Extend chartmap spline boundary range beyond [0.1, 0.99]

[krystophny]

Priority: High

Problem

Chartmap splines are currently restricted to the range [0.1, 0.99] in rho (equivalently [0.01, 0.98] in s). This limitation exists because VMEC coordinate inversion fails at exact boundary values.

Particles that venture beyond rho=0.99 use extrapolated spline values, which may be inaccurate.

Current Workaround

In field_splined.f90:create_splined_field:

real(dp), parameter :: RHO_SPLINE_MIN = 0.1_dp
real(dp), parameter :: RHO_SPLINE_MAX = 0.99_dp

Impact

• Boundary layer physics may be less accurate
• Loss detection based on rho=1.0 uses extrapolated field values
• Recently changed from 0.9 to 0.99 which improved accuracy

Proposed Solution

1. Improve VMEC coordinate inversion near separatrix (related to #TBD)
2. Consider hybrid approach: use VMEC directly near boundary, splines in interior
3. Add warning when particles access extrapolated region

Related

• VMEC from_cyl Newton iteration robustness issue
• See DOC/coordinates-and-fields.md Appendix A.1