ExB/electron profile conversion subtracts the diamagnetic rotation

[krystophny]

Summary

calc_omega_profile documents that iread_omega_ExB adds the ion diamagnetic term to obtain ion rotation, but the implementation subtracts it. This conflicts with maintained M3D-C1 post-processing definitions, the published M3D-C1 rotation relation, and a native initialization-only discriminator.

This report concerns the relative sign inside M3D-C1. It does not infer a foreign equilibrium's COCOS and does not propose flipping any plotted result.

Current source

At public physics revision c7f9c14a26fc72dc679598609b2c424952b0300c, unstructured/gradshafranov.f90 has:

else if(iread_omega_ExB.ne.0) then
   ! we're reading in ExB rotation; add ion diamagnetic term
   ...
   dia = db*(ppval/nval - z_ion*(1.+thermal_force_coeff)*tep &
        - z_ion*te0*np/nval)
...
omega_spline%y(i) = omega_spline_0%y(i) - dpsii*dia

The iread_omega_e path uses the same final subtraction.

Independent M3D-C1 contracts

The bundled diagnostics consistently use the opposite relation:

• unstructured/idl/plot_omega.pro: w_star_i = db*piprime/den, then omega_ExB = v_omega - w_star_i;
• unstructured/idl/read_field.pro: omega_*i = db*d(p-p_e)/dpsi/den, then omega_ExB = omega - w_star_i;
• unstructured/idl/rmp.pro and schaffer_plot.pro use omega_ExB = omega_i - w_star_i.

These all imply omega_i = omega_ExB + omega_*i.

Ferraro et al., Nuclear Fusion 53 (2013) 073042, DOI 10.1088/0029-5515/53/7/073042, printed page 5, states for M3D-C1 that the perpendicular rotations satisfy omega_{e,i}=omega_ExB+omega_{*e,*i}, with omega_*i=(d p_i/dpsi)/(n_e e).

In M3D-C1's explicit right-handed cylindrical representation,
B=grad(psi) x grad(phi)+F grad(phi), E=-Phi'(psi) grad(psi), and positive-ion v_*i=B x grad(p_i)/(q_i n_i B^2). The toroidal coefficients again give omega_i=omega_ExB+(1/(q_i n_i)) dp_i/dpsi.

Native discriminator

An initialization-only run selected iread_omega_ExB=1, db=0.0322, and wrote the native profile before any time step. GDB recorded dpsii=3.1702203540215126 after define_profiles. At normalized psi zero:

normalized input omega_ExB       0.06959516098919606
native dia                       -0.013683542009059833
native omega_i                   0.1129750044
current minus prediction         0.11297500438142596
documented plus prediction       0.02621531759696616
native/current residual          1.86e-11
native/documented separation     8.68e-2

Thus the executable exactly follows the final minus sign; this is not a display, interpolation, or COCOS ambiguity.

Suggested resolution

Please confirm the intended iread_omega_ExB and iread_omega_e contracts. If the comments, bundled diagnostics, and published relation are intended, change the final operation to addition and add a regression with nonzero pressure gradients. The regression should cover both input paths, both signs of the diamagnetic term, and the intended behavior of iflip_j/iflip_v rather than assuming those modifiers.

No M3D-C1 production source was changed during this audit. The reproducer, hashes, source-token checks, raw GDB trace, and exact arithmetic are maintained externally in verify_m3dc1_profile_rotation.py.