RK45 refcoords (chartmap vmec_to_wall): missing footprint loss cluster vs symplectic

[krystophny]

Summary

RK45 integration in reference coordinates (magfie REFCOORDS, integmode=0) shows a missing class of losses compared to the symplectic runs for the same vmec_to_wall chartmap case.

The missing losses appear as an entire footprint cluster in (theta,zeta) / (R,Z) for chartmap_wall_125mm_rk45_refcoords, while the corresponding symplectic chartmap_wall_125mm run shows that cluster clearly.

Context

In the SQUID chartmap validation dataset (/home/ert/data/SQUID/SIMPLE/rerun_2026_chartmap), we compared:

• chartmap_wall_125mm (symplectic, integmode=3, canonical MEISS)
• chartmap_wall_125mm_rk45_refcoords (RK45, integmode=0, isw_field_type=REFCOORDS)

Both use the same physical wall chartmap:

• coord_input = chartmaps/squid_5c_vmec_wall_125mm.chartmap.nc (rho_convention=vmec_to_wall, rho=1 is wall)

Observations

1. Loss fraction difference

• Symplectic wall: 190/8192 lost (2.319%)
• RK45 refcoords wall: 79/8192 lost (0.964%)

2. Missing footprint cluster
   A cluster in the approximate angular window

• theta in [80°, 170°]
• zeta in [0°, 55°] (nfp=4)
  accounts for 92 of the symplectic losses, but 0 of the RK45/refcoords losses.

3. Those missing-band particles do not appear to be saved by simply tightening tolerances
   A quick RK45/refcoords run with tighter settings (512 particles, relerr=1e-10, ntimstep=4000, npoiper2=128) still showed 0 losses in that band.

4. Geometric closeness to the wall surface
   For RK45/refcoords wall losses, the lost points are close to the chartmap wall boundary (rho=1), consistent with the loss test being tied to rho.
   However, the missing-band particles (lost in symplectic) end RK45/refcoords at rho<1 and typically remain O(10 cm) away from the wall at their final (theta,zeta).

This suggests the discrepancy is not just a plotting artifact; it is a real integration/trajectory difference.

Hypothesis / Suspects

• RK45/refcoords trajectory differs qualitatively because it uses magfie_refcoords (splined A,h,B derivatives + computed hcurl), while symplectic uses canonical field (MEISS) and a different integration scheme.
• There may be a bug or inconsistency in magfie_refcoords evaluation for chartmap coordinate systems (metric/basis/Jacobian handling, periodic wrapping, derivative scaling), producing different drift behavior in some regions.
• Alternatively, the chamber/loss check path differs between the RK45 and symplectic pipelines.

Note: In this repo, chamb_can is currently a stub (src/chamb_m.f90) that flags outside when y(1) >= 1, which means for RK45/refcoords runs it effectively checks rho>=1 (and ignores toroidal angle).

Reproduction (from dataset repo)

1. In SQUID/SIMPLE/rerun_2026_chartmap/, run the RK45/refcoords wall case:

• runs/validation_vmec_theta/chartmap_wall_125mm_rk45_refcoords/simple.in uses isw_field_type=5 (REFCOORDS) and integmode=0.
• Execute with ~/code/SIMPLE/build/simple.x simple.in in that directory.

2. Compare footprints against the symplectic wall case using tools/plot_validation.py.

Evidence

• Combined plot set (includes symplectic wall + RK45/refcoords wall):
  runs/validation_vmec_theta/fig/triage_125mm_rk45_compare_footprints_theta_zeta.png

Desired next steps

• Add a targeted diagnostic for magfie_refcoords / REFCOORDS+RK45 in chartmap coordinates:
  • Evaluate/plot key quantities along a representative orbit from the missing band (e.g., Bmod, sqrtg, hcurl, and their derivatives)
  • Compare against the canonical MEISS field evaluation along the same physical points.
• Verify that REFCOORDS+RK45 path uses consistent wall/loss check logic with other integrators.