Fix RK near-axis pseudo-Cartesian coordinates#402
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Summary
Fix the RK near-axis pseudo-Cartesian transform used by
orbit_timestep_axis.The old path entered the near-axis chart as
(s cos theta, s sin theta)but treated it as(sqrt(s) cos theta, sqrt(s) sin theta)when evaluating velocity and returning to flux coordinates. That made the axis an artificial sink for some mirror-trapped particles.This PR makes the chart consistent:
(sqrt(s) cos theta, sqrt(s) sin theta)s = x^2 + y^20.5chain-rule factor invelo_axisThis is the RK-only extraction from PR #401. The symplectic near-axis experiment stays stacked there.
Verification
fo check