PerturbedEquilibrium - FEATURE - Emit the Lagrangian field-strength perturbation in the Boozer and Hamada field-line gauges #560

#543 writes the perturbation that drives neoclassical transport in the perpendicular-displacement gauge (dBoB_lagrangian, div_xi_perp). NEO-2, NEO-RT and other Boozer- or Hamada-based consumers need the Lagrangian field-strength perturbation in their own field-line gauge instead. Changing the gauge adds a displacement w along the field line, which is found from the magnetic differential equation

D w = -(div xi_X + a * delta B_X / B),   a = 2 (Boozer), a = 0 (Hamada),

where angles are in turns and delta B_target = delta B_X + w * partial_theta B. Nonzero resonant sources must fail explicitly rather than being regularized silently.

The Fortran implementation, with its derivation and FortSym-generated kernels, is in GPEC#344 (docs/pmodb_target_gauge.rst, gen/pmodb_gauge/). That PR will not be merged in Fortran, because new features now go to the Julia code. Its tests should be carried over: cancellation of a parallel displacement, zero source, and resonant source rejection. A Hamada-to-Boozer cross-check is also available against an independent kernel.

Proposed scope: after #543 lands, add the gauge solve and dBoB_lagrangian_boozer / _hamada outputs, either to the on-demand helper of #429 or as new HDF5 datasets, whichever the #429 decision prefers. The gauge contracts are documented in #540.

Chris&AI