Non-LTE atomic kinetics + line transfer — the CRETIN architecture

Layers 1–5 treated trapping as a Holstein eigenvalue problem with a fixed (linear or saturated) absorption coefficient. CRETIN (Scott, JQSRT 71:689, 2001 — the canonical paper) does something more ambitious: it computes the atomic populations and the radiation field self-consistently, with arbitrary levels, collisional + radiative + autoionisation rates, and explicit line transfer in 1D / 2D / 3D.

This matters when the atomic populations are not in local thermodynamic equilibrium with a Maxwellian electron distribution — the NLTE regime — which is the case in: ICF capsules, tokamak divertors, X-ray laser plasmas, low-pressure discharges, and (the operator's interest) sodium-vapour TPV emitters. In all of these, the Holstein eigenmode method breaks down because the absorption coefficient itself is a function of the radiation field being computed.

CRETIN's three-phase architecture

Scott 2001 §3 splits the radiation transport into three independent passes, each with its own frequency grid. This is the key trick that makes 3D NLTE feasible without exploding memory.

The phases are isolated from each other in the iteration loop. Phase 1 gets the overall energy balance right at coarse spectral resolution; Phase 2 handles the optically-thick line kinetics; Phase 3 produces the high-resolution spectra a detector would see. This is the architecture Layer 8's LightCell calculator will reuse.

Λ-iteration and its accelerations

For a steady-state two-level atom with line source function $S$, the formal transfer equation gives $J = \Lambda[S]$ where $\Lambda$ is the line transport operator. The rate equation gives $S = \varepsilon B + (1-\varepsilon) J$ where $\varepsilon$ is the destruction probability (collisional de-excitation per scatter) and $B$ is the Planck function. Combining:

\[ S = \varepsilon B + (1-\varepsilon)\Lambda[S] \]

Simple Λ-iteration is $S^{(n+1)} = \varepsilon B + (1-\varepsilon)\Lambda[S^{(n)}]$. This converges in roughly $\bar p$ iterations, where $\bar p$ is the mean number of scatterings (= trapping factor $g_0$). At lamp opacities $\bar p \sim 100$, so 100 iterations to converge. At ICF capsule opacities $\bar p \sim 10^4$ — Λ-iteration is unusable.

Accelerated Λ-iteration (ALI) builds an approximate Λ operator $\Lambda^*$ that captures the local trapping; the iteration becomes $S^{(n+1)} = (\mathbb{1} - (1-\varepsilon)\Lambda^*)^{-1}\{\varepsilon B + (1-\varepsilon)(\Lambda - \Lambda^*)[S^{(n)}]\}$ — converges in $\sim \log(\bar p)$ steps. Auer–Heasley uses a tridiagonal approximate operator; Rybicki–Hummer uses a diagonal one.

Explore

Why "escape factor" reappears in CRETIN as a 1D fallback

Even in CRETIN, the escape-factor approximation (Layers 1–4) survives as a degraded mode for 1D and restricted 2D problems where full line transfer is overkill. Scott 2001 §3 mentions this explicitly: "Multiple formulations are available, corresponding to different geometries and line profiles." When you're modelling a fluorescent lamp or an atomic-line filter, the 3D line-transport machinery is gratuitous — the escape-factor is the right tool. CRETIN keeps both available.

This is the heart of the bridge between Layers 1–4 (escape-factor / Holstein eigenmode) and Layers 7–8 (full 3D NLTE). They are not opposing methods; they are different operating points on the same code's capability surface, calibrated to different regimes.

The Sequoia–Tillack–Scott 2006 disagreement

Honest moment: Sequoia, Tillack, Scott (UCSD-CER-06-09, 2006) compared Cretin's inverse-bremsstrahlung absorption (IBA) coefficient against Hyades, an older 1D radiation-hydrodynamics code, for the specific case of laser absorption in an underdense SiO₂ aerogel plasma. They disagreed by 30–50% at $T_e \in [1, 100]$ eV and the discrepancy collapses above 100 eV — somewhere in the screened-hydrogenic-atom IBA model, the two codes differ.

Caveat: IBA is a free-electron process — laser photons absorbed by free electrons via bremsstrahlung in a tens-of-eV plasma. It does not appear in the LightCell architecture at all. LightCell is combustion-driven heavy-particle thermal physics with bound-bound radiative transfer; there is no free-electron plasma being laser-heated. Citing this disagreement as if it constrains LightCell modelling would be a category error. We surface it here for a different reason:

The lesson is about code-validation discipline, not about LightCell specifically. Two well-engineered production NLTE codes can disagree by a factor of 2 on a specific cross-section in a specific regime. The right inference from this is general: NLTE radiative-transfer codes need experimental anchoring for every regime they're trusted in, and code-vs-code agreement is not sufficient evidence of correctness. What matters for LightCell from CRETIN-class modelling is not the IBA coefficient — it's the line-transport machinery and the multi-level CRM architecture, both of which are well-validated in the regimes they apply to.

What this layer does NOT do

• Does not implement a full CRM solver — we model the iteration convergence pedagogically. Real CRETIN has $>10^4$ atomic levels for high-Z plasma cases.
• Does not handle dielectronic recombination or autoionising-state cascades.
• The Scott 2001 Fig 3 tokamak-divertor reproduction is qualitative — order of magnitude visible, exact line ratios not validated.
• Does not address the Stewart-Pyatt continuum lowering (Scott 2001 §2.1) — relevant for $n_e > 10^{22}$ cm⁻³, far above LightCell.

FEYNMAN ✓ ALI vs Λ-iteration shown explicitly · Victor ✓ three reactive controls · Kay ✓ three-phase architecture documented · Scott ✓ Scott 2001 architecture + Sequoia 2006 honest disagreement · Molisch ✓ M&O Sec 18.6 plasma boundary noted