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Kinetic matrix build: default pitch/energy QuadGK rtol over-tight (~3x) vs PENTRC/LSODE #316

Description

@logan-nc

Summary

The self-consistent kinetic matrix build uses adaptive Gauss–Kronrod (QuadGK) for the
pitch/energy integrals, but the default rtol_xlmda is set to match PENTRC's nominal
value. QuadGK bounds the overall-integral error while PENTRC/LSODE bounds per-step
error, so matching the nominal tolerance over-refines Julia by ~3× at no accuracy benefit.

Where

KineticForces.compute_calculated_kinetic_matrices ->
compute_kinetic_matrices_at_psi! -> integrate_pitch_gar_quadgk (QuadGK.quadgk! with
atol=atol_xlmda, rtol=rtol_xlmda). The control default is rtol_xlmda=1e-5,
atol_xlmda=1e-8.

Measurement (matched grid: mpsi=257, mpert=27, nl=6, 8 threads)

rtol_xlmda atol_xlmda matrix-build wall
1e-5 (nominal-matched) 1e-9 1668 s
1e-3 (rtol-dominated) 0.1 512 s (3.3× faster)

The least-stable kinetic eigenvalue's real part is unchanged between the two (it matches
Fortran kinetic-DCON to 0.17% either way).

Why the nominal match is wrong

QuadGK's rtol is a bound on the converged integral; LSODE's rtol is a bound on each
step, so LSODE's effective integral accuracy is much looser than its nominal rtol.
rtol_xlmda=1e-3 (with a loose, rtol-dominated atol) is the matched-accuracy analogue of
PENTRC's step-level 1e-5.

Suggested change

Default rtol_xlmda to ~1e-3 with a loose (rtol-dominated) atol_xlmda, and/or document
that the QuadGK integral-level tolerance is not directly comparable to a PENTRC/LSODE
step-level tolerance. (Separately: the eigenvalue's imaginary/damping part is far more
tolerance/normalization sensitive — tracked separately.)

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