[WIP] Space Charge: bound the dynamically resized mesh

[ax3l]

ResizeMesh fitted the box to the exact particle extent on every slice step, so the resolution drifted continuously and the FFT solver rebuilt its Green's function each time. This gives the padding a band instead, and within it picks the mesh from a geometric progression (also used in industry), so a beam of nearly the same size lands on exactly the same mesh and the Green's function can be reused. On the new expanding-acc test that takes builds from 100 to 10 and runtime from 0.95 s to 0.41 s, and on cfchannel from 50 to 4.

The allowed mesh lengths are $L_k = 2^{k/m}$ m, with $m = \lceil 1 / \log_2 r \rceil$ and $r$ the width of the band, prob_relative_max divided by prob_relative[0]. Here $L_k$ is the mesh edge length along one axis, $k$ the whole number making $L_k$ the smallest such length that still covers the padded beam, and $m$ how many allowed lengths there are per factor of two. Rounding $m$ up keeps the mesh inside the band, and keeping it a whole number per doubling makes two meshes a factor of two apart differ by exactly two, which the solver relies on to reuse a Green's function built at another scale.

geometry.prob_relative is now the smallest the mesh may be and geometry.prob_relative_max the largest, defaulting to 10% above it for the FFT solver, so $m = 8$. Setting them equal fits the beam exactly and is bit-identical to before. The longitudinal axis is sized in the frame the solver works in, and that stretch is derived here the same way the solver derives it, because reconstructing it from a velocity costs about $\varepsilon\gamma^2$ and would leave the mesh never quite repeating. Depends on BLAST-WarpX/warpx#7178, which is what actually reuses the Green's function.

Testing detail

Adds tests/python/test_igf_greens_cache.py. It compares the reusing solver against ablastr.igf_rebuild_always=1 and requires exact equality of all beam moments, covering the store disabled and enabled, an exactly fitted mesh and a banded one, and an accelerating lattice. Each configuration runs in a single-threaded subprocess: charge deposition sums thread-dependently, so under the suite's OMP_NUM_THREADS=2 even two identical runs differ in the last digits and the comparison would otherwise be vacuous. Running apart also keeps ParmParse from leaking between configurations. Further tests assert the mesh is one of the allowed lengths for bands giving 4, 8 and 16 lengths per doubling, with a negative control asserting an exactly fitted mesh is not, and that a band below prob_relative[0] is rejected.

How wide the band can get, scanned on expanding-acc against its own envelope comparison at rtol 0.79%: 1.21 gives 0.496% and 76 of 100 reused, 1.5 gives 0.554% and 90 reused, 2.0 gives 0.640% and 94 reused, 3.0 gives 1.115% and fails. So the default is conservative and roughly 2.0 is the ceiling for this test. Emittances are unchanged to 0.00% throughout. expanding-2d-acc passes at every band and reuses 91 of 100 at the default, though the Green's function is only about 2% of its runtime.

Space-charge regressions: 66 of 66 pass, including both new acceleration tests. The 100-slice expanding-acc case remains byte-identical to rebuilding every step while reusing 90 of 100, since the meshes recur exactly rather than approximately.

Also consolidates the two diverging copies of read_mr_prob_relative, in impactx::initialization:: and impactx::detail::, which had to be kept in sync by hand for every new geometry parameter.

🤖 Generated with Claude Code

[codspeed-hq]

Merging this PR will not alter performance

✅ 70 untouched benchmarks

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_{Comparing ax3l:topic-igf-greens-cache (f5f22e1) with development (2a2c2a7)}