotaf at add_fluxes.f90:70-71 restores iota = chi'/phi' at both ends.