sbeg radial meaning differs between Boozer (s) and scaled REFCOORDS (sqrt(s)) sampling paths

[krystophny]

Problem

sbeg is fed verbatim as the radial coordinate to whichever magfie is
active during init_starting_surf, so its physical meaning depends on the
sampling path:

• VMEC equilibrium runs (any field type) sample via VMEC magfie, whose
  x(1) = s (normalized toroidal flux): sbeg = s.
• Boozer runs sample via magfie_boozer, x(1) = s: sbeg = s.
• The scaled REFCOORDS path samples at x(1) = rho (scaled_to_ref_coords:
  chartmap reference u_ref = x_scaled; VMEC reference u_ref = x_scaled**2,
  so the integration coordinate is sqrt(s)): sbeg = rho = sqrt(s).

So sbeg = 0.5 starts at s = 0.5 on the Boozer/VMEC path but at
s = 0.25 on the scaled REFCOORDS path. Comparing a VMEC run on one path
against a chartmap run on the other starts particles on different physical
surfaces. export_boozer_chartmap_tool also writes start points as
rho = sqrt(s), so a start.dat carries the reference convention of the
run that produced it.

Geometric/UNKNOWN (map2disc) references have no toroidal flux, so s is
undefined there.

Proposal

Anchor sbeg to normalized toroidal flux s wherever a toroidal flux is
defined: convert s to the active sampling coordinate (identity for
Boozer/VMEC, sqrt for the scaled REFCOORDS path) at the points that seed
start positions (init_starting_surf, sample_grid, volume-sampler
bounds). For geometric/UNKNOWN references keep sbeg as the reference
radial coordinate and state that at startup. Add a characterization test
asserting sbeg = s_target starts on the same physical surface for VMEC
and a rho_tor chartmap of the same equilibrium. Expect golden-record
movement on the REFCOORDS/RK45 path; regenerate with justification.

[krystophny]

Review-policy follow-up: add a characterization test before changing behavior.

Acceptance target:

• For one VMEC equilibrium and its rho_tor chartmap, sbeg = s_target seeds particles on the same physical surface for VMEC/Boozer and chartmap paths.
• The test records the convention explicitly: VMEC/Boozer use s; scaled REFCOORDS must not silently interpret the same input as sqrt(s).
• Any golden-record movement from the fix explains the changed starting surface and expected direction.