Production deterministic-transport MGXS (switch-free, real geometry + thermal in-kernel)

[jon-proximafusion]

Builds on #113. One clean module routine for a switch-free deterministic-transport weighting (real layered geometry + free-gas thermal folded into the transport). Distils #114/#115/#116. Plan in the first comment.

[jon-proximafusion]

Plan: production switch-free deterministic-transport MGXS

Distils the #114/#115/#116 investigations into one clean module routine, off the
transport-free base (#113). Adds convert_to_multigroup(method="deterministic_transport")
alongside material_wise / stochastic_slab.

Why (what we learned)

• Pure transport-free NR (Convert to multigroup transport free #113) wins or ties slab on ~9/10 materials; the one clear,
  above-noise loss is Fe-56 (and the resonant metals generally) — the inter-material
  cross-talk a per-material collapse can't see.
• A deterministic transport pass supplies that cross-talk: slab transport + thermal-NR
  gives Fe-56 total 0.60 / scatter 0.69, both beating slab (1.39 / 1.45).
• "Switching" (NR near-source / transport deep; NR thermal / transport fast) is NOT
  fundamental — it was a crutch for two prototype approximations (slab-vs-sphere test
  geometry; no thermal in the transport). The production version removes both.

Design (no switches)

1. Read the model's real layered geometry (material order + thicknesses) from
   model.geometry — like stochastic_slab reads materials, but keeping the real order.
2. One 1D transport solve with the free-gas thermal kernel folded into the scatter
   source -> phi(region, E) for every region at every energy.
3. Collapse each material against its region's local flux (reusing Convert to multigroup transport free #113's
   collapse_material / scatter_matrix with the kernel scatter XS incl. multiplicity).
4. No region switch (geometry gives near-source=hard vs deep=degraded automatically);
   no energy switch (thermal handled in-kernel). Knob-free.

Geometry

1D slab in the model's layer coordinate is the right model for a fusion shield (thin shell
on a large radius, surface plasma source). Curvilinear (spherical/cyl) only if a problem
truly needs it; #116 shows it is numerically harder with little gain.

Validation

Full 10-material stack (CCFE-709 + UKAEA-1102): total + scatter row-sum + shape, vs
material_wise and converged stochastic_slab -> the definitive all-materials win-count.
Then the decisive random-ray-vs-CE downstream check.

[jon-proximafusion]

Inelastic + (n,2n) down-scatter added → TOTAL 7/10 → 9/10

The transport down-scatter source was elastic-only. Added inelastic + (n,xn) via a coarse
per-material transfer matrix M[out,in] (incl. multiplicity; the inelastic outgoing is smooth,
so a coarse grid + interpolation is accurate), applied in an outer iteration (elastic solve →
add inelastic source from that flux → re-solve, ×2). +71 s. New file prototype/inel_source.py
(commit 28313c375).

Result (CCFE-709, vs converged stochastic_slab)

material	TOTAL det/slab	scatter ROWSUM det/slab	vs elastic-only
steel	0.25 / 0.48	0.42 / 0.51	0.70 / 0.89 → now beats slab on both
Fe-56	0.44 / 1.41	0.51 / 1.47	0.32 / 0.40 (still crushes slab)
Zircaloy	0.57 / 0.91	0.94 / 1.00	win
tungsten	3.79 / 2.57	5.26 / 2.34	unchanged

Inelastic fixed steel (the win) and took TOTAL to 9/10. Tungsten is the lone holdout.

Why tungsten is immune — it's geometry, not physics

M_inel[tungsten] builds correctly (all 5 W isotopes' MT51–91 + (n,2n)) and is applied to the
W cells, yet the collapse doesn't move. So tungsten's error is source-region geometry:

• In material_wise (the truth) tungsten is mixed through the whole domain → it sees the
  fully built-up equilibrium (~1/E) slowing-down spectrum.
• In the slab it sits only at the front 6 cm → its flux is the 14 MeV source lightly
  self-slowed → too hard. Deep materials don't have this (they sit where a slowed spectrum
  is physical, which is exactly why inelastic fixed steel).
• NR assumes that equilibrium 1/E, so NR is better for the first wall (1.96 vs 3.79).

Clean switch-free rule (no arbitrary threshold)

NR for the source layer (no upstream material → flux is the source spectrum → NR exact)
+ transport for everything downstream. The geometry itself defines the rule — it's "use NR
where there's nothing upstream to slow neutrons down," not a tuned cutoff.

Bottom line: #117 delivers the deep-penetration goal — 9/10 on total, the deep/cross-talk
resonant metals (Fe-56, steel, Zircaloy) all cracked vs slab. The remaining holdout is the first
wall, where NR is the correct tool anyway.

[jon-proximafusion]

Cross-talk benchmarks refine where deterministic transport earns its place

Companion to the cross-talk comment on #113. Controlled 2-material adjacency tests (W│H₂O, steel│Fe-56) vs material_wise, both orderings. Two findings that sharpen #117's scope:

1. Transport's value is intra-region spatial-spectral resolution for resolved-resonance metals — not inter-material cross-talk. Fe-56: NR ~3% → transport ~0.8%, and this holds whether Fe-56 is behind steel (3.01 → 0.66) or at the front (3.25 → 0.90). The neighbour's identity barely moves it (≲ MC noise). What transport fixes is the depth-varying slowing-down spectrum through the thick resonant region that a single 0-D flux cannot represent.

2. Transport is WORSE than NR for tungsten — even when W is deep. W behind 12 cm of water: NR 1.06 vs transport 3.26 (and W at the front: 1.30 vs 2.91). So #117's tungsten regression is not merely the near-source artifact — the 1D slab transport is genuinely the wrong tool for W (URR-dominated; NR+URR is excellent at ~1%). This generalizes the source-layer-NR recommendation to "NR for URR-dominated metals (W), transport for resolved-resonance metals (Fe-56)."

Net: #117's deterministic transport pays off on exactly the materials where the NR method (#113) has its only real gap — thick resolved-resonance metals (Fe-56-like). For moderators and URR metals, #113's NR+URR is as good or better, and transport should defer to it.

[jon-proximafusion]

How the four MGXS methods compare (reference, fusion shield, VITAMIN-J-175)

A head to head of all four generation methods on one fusion shield, scored as the mean
absolute % difference versus material_wise (the reference). Kept here as a durable
reference for how these methods stack up.

Geometry (point 14 MeV Muir source in the plasma, concentric shells):
50 cm DT plasma, 1 mm tungsten, 3 cm 50/50 water+steel, 60 cm 80/20 lithium-lead+helium,
5 cm graphite, 2 cm steel, 1 m void, 2 m concrete.

Methods: slab = stochastic_slab (Monte Carlo). css = collapsed_self_shielding
(PR #118, deterministic collapse against an assumed NR flux). det = deterministic_transport
(this PR, 1D Sn transport solve giving a cross-talk-aware local flux). material_wise is the
reference and is run with two seeds so its own Monte Carlo noise is shown.

All numbers are % difference vs material_wise; lower is closer. Ref noise is the
reference's seed-1 vs seed-2 difference (how trustworthy the reference itself is).

Material	Ref noise (tot / scat)	Total: slab / css / det	Scatter: slab / css / det
plasma	0.00 / 100	0.03 / 0.80 / 0.77	100 / 0.07 / 0.10
tungsten	0.13 / 0.23	5.91 / 8.90 / 12.79	5.30 / 7.60 / 10.73
water_steel	0.02 / 0.03	0.08 / 0.96 / 0.91	0.08 / 1.07 / 1.03
lipb_he	0.01 / 0.23	0.62 / 1.06 / 1.03	0.62 / 0.25 / 0.22
graphite	0.05 / 0.05	0.07 / 0.70 / 0.54	0.07 / 1.12 / 0.98
steel	0.10 / 0.17	0.23 / 3.30 / 1.17	0.27 / 3.10 / 0.98
concrete	0.04 / 0.06	0.21 / 0.85 / 0.92	0.22 / 1.26 / 1.32

(plasma scatter 100 % is near-void DT, physically meaningless; note it is the noisy one for
Monte Carlo slab, while the deterministic methods are clean.)

How they compare

• material_wise is well converged (seed to seed noise at most 0.23 %), so every
  difference is a real method difference, not noise.
• stochastic_slab is closest to the reference on every material except the thin near-source
  tungsten. It is itself Monte Carlo, so it shares the reference's transport physics and its
  mixed-material spectrum resembles the true degraded in-place spectra.
• collapsed_self_shielding (Add collapsed_self_shielding MGXS generation method #118) is competitive (sub-% to a few %) but trails on the deep
  resonant metal steel (3.3 %) and near-source tungsten. Its value is determinism, zero noise,
  and a valid positive cross section in every group, not accuracy on this metric.
• deterministic_transport (this PR) beats css on the deep resonant metal steel by about
  3x (total 1.17 vs 3.30, scatter 0.98 vs 3.10), the cross-talk win it was built for, and is
  modestly better or tied on most other materials. But it regresses on the thin near-source
  tungsten (12.8 vs 8.9), and it does not beat stochastic_slab anywhere. It is also much
  heavier (a 1D transport solve plus a geometry reduction).

Takeaway

On this collapse vs material_wise metric, stochastic_slab is closest overall; the
deterministic-transport method fixes collapsed_self_shielding's deep resonant metal weakness
at the cost of the near-source first wall. material_wise as the truth structurally favors the
other Monte Carlo method, so the decisive test of whether the deep-metal win matters is
downstream transport (random ray or Sn vs continuous energy), not this table.