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InnerLayer.CCC - FEATURE - Add the Cho, Choi and Choi drift-resistive linear MHD inner layer - #654
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… layer as a ToroidalLayer model CCCModel solves the drift-resistive layer equations of Cho, Choi & Choi, IEEE Trans. Plasma Sci. PS-15, 418 (1987), in the form of Kim, Cho & Choi, Phys. Fluids 31, 2659 (1988), Eqs. (1a)-(1c): the GGJ layer with the electron diamagnetic frequency Q* in Ohm's law and vorticity and the perpendicular-transport weight M⊥/M on the pressure equation. CCCParameters holds a GGJParameters plus Qstar and mperp and takes GGJ's scales, Mercier exponents and Δ normalization. Its equations, its Wasow basis (a block- diagonalizing T equal to GW2020's at Q* = 0, m = 1, with a general Sylvester splitting solve) and the rates of its two exponential families (Kim Eq. 2) run on the shared rotated-ray solver; only :ray is available. The library gains two optional hooks for models whose exponential pairs have different rates, parabolic_resolution_rate and ray_angle_admissible, whose defaults leave GGJ unchanged.
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…aring, Match and the deck through the ToroidalLayer interface
…tes with the electrons as SLAYER's does With s = γ − iω, Kim's Ohm's law Q + iQ* vanishes at ω = Q*Q₀ in the E×B frame, so Q* = ω*ₑ/Q₀ with SLAYER's ω*ₑ = n·layer_omega_star_e. Q* from kinetic data had the opposite sign and put the CCC electron resonance at n·Ω_E − ω*ₑ instead of n·Ω_E + ω*ₑ. A test pins both layers' resonances at the same lab frequency, with and without E×B rotation. The SurfaceCoupling docstring now states s = γ − iω like the rest of the toroidal-layer path.
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Release note
Adds
CCCModel, the drift-resistive linear MHD inner layer of Cho, Choi & Choi (1987) in the form of Kim, Cho & Choi (1988): the GGJ layer with electron diamagnetic drift (Q*) and perpendicular transport (M⊥/M), solved with the rotated-ray backend.Wasow analysis was done in mathematica to obtain the asymptotic series using a wolframscript routine I have been using for my other derivation which essentially just re-implemented Zhirui's mathematica notebook from GW2020. This is essentially the same as the GGJ ray solver but with coefficients and asymptotic series for the Cho-Choi-Choi layer, so this is a small, drop-in change.
Regression report
Fan-out on ITER's SDCC cluster, all 28 cases, the base branch
refactor/toroidal-layer-library@ 89c4807 vs this branch @ 979f829: all 27 existing cases unchanged, every tracked quantity diff 0.0e+00 (385 compared quantities; checksums identical), including the GGJ inner-layer, GGJ tearing and SLAYER tearing cases. The new caseccc_ray_q5i(q = 4 surface, Q* = 0.5, M⊥/M = 1.4, Q = 5i) has no base-branch value, asCCCParametersdoes not exist there.The test files touched by this PR (innerlayer, dispersion ggj/coupled/coupled_full/residual/rotation, slayer_runner, matching_models, resist_eval, solve_api, deck_roundtrip, h5_schema) pass on ITER's SDCC cluster at 979f829.
Report: per-case summary, and the inner-layer and tearing cases in full
Validation and benchmarks
These runs used the prototype of this model (the same equations threaded through GGJ on an earlier branch);
CCCModelreproduces it to 1.5e-8 at the pinned point (q4 surface, Q* = 0.5, M⊥/M = 1.4, Q = 5i).Kim, Cho & Choi (1988) Figs. 1b and 2b. Their surface (E = −0.01, F = H = 0, G = K = 100, M⊥/M = 1), tearing (odd) parity, Q* = 0 (Fig. 1b) and Q* = 0.05 (Fig. 2b). Roots of Δ₋(Q) = Δ₀ found by secant continuation along Δ₀, overlaid on the published curves with the scan axes calibrated from their tick marks. Kim et al. plot their Fourier-space tearing quantity Δ_o, which their Eq. (10b) relates to the real-space Δ′_o we compute; we convert with that equation and fit nothing.
The Δ₀ = 0 roots, which do not depend on how Δ is normalized, land on the published curves:
Away from Δ₀ = 0, Kim's axis is Δ_o = C_o·Δ′_o with C_o = |Γ(1+p₊)/Γ(−p₊)·cot(πp₊/2)| and p₊ = −1/2 + √(−D_I) (Eq. 10b); for this surface C_o = 0.6293327. With that conversion our curves overlay all of Fig. 1b and all four Q* = 0.05 curves of Fig. 2b. C_o depends only on the Mercier exponent, so the same value serves both Q*. Our Δ uses the GGJ normalization cross-checked against Fortran
rmatch.Convergence to GGJ. On the q4 benchmark surface, Q* from 1e-7 to 1 and M⊥/M − 1 from 1e-7 to 1, at Q = 0.01, 0.1 + 0.1i, i, 3 + 3i, 10i and 100i:
Accuracy and cost.
delta_convergencespread (contour angle, mesh, series order and radius, march tolerance, BVP edge, decaying-pair separation) on the q4 surface with Q* = 0.5, M⊥/M = 1.4: ≤ 3.4e-7 at Q = 0.5 + 0.5i and ≤ 7.8e-8 at Q = 5i.Single-solve times on one laptop core:
The cost grows with K·|Q|·Q*², because the march resolves the faster exponential family across the slower one's whole band.
Tearing roots on GPEC examples (dispersion roots by continuation from the SLAYER root, Q* = −ω*ₑ/Q₀ from the kinetic profiles, M⊥/M = 1; not yet wired into
TearingProblem):examples/DIIID-like_SLAYER_example, Q* ≈ 1.2–1.5 at 2/1–4/1). The CCC roots rotate at SLAYER's lab frequency on 2/1 and 3/1 (within 3%) and near it on 4/1 (−3.6e3 against −2.8e3 rad/s). The damping on 3/1 and 4/1 comes out at −310 and −420 s⁻¹, against SLAYER's −145 and −450 s⁻¹, while plain GGJ gives −1230 and −1756 s⁻¹. 2/1 differs: SLAYER is unstable at +164 s⁻¹ (without its curvature offset), CCC damped at about −330 s⁻¹ (not converged to tolerance), GGJ −1004 s⁻¹.Notes for reviewers
ToroidalLayerlibrary); review only the commits above89c4807e1.CCCModel/CCCParameters(src/InnerLayer/CCC/) implement theToroidalLayerParametersinterface: Kim (1988) Eqs. (1a)–(1c) as rows and weak form, a Wasow basis from Kim's A₀–A₂ with a block-diagonalizing T that equals GW2020's at Q* = 0, M⊥/M = 1, a general Sylvester splitting solve, and the two exponential families of Kim Eq. (2) setting the ray angle and mesh.CCCParametersholds aGGJParametersplusQstar,mperp, and takes GGJ's scales and Δ normalization. Only:rayis available.parabolic_resolution_rateandray_angle_admissible, whose defaults leave GGJ unchanged.runtests_innerlayer.jl): the Wasow matrices reproduce the ODE matrix to 1e-16; the first-order Ξ series coefficient matches a closed form from a separate Mathematica derivation to 1e-8; Δ is independent of the contour angle to 1e-7;CCCModelat Q* = 0, M⊥/M = 1 reproduces GGJ to 3e-10; Kim Figs. 1b and 2b (tearing dispersion at Q* = 0 and 0.05) are reproduced with no fitted parameter once our real-space Δ′_o is converted to their Fourier-space Δ_o (Kim Eq. 10b; factor 0.6293 for this surface).ToroidalLayerModel: the library gainslayer_parameters,check_layer_inputs,mercier_di,growth_rate_scaleandlayer_parameter_columns, sosolve(TearingProblem, CCCModel()),solve(MatchProblem, CCCModel())and their HDF5 output (Q_star,M_perp_ratiobeside GGJ's columns) need no CCC-specific code there.CCCModel(; Qstar, mperp)carries the model's inputs, a number or one value per surface; withoutQstar, Q* = n·ωₑ/Q₀ comes from the kinetic profiles, with ωₑ per unit n fromlayer_omega_star_e, so that QQ₀ is SLAYER's ωₑ. In a deck,inner_model = "CCC"under[Tearing]or[Match], withQstar,mperpand the solver options in[CCC]; decks list their toroidal models inTOROIDAL_LAYER_MODELS.GGJModelis structurally unchanged.runtests_solve_api.jl) pins the two zeros to the same lab frequency at Ω_E = 0 and Ω_E ≠ 0, through the code's own Doppler and Q mappings.ccc_ray_q5i, and tests for CCC tearing and matching (Q* = 0 reproduces GGJ to 1e-6), Q* from kinetic profiles, and deck/API parity under[Match].🤖 (Partially :P) generated with Claude Code