[logan-nc]

Adds Utilities.BootstrapCurrent: the flux-surface-averaged bootstrap current ⟨j_bs·B⟩ from the Redl et al. (2021) closure, assembled the way OpenFUSIONToolkit TokaMaker assembles it, so that a GPEC calculation and a TokaMaker equilibrium carry the same bootstrap current.

What is added

• bootstrap_current(equil, kinetic=equil.kinetic; psi_N, Z_dom) returns ⟨j_bs·B⟩, j_φ,bs = ⟨j_bs·B⟩ F⟨1/R⟩/⟨B²⟩ (the field-aligned part; TokaMaker's jphi_bs adds the pressure-driven P′(⟨R⟩ − F²⟨1/R⟩/⟨B²⟩)), and the intermediates (f_t, ν*_e, ν*_i, ε, R_geo, q, F, ⟨B²⟩, ⟨1/R⟩, ⟨1/R²⟩, L31, L32, L34, α) on a ψ_N grid.
• The pieces are public:
  • redl_coefficients (Redl Eqs. 10–21, L34 = L31);
  • jdotB_bootstrap;
  • circulating_fraction (Sauter's ¾ f_tu + ¼ f_tl from surface moments of |B|);
  • surface_moments;
  • coulomb_log_i, nu_star_e_floored and nu_star_i_koh.
• Z_eff comes from the kinetic zeff profile, or else from the same quasineutral closure the inner layers use.
• Docs: a "Bootstrap current" section in docs/src/utilities.md and the two citations.
• Nothing in the existing pipeline calls it yet, so no output changes. It is meant to feed the bootstrap term of the modified Rutherford equation (#665: MRE with saturated-island roots, applied-field forcing and a Callen preset) on one normalization with the curvature term, and the bootstrap-current change across a flattened island.

Verification

• Unit tests against TokaMaker (test/runtests_bootstrap_current.jl, 60 tests):
  • coefficients and assembly match TokaMaker's redl_bootstrap (OFT 637ddb5) to 1e-12 at six points spanning f_t, Z_eff and both collisionalities;
  • the Coulomb logarithms match calculate_ln_lambda;
  • the circulating fraction matches its definition, converges with grid, has the 1.46√ε limit, and agrees with the exact pitch-angle integral to 2 %;
  • end to end on the DIII-D-like SLAYER example, the result is co-directed with the equilibrium ⟨j·B⟩.
• End to end against TokaMaker on its public ITER H-mode example: TokaMaker solve, then gEQDSK, then GPEC, with the same kinetic arrays. The figure is in the review package: https://claude.ai/artifact/FyFtgZ1oZw9civQiBEiutm
  • ⟨j·B⟩ agrees to 0.48 % over ψ_N 0.1–0.9, independent of resolution.
  • Passing TokaMaker's intermediates through these functions agrees to 4e-16. q, f_t, F, ⟨1/R⟩ and ⟨B²⟩ agree to ≤ 0.02 %.
  • The 0.48 % comes entirely from the ε and R definitions. The installed reference (OFT 26.6 Python) uses ε = ⟨a⟩/⟨R⟩ and ⟨R⟩. This PR uses (R_max − R_min)/(R_max + R_min) and R_geo, which are the current TokaMaker defaults (use_sauter_eps = True at 637ddb5). Substituting the 26.6 values closes the gap to 0.024 %.

Question for @d-burg: is (R_max − R_min)/(R_max + R_min) with R_geo the convention TokaMaker will keep? If not, the change is one line in surface_moments.

Release note

• Audience: users
• Numerical impact: none (harness @ e0467b7; the later 6f8ae85 only adds input checks to a function no pipeline stage calls)
• Migration: none

GPEC can compute the bootstrap current ⟨j_bs·B⟩ from kinetic profiles with the Redl 2021 closure, matching OpenFUSIONToolkit TokaMaker, via Utilities.bootstrap_current.

Part of #630 (general MRE).