fix(spectrax1d): separable per-axis Hou-Li filter#274
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The previous 3D-radial formula filter[n,m,p] = exp(-α·(√(n²+m²+p²)/h_max)^p) used a single h_max = √((Nn-1)²+(Nm-1)²+(Np-1)²) for all axes. When mode counts are anisotropic (e.g. Nn=64, Nm=4), h_max is dominated by the longest axis and the short axes never reach the filter knee — every mode on the short axis sees filter ≈ 1.0, leaving the top mode there with no dealiasing. This caused energy to pile up at the highest m mode under Lorentz-force coupling and led to numerical blow-up in SRS configurations with low Nm. Replace with a separable tensor product f_n(n) · f_m(m) · f_p(p) so each axis has its own taper exp(-strength · (i/(N_axis-1))^order). The top mode on every axis is now damped at the configured strength regardless of how the mode counts compare to each other. 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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Summary
The Hou-Li dealiasing filter in
SpectraxVectorField._houli_filteris built as a single 3D radial taper, but the radius is normalized by the diagonalh_max = √((Nn-1)² + (Nm-1)² + (Np-1)²). When mode counts are anisotropic (e.g.Nn=64, Nm=4, Np=1),h_maxis dominated by the longest axis and the short axes never reach the filter knee — every mode onmandpseesfilter ≈ 1.0.Concretely with
Nn=16, Nm=4, Np=1, strength=36, order=36:So the top
mmode has zero damping. In SRS-like configurations where the Lorentz force pumps energy into the highest retained transverse Hermite mode, this leads to a numerical pile-up that eventually blows the run up. We hit this withNn=16, Nm=4, dt=0.1at1e15 W/cm²on a 0.5 ps run — Ey grew cleanly to ~0.08 then wentNaNat t ≈ 0.22 ps.Change
Replace the 3D-radial formula with a separable tensor product
f_n(n) · f_m(m) · f_p(p), where each axis has its own 1D taperexp(-strength · (i/(N_axis-1))^order). The top mode on every axis is nowdamped at the configured strength regardless of how the mode counts compare.
The 1-mode axis edge case (
N=1) returns[1.0]to avoid the0/0in the normalization.Test plan
Nn ≫ Nm) survives long-time integration without NaNNn=Nm=Np) gives ≈ the same filter values as before at the corners (radial and separable taper agree on the diagonal up to small differences from thei^ordervs√(n²+m²)^ordershape)🤖 Generated with Claude Code