Deterministic transport pre-pass for inter-material cross-talk (MGXS)

[jon-proximafusion]

Builds on #113 (pure transport-free MGXS). Adds an optional, fully deterministic (no Monte Carlo) transport pre-pass to capture inter-material cross-talk — the one place the per-material transport-free collapse loses to stochastic_slab (resonant metals in a deep stack, e.g. Fe-56).

The full plan is in the first comment below.

[jon-proximafusion]

Plan: deterministic transport pre-pass for inter-material cross-talk

This branch builds on convert-to-multigroup-transport-free (PR #113). That base branch is the pure transport-free method — each material is collapsed in isolation against an assumed weighting flux (narrow-resonance + URR probability-table self-shielding + exact elastic/inelastic kernels). No Monte Carlo, no transport solve. It already matches or beats stochastic_slab on most materials and metrics (scatter-matrix shape solved on all 10 test materials; total XS competitive 7/10; deterministic, noise-free, fast at any group count).

Why this branch exists — the one residual gap

The single place the base method loses to stochastic_slab is resonant materials in a deep multi-material stack (Fe-56: ~3.3 % at CCFE-709 / ~1.9 % at UKAEA-1102 on total + scatter row-sum, vs slab ~1.4 % / ~0.8 %; reference noise ~0.5 %, so the gap is real).

Root cause, established conclusively on the base branch:

• The total collapse Σ_t,g = ∫φΣ_t/∫φ differs from material_wise only through φ (the pointwise Σ_t is identical).
• Every transport-free single-material weighting fails or is equivalent: NR ≈ exact 0-D slowing-down flux (≤0.02 %), crude IR (+0.3 %), a global spectral tilt (inert), and a homogenized-material-mix flux (worse, +1.1 %). First-flight upstream attenuation is also worse (+2 %).
• The missing physics is inter-material cross-talk: the flux reaching a deep material carries the resonance imprint of the upstream materials, partially filled back in by scattering. stochastic_slab captures this because convert_to_multigroup loads all materials into one (MC, randomized-slab) transport solve. A per-material isolated collapse structurally cannot — and at fine groups the imprint is within-group, so it is not even recoverable from random ray's group fluxes.

So the gap is a genuine transport effect. The base method deliberately avoids transport; this branch adds it back — deterministically (the user's constraint is no Monte Carlo, not no transport).

Goal

An optional, fully deterministic transport pre-pass that computes a cross-talk-aware weighting flux over all the model's materials (the noise-free analog of stochastic_slab), then collapses each material against its local flux. Target: match or beat stochastic_slab on Fe-56 and the resonant metals — deterministically, noise-free, and cheaply.

Approach (SCALE CENTRM/PMC-style)

1. 1D geometry reduction — auto-build a layered slab/sphere from the model's material adjacency (analogous to how stochastic_slab auto-builds its randomized slab, but using the real ordering — no randomization).
2. Fixed-source deterministic transport on a fine pointwise / ultra-fine-energy mesh, with scattering (the scatter fill-in is what the cheap shortcuts missed). Solver options, cheapest first: collision-probability (CPM) → 1D Sₙ / MOC.
3. Collapse each material against its local φ(region, E). Cross-talk now represented.

Design constraints (carried from the base method)

• No Monte Carlo — fully deterministic, reproducible (bit-identical), noise-free.
• Knob-free / most-accurate-by-default — the solver's discretization parameters (energy mesh, spatial mesh, Sₙ/Pₙ order, source-iteration tolerance) are auto-set to converged values, not user accuracy knobs. Unlike MC nparticles (statistical noise ∝ 1/√N, "always converged" unaffordable), deterministic discretization converges monotonically to the exact answer and is cheap in 1D, so "fully converged" can simply be pinned internally. (Being verified against how CENTRM/APOLLO pin these — finding will be appended.)
• Optional / layered — the base transport-free method stays the default; this pre-pass is an opt-in enhancement for cross-talk-sensitive deep multi-material problems.

Phases

1. Minimal 1D CPM fixed-source solver on the pointwise grid (scatter-iterated); validate its flux shape against a material_wise flux tally.
2. Wire φ(region, E) into the per-material collapse.
3. Validate on Fe-56, steel, SiC, and the full 10-material stack at CCFE-709 + UKAEA-1102: deterministic-pre-pass vs material_wise vs stochastic_slab (total + scatter row-sum + shape). Target: ≤ slab, noise-free.
4. RR-vs-CE shielding benchmark — the decisive arbiter of whether the cross-talk correction matters at the flux/dose level.
5. API integration into convert_to_multigroup, keeping it knob-free.

Open questions

• The 1D geometry-reduction heuristic (layer ordering/thickness from an arbitrary model).
• CPM vs Sₙ vs MOC accuracy/cost trade-off for deep penetration + anisotropy.
• Default vs opt-in, and how the option surfaces in convert_to_multigroup.

[jon-proximafusion]

Proof of concept — deterministic 1D transport cracks Fe-56 (beats stochastic_slab, noise-free)

A working prototype of the planned deterministic transport pre-pass is validated. It closes the one gap the pure transport-free method had (resonant metals in a deep stack) and does so deterministically — no Monte Carlo.

Method (prototype)

1D slab Sₙ (S8) slowing-down transport along the cross-talk path (source → upstream shells → target material), on the fine pointwise energy grid:

• Neutrons enter at x=0 (14 MeV muir), slow down (isotropic-CM elastic kernel) and attenuate through the upstream layers; the flux reaching the target carries the upstream resonance imprint (the inter-material cross-talk stochastic_slab gets by loading all materials at once).
• On a fine energy point grid elastic scatter is strictly down in energy ⇒ a single high→low energy sweep, each energy one Sₙ spatial pass (no within-energy scatter, no iteration).
• Collapse the target against its local (layer-averaged) flux.

Result — total XS, % error vs material_wise

material	det-NR (isolated, base branch)	det-TRANSPORT	stochastic_slab	ref-noise
Fe-56 @ CCFE-709	3.26	0.60	1.39	0.46
Fe-56 @ UKAEA-1102	1.88	0.35	0.81	0.52
steel @ CCFE-709	0.57	0.47	0.48	1.40
SiC @ CCFE-709	0.12	0.08	0.06	0.86

Fe-56 is cracked: det-transport beats slab by ~2× and lands at the material_wise noise floor — i.e. as accurate as the MC reference can be measured — with zero stochastic noise. Steel/SiC tie or improve (already within reference noise). The cross-talk hypothesis is confirmed: every isolated weighting (NR, IR, exact 0-D slowing-down, tilt, homogenized-mix) failed because none carries the upstream imprint; a real (deterministic) transport solve does.

Performance & knobs

• ~7 s/material (CCFE-709, after thinning the grid to ~32k points by min-lethargy spacing Δu=4e-4 — identical result to the full 466k-point grid, which took 756 s) and fully vectorized. Scales fine to UKAEA-1102.
• No accuracy knobs exposed. Discretization is pinned to converged defaults (S8, Δu=4e-4 energy mesh, 1 cell/cm, single energy sweep). These converge monotonically/deterministically (unlike MC nparticles), so "converged" is cheap to hardcode — the API stays a single knob-free call.

Honest caveats / next steps

• Prototype uses a slab approximation of the spherical reference and elastic-only down-scatter; despite both, it nails Fe-56 (the imprint is dominated by attenuation, which the full Σ_t carries). A spherical solver / inelastic source are refinements, likely marginal.
• Next: (1) integrate into a clean, self-contained module routine (auto-derive the 1D path from the model geometry, like slab auto-builds its slab); (2) extend the scatter-matrix collapse (not just total); (3) the decisive random-ray-vs-CE benchmark.

[jon-proximafusion]

Update — deterministic transport now cracks the SCATTER MATRIX too (commit bc779b5)

RR needs the group-to-group scatter matrix, not just the vector total. Extended the prototype: the scatter matrix is built the SCALE/AMPX way — kernel shape (weighting-insensitive) renormalised to the transport-flux scatter cross section (direct group collapse of the 1D-transport local flux). Fe-56 vs material_wise:

Fe-56	det-NR (isolated)	det-TRANSPORT	stochastic_slab
total @ CCFE-709	3.26	0.60	1.39
total @ UKAEA-1102	1.88	0.35	0.81
scatter row-sum @ CCFE-709	3.40	1.04	1.45
scatter row-sum @ UKAEA-1102	1.96	0.60	0.86
scatter shape (leth)	0.011 / 0.008	0.011 / 0.008	0.010 / 0.008

det-TRANSPORT beats stochastic_slab on total and scatter row-sum, and ties on shape — deterministically, noise-free. Both total and scatter are at/near the material_wise reference noise floor.

Note: a separate scatter_matrix builder bug

The direct group-collapse of the scatter XS with the transport flux is correct (1.04%). The scatter_matrix(phi_ext=…) path gives a wrong row-sum (4.68%) — a normalisation bug in that path. Sidestepped here by the shape×rowsum recipe (which is the principled SCALE approach anyway); to be fixed properly at module integration.

Geometry decision (from discussion)

• 1D slab chosen over sphere/cylinder: faster, far simpler (no curvilinear angular-redistribution term), and for a fusion blanket — a thin shell on a large radius — slab is actually the more faithful local model. Curvature barely affects the spectral weighting (slab nailed a spherical reference at 0.60%).
• Geometry → 1D: read the radial material build from the geometry layers (source-outward order); for complex 3D, harvest material paths from random-ray's source-sampled rays. Volumetric (plasma) source = just a distributed inner-region source term; the shield sees ~14 MeV at its inner face either way.
• Sparse materials are the easy case (dilute → flux set by surroundings → clean local flux; deterministic has no MC-noise failure mode where material_wise would).

[jon-proximafusion]

Full 10-material sweep — one full-stack 1D Sₙ solve, each material collapsed against its own layer flux

Replaced the per-target truncated path with a single transport solve through the whole stack (source → all shells → outer vacuum), so every layer has its real upstream and downstream. CCFE-709, total + scatter row-sum + scatter shape, det-TRANSPORT vs material_wise vs stochastic_slab:

material	TOTAL NR / TR / slab	ROWSUM NR / TR / slab	SHAPE TR / slab
tungsten	1.96 / 5.51 / 2.56	3.60 / 6.29 / 2.36	0.004 / 0.006
steel	0.57 / 0.70 / 0.48	0.75 / 1.19 / 0.56	0.008 / 0.008
Fe-56	3.26 / 0.32 / 1.39	3.40 / 0.76 / 1.45	0.011 / 0.010
CuCrZr	0.85 / 1.06 / 1.02	1.34 / 1.71 / 1.12	0.017 / 0.017
Zircaloy	0.79 / 0.56 / 0.91	1.02 / 1.45 / 0.99	0.014 / 0.014
SiC	0.12 / 0.06 / 0.06	0.40 / 0.09 / 0.06	0.023 / 0.018
Li₄SiO₄	0.06 / 0.06 / 0.42	0.39 / 0.14 / 3.26	0.041 / 0.218
concrete	0.05 / 0.05 / 0.09	0.29 / 0.06 / 0.10	0.035 / 0.106
H₂O	0.03 / 0.02 / 0.05	0.17 / 0.03 / 0.05	0.016 / 0.041
Helium	0.04 / 0.04 / 0.39	0.17 / 0.05 / 9.66	0.117 / 0.529

Verdict

• Deep / cross-talk-dominated materials → big wins on all three metrics: Fe-56, Li₄SiO₄, concrete, H₂O, Helium (e.g. Helium row-sum 0.05 vs slab 9.66; Li₄SiO₄ 0.14 vs 3.26), plus Zircaloy (total) and SiC (tie). These are exactly where a single NR weighting and slab both struggle, and where the inter-material cross-talk matters most. Deterministic, noise-free, one ~30 s solve for the whole stack.
• Near-source structural metals → TR loses (tungsten, steel, CuCrZr). Root cause is the slab vs sphere geometry: a slab over-reflects backscatter toward the centre (a sphere subtends less solid angle there), so the innermost shells' flux is over-softened. Confirmed by a spherical-volume-weight test (made tungsten worse, isolating it to the transport, not the averaging).

Why this is fine, and the fix

• The near-source metals are precisely where NR is already excellent (≤ 2 %). Practical recipe: NR near the source, transport for the depth — and the transport flux itself signals which regime a region is in.
• It is also partly a test-geometry artifact: the reference is a centre-point-source sphere. Real fusion has a surface/volumetric plasma source with a thin-shell blanket on a large radius → locally planar → the first-wall artifact wouldn't appear.
• Clean uniform fix: 1D spherical Sₙ (matches the reference geometry; correct near-source backscatter). The slab prototype already proves the physics and the deep-material wins.

[jon-proximafusion]

Root cause of the scatter-matrix "phi_ext bug": there isn't one — it was a cross-section-definition mismatch + invalid thermal flux

No phi_ext/grid_ext bug. Passing the internal NR flux through phi_ext reproduces the default NR scatter matrix exactly (max row-sum diff 0.00 %); grid_ext matches the default grid. The mechanism is bit-correct.

The "4.68 vs 1.04" was me comparing two different cross sections. scatter_matrix's row-sum uses the kernel scatter XS with (n,2n)/(n,3n) multiplicity — which is what the MC reference tallies (outgoing neutrons). My "direct collapse" used total−absorption (no multiplicity). The kernel definition is the correct one (it matches NR's validated 3.40 % vs material_wise).

Why the correct number (4.63 %) looked worse than NR — the thermal flux. Per incoming-energy decade vs material_wise:

decade	NR err	transport err
1–20 MeV	2.1 %	1.2 %
10 keV–1 MeV	13.7 %	2.2 %
100 eV–10 keV	0.0 %	0.0 %
1–100 eV	0.0 %	0.0 %
< 1 eV (75 rows)	(ok)	23.9 %

The transport flux is better than NR in every decade above 1 eV (the cross-talk win: epithermal 13.7 %→2.2 %), but the 1D transport flux is invalid in the thermal range (no thermal scattering treatment; this single-target path also lacks the downstream moderators), corrupting 75 thermal rows at 23.9 % and dragging the naive average to 4.63 %.

Fix — thermal-NR fallback. Weight the scatter collapse by the transport flux above the thermal cutoff and by NR below (NR is exact in the thermal). Result for Fe-56 scatter row-sum:

• pure NR 3.40, pure transport 4.63, hybrid 0.69, slab 1.45.

So the transport beats slab on both total (0.60) and scatter row-sum (0.69) for Fe-56, once the thermal range falls back to NR. The recipe: transport flux for fast/epithermal, NR (or proper thermal) below the free-gas threshold.