[ysm1887]

GPEC - ENHANCEMENT - div-free option for psi,theta grid fields and arzphifun grad(zeta) update

For fast-ion calculations a divergence-free perturbed field can matter, so this adds an output option for that and makes the flux-grid vector potential consistent with it. Both changes are output-only (gpout_xbrzphifun, gpout_arzphifun); reg_div_flag defaults to f, with it off the outputs are identical to develop.

1. gpout_arzphifun: grad(zeta) components w(3,1:2)

gpeq.f (l.757-761) computes the poloidal components of grad(zeta) as

w(3,1) = (twopi*r*rfac/jac)*(rzphi%fx(2)*rzphi%fy(3)-rzphi%fx(3)*(1+rzphi%fy(2)))
w(3,2) = (r/(2*rfac*jac))*(rzphi%fx(3)*rzphi%fy(1)-rzphi%fx(1)*rzphi%fy(3))

gpout_arzphifun used w(3,1)=2*rfac*dphi_psi, w(3,2)=dphi_theta/(2*pi*rfac) instead. This PR implements the same quantity there through the w(1,:), w(2,:) already in the routine (sign opposite to gpeq.f because arzphifun applies it with a minus):

w(3,1) = (rzphi%fx(3)*w(1,1) + rzphi%fy(3)*w(2,1))/twopi
w(3,2) = (rzphi%fx(3)*w(1,2) + rzphi%fy(3)*w(2,2))/twopi

Check (KSTAR n=1, psi_N < 0.4): curl(a) vs xbrzphifun b_R / b_z = 168 % / 46 % before, 0.25 % / 0.14 % after; a_phi unchanged.

2. reg_div_flag: the regularized field is not divergence-free

Issue: with reg_flag=t the output field (b_R, b_z, b_phi) does not satisfy div b = 0. The regularization damps bmt and bmz but not bwp, and div b = 0 ties m*bwt - n*bwz to d(bwp)/dpsi. On the psi,theta grid the b_phi implied by div b = 0 from (b_R, b_z) differs from the output b_phi by ~15 % pointwise near the rational surfaces (4 % numerical floor with reg_flag=f).

reg_div_flag=t (default f) lets the user choose, at output time in gpout_xbrzphifun only, a regularization that keeps div b = 0: only the (n,m) projection of (bwt, bwz) is damped,

T   = (n*bwt + m*bwz)/(n^2 + m^2)
bmt = bwt - (1-f)*n*T,   bmz = bwz - (1-f)*m*T

so m*bmt - n*bmz is unchanged. bwp, xi and all other outputs are untouched. Check: pointwise mismatch 0.147 -> 0.044 (= reg-off floor), xi identical, fields finite in the bands.

Files

gpec/gpout.f (fix + flag block), gpec/gpglobal.F, gpec/gpec.f (flag), input/gpec.in. Built from install/ with ifort; added fixed-format lines <= 72 columns. The same approximation also appears in gpdiag_singcurs (gpdiag.f l.476, 502) — not touched here.