[logan-nc]

Adds a steady modified Rutherford equation (MRE) to Tearing as ModifiedRutherfordProblem: every term switchable, seed thresholds and saturated widths per rational surface, and the coil forcing with its critical fields. Callen's reduced steady state becomes a preset of it, and CallenProblem is retired. The branch also carries a trapped-fraction fix in Utilities, previously its own PR.

Closes #630. Part of #629: the critical resonant field and the vacuum-island widths are here; saturated-island pressure flattening is not.

What it computes

For each rational surface of a single-n force-free-states (FFS) solve, F(w) is the sum of the switched terms below, with w the full island width in ψ_N:

• Classical: Δ′(w) from the computed Δ′ with the finite-pressure Mercier power (Benjamin et al. 2026 Eq. 10). A constant Δ′ and Callen's Δ_c are alternatives.
• Saturation: a finite-width correction to Δ′ (Fitzpatrick 2023 Eqs. 9.15–9.21). Its coefficients come from the Grad–Shafranov current profile with a windowed fit. Off by default.
• Bootstrap: the Hegna D_nc as Fortran RDCON evaluates it, with the transport threshold w_d (Benjamin Eq. 11).
• Curvature: Lütjens et al. 2001 (default), matched to SLAYER's toroidal critical offset at small w, or Benjamin Eq. 12.
• Polarization: Benjamin Eq. C.1 (sign as written, consistent with Wilson et al. 1996), a reduced form, or Callen's. The island frequency is the electron diamagnetic one (Wilson 1996), an island locked in the laboratory, or a given ω/ω_*i.
• Coil forcing: taken from a perturbed-equilibrium solve on the same equilibrium.

From F(w) it reports:

• the seed threshold w_m, and every saturated width together with the seed that reaches it;
• the resonant field of a vacuum island as wide as each threshold;
• the critical and trigger fields of the forcing;
• validity flags, including linearly unstable, interchange-unstable, below the ion banana width, unconverged saturation coefficient, gate disagreement and collisional (ν*_e > 1, outside the banana-limit bootstrap).

The deck section is [Tearing.ModifiedRutherford] (preset = "callen" for Callen's form); output goes to Tearing/ModifiedRutherford/ in gpec.h5. With [Tearing] present, the linear layer solve is the MRE's gate. Docs: docs/src/inner_layer.md.

Also in this branch

• Trapped fraction. Utilities.NeoclassicalResistivity.trapped_fraction evaluated a different expression from the Lin-Liu & Miller (1995) bound it cites. It ran 15–45 % above the exact effective trapped fraction and now evaluates Eq. (4) as written, to within 3 %. Its one caller is ResistEval, which sets the F_33 neoclassical resistivity, so η falls and S rises on every surface. The recommended weighted average (Eq. 18) needs a further surface average and is left for later.
• layer_plasma (InnerLayer, new API): one view of the kinetic plasma for every layer consumer.
• Tearing/ HDF5 output. A TearingResult write now clears only the keys it owns, so MRE output written before it is kept.

Release note

• Audience: users
• Numerical impact: Only the SLAYER cases move, all from the trapped fraction: in diiid_slayer_n1, S rises 45–60 % on the 2/1–4/1 surfaces and each tracked growth rate falls about 30 % in magnitude (the unstable 2/1 from 164 to 119 s⁻¹), with Q roots, P_perp and the critical b_r moving with them; the chi_perp_e, winding, coupled and toroidal variants move alike. The other 22 existing cases are unchanged. diiid_slayer_n1_mre and diiid_n1_callen are new and have no develop baseline. (harness @ 8e9e0b6 vs develop f11d75a, matching environments) The full test suite passes except runtests_equil.jl:312 (TokaMaker i-file), which fails identically on develop.
• Migration: CallenProblem is removed; use ModifiedRutherfordProblem(ffs; pe, CALLEN_PRESET...) or [Tearing.ModifiedRutherford] preset = "callen".

New [Tearing.ModifiedRutherford] section: a configurable steady modified Rutherford equation giving seed thresholds, saturated widths and coil-forcing critical fields per rational surface. The neoclassical trapped fraction behind the Sauter and Redl resistivity models was 15–45 % too high and now follows Lin-Liu & Miller Eq. (4), so η is lower and S higher on every surface.

🤖 Generated with Claude Code

https://claude.ai/code/session_01BgNxCBwLNHQmVq7iXMCTae