Toroidal HDF5 grid/Bp stores B^zeta instead of physical B_phi

[krystophny]

Summary

For toroidal geometry (Igeometry=3), the HDF5 grid/Bp dataset is documented as the physical cylindrical toroidal component B^varphi, but write_grid stores the contravariant coordinate component B^zeta. The cylindrical scale factor R is missing.

Source-level cause

At current master (b23a2408fc3f1dfbc14896e16d73a57f7d1d9e88), src/sphdf5.f90 describes the grid outputs as cylindrical (B^R,B^varphi,B^Z) components. In the Igeometry=3 branch, however, the assignment is:

ijimag(jk) = ( one ) * gBzeta / sg(jk,0) ! Bp

Here gBzeta/sqrt(g) is B^zeta. Since zeta is the physical cylindrical angle in stzxyz, the physical unit-vector component is

B_phi = R * B^zeta.

The neighboring BR and BZ expressions already apply the coordinate-basis derivatives; only Bp omits its scale factor.

Reproduction

1. Build current master and run the shipped toroidal case:

mkdir -p /tmp/spec-bp-repro
cp InputFiles/TestCases/G3V01L0Fi.001.sp /tmp/spec-bp-repro/
build/build/bin/xspec /tmp/spec-bp-repro/G3V01L0Fi.001.sp

2. Inspect the first nonsingular radial grid point at theta=zeta=0 in the resulting HDF5 file. On current master the native values are:

R                 = 10.15625
grid/Bp           = 0.066064035949282...
R * grid/Bp       = 0.670962865109...

An independent reconstruction from the stored A_theta/A_zeta Fourier-Zernike coefficients gives the physical cylindrical component B_phi = 0.670962865109..., while it gives the contravariant component B^zeta = 0.066064035949282....

Across every nonsingular point in the shipped 32 x 32 x 8 grid:

max |grid/Bp - independently reconstructed B_phi|     = 6.7139900606e-1
max |R*grid/Bp - independently reconstructed B_phi|   = 1.67e-15
max |grid/BR - independently reconstructed B_R|       = 1.81e-16
max |grid/BZ - independently reconstructed B_Z|       = 1.53e-16

The independent reconstruction uses the native phase m*theta-in*zeta, the A_s=0 curl identities, the signed Jacobian, and the Cartesian map (R cos(zeta), R sin(zeta), Z); it does not call SPEC field helpers.

Expected behavior

For Igeometry=3, grid/Bp should store the physical cylindrical component consistently with its documentation and with grid/BR and grid/BZ:

ijimag(jk) = Rij(jk,0,0) * gBzeta / sg(jk,0) ! Bphi

Actual behavior

grid/Bp stores B^zeta, so consumers treating it as a cylindrical field component understate B_phi by a factor of R.

Suggested regression

For G3V01L0Fi.001.sp, independently reconstruct (B_R,B_phi,B_Z) from the vector-potential coefficients and geometry, then compare all three arrays pointwise. Keep a negative assertion that raw B^zeta differs from B_phi whenever R != 1.

This report concerns only the toroidal HDF5 grid component. It does not claim that the internal contravariant field, field-line equations, or BR/BZ outputs are wrong.