39-EFT.WP.Plasma.Confinement v1.0 | Chapter 14 — Simulation Stack & Benchmark Cases (Methods.SimStack.Plasma)

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Chapter 14 — Simulation Stack & Benchmark Cases (Methods.SimStack.Plasma)

I. Chapter Objectives & Structure

1. Objective: Build a multi-layer Simulation Stack (SimStack.Plasma) for Plasma Confinement that executes, under a unified dialect, the full forward → inversion → validation → release workflow from netlist/geometry/coils/binding, equilibrium and waves/heating, guiding-center & transport, Edge/SOL to synthetic diagnostics—assimilation—publication; provide reproducible alignment and a benchmark-case library.
2. Structure: Stack layers → Shared dialect & records → Numerical methods & stability → Benchmark cases → Multi-domain/experiment alignment → Falsifiability → Data structures & export → Compliance templates → Cross-chapter closure.
3. Shared arrival-time dialect (two equivalent forms; explicit gamma(ell) & d ell; record delta_form):
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )

II. Simulation Stack Layers (Plasma, bottom-up)

• Physics Core (S20-/S30-/S40-): minimal equations, Grad–Shafranov equilibrium, energy principle δW & Δ'.
• Waves (S50-): dispersion & n_eff(omega), ray/full-wave, α_abs & P_dep(r), T_arr.
• Guiding-Center & Neoclassical (S60-): drifts v_E/v_{∇B}/v_{curv}, invariants μ/J_∥, D_nc/χ_nc/J_bs.
• Transport (S70-): QL/mixing-length closures, scaling/tabulated closures, flux-surface averaging & global energy closure.
• Edge/SOL (S80-): 1D along-field minimal equations, sheath matching & Bohm gate, recycling/impurity/radiation, heat loads & detachment.
• Binding (I10-): geometry–coil–boundary–metric generation, outputs B(x)/psi/q(psi)/V'(ψ)/g_ab.
• UQ & Inversion (M10-/Mx-*): observation operators, covariances, assimilation/evidence, PPC & uncertainty propagation.
• I/O & Cards: data/model/pipeline cards; mandatory arrival and qa_gates; version locks & reproducible seeds.

III. Shared Dialect & Records (mandatory)

• Units/dimensions: SI; key equalities check_dim = pass.
• Energy/power closure (hard gate): P_in = P_ref + P_rad + P_wall + ∫ P_dep dV within u.
• Topology consistency: q(ψ), LCFS/X/separatrix consistent with imaging/magnetics (S30-/I10-).
• Stability gates: δW_min > 0, Δ' ≤ 0, local {D_S,D_M} > 0 (S40-).
• Arrival consistency: two-dialect T_arr within u(T_arr) (S50-/M10-).
• Versioned spectral windows/calibration: AF/PF/window/bw/fs/Δt_sync recorded in dataset cards.

IV. Numerical Methods & Stability (Plasma focus)

• Equilibrium (GS): Δ*ψ = − μ0 R^2 p'(ψ) − F F'(ψ); free/fixed boundary, coil coupling (BEM/FEM/hybrid); smooth/monotone p'(ψ)/F'(ψ).
• Stability: energy-principle discretization (vacuum/coil boundary terms), tearing inner-layer matching & Δ'; PPC check of δW + ∫ E·J dV vs Poynting flux.
• Waves/heating: cold/warm dispersion matrices, cutoff/resonance handling (band-limited regularization), Hamiltonian rays with adaptive steps, full-wave meshing & CFL.
• Guiding center: symplectic/Boris variants, μ-invariance gate, orbit classification (passing/trapped) & banana width.
• Transport: QL/mixing-length γ_k/k_⊥^2, tabulated closure band-limited interpolation/extrapolation, flux-surface averaging with consistent metrics.
• Edge/SOL: 1D along-field steady/transient, sheath BCs, recycling/impurities, heat loads & detachment windows.
• Stability tactics: mesh convergence, spectral flatness, residual whitening; monitor spectral radius/condition numbers of GS/full-wave/assimilation operators.

V. Benchmark Case Library (Plasma, minimal reproducible)

• SIM-PC-01 | Equilibrium (GS): geometry/coil import → ψ/q(ψ) regression vs magnetics/imaging; gates: force-balance residual, topology consistency.
• SIM-PC-02 | Stability: δW/Δ' aligned to diagnostic spectral features; gate: δW_min>0 ∧ Δ'≤0.
• SIM-PC-03 | Waves/deposition: n_eff/k_∥/k_⊥ → α_abs/P_dep & power closure; gate: ∫P_dep ≈ P_in−P_ref−P_rad−P_wall.
• SIM-PC-04 | GC/neoclassical: μ̇≈0, D_nc/χ_nc/J_bs vs tables/theory; gate: relative deviation ≤ threshold.
• SIM-PC-05 | Transport scaling: D,χ vs D_GB/scalings; gate: R^2 ≥ R^2_gate and residual ≤ ε_gate.
• SIM-PC-06 | Edge/SOL detachment window: q_t vs P_in/R/geometry; gate: q_t ≤ q_gate and detachment criteria met.

Each ships dataset_card/pipeline_card/env_lock with reference outputs for regression & release.

VI. Multi-Domain/Experiment Alignment (I10-/S30-/S50-/S60-/S70-/S80-/M10-)

• Geometry/coil binding (I10-): import S_wall/ports/divertor, C_i(s)/A_i/I_coil; generate B(x) & psi_bc; construct (ψ,θ,ζ)/V'(ψ)/g_ab.
• Equilibrium (S30-): solve GS for ψ/q(ψ)/J_∥; QA topology/force balance.
• Stability (S40-): evaluate δW/Δ'/{D_S,D_M} & map to spectra.
• Waves/heating (S50-): dispersion → ray/full-wave → α_abs/P_dep/T_arr/T_group; power closure & arrival agreement.
• GC/neoclassical (S60-): orbits & D_nc/χ_nc/J_bs; metric consistency.
• Transport (S70-): QL/tabulated closures → Γ/Q/Π_ψ with flux-surface averaging & global closure.
• Edge/SOL (S80-): 1D along-field, sheath match, q_t & detachment window.
• Synthetic diagnostics & assimilation (M10-): build H(x) & R/B; assimilate to x_a; QA power/topology/arrival gates.

VII. Falsifiability (SimStack.Plasma)

• F-PC-1 (Energy/power non-closure): P_in − P_ref − P_rad − P_wall − ∫P_dep dV beyond u → reject α_abs/P_dep or power dialect.
• F-PC-2 (Topology inconsistency): ψ/q(ψ)/LCFS/X disagree with imaging/magnetics → reject boundary/coil/metric mapping.
• F-PC-3 (Stability gates fail): δW_min ≤ 0 or Δ' > 0 → deny release or revise profiles/boundary terms.
• F-PC-4 (Deposition/arrival mismatch): P_dep peak/width or two-dialect T_arr disagree → reject dispersion/ray/sync correction.
• F-PC-5 (Transport scaling off): D/χ regression residuals vs D_GB/tables exceed gates → reject closure or input profiles.
• F-PC-6 (Neoclassical conflict): D_nc/χ_nc/J_bs disagree with ν_* , q , ε relations → reject coefficients or collision model.

VIII. Data Structure & Export (minimal template)

simstack_plasma:

case_id: "SIM-PC-03"

model_id: "PC-eft-ms"

freq_grid_Hz: [...]

geometry_ref: "GEOM-COIL-0001"

binding_ref: "I10-PC-0001"

i10_binding: "/artifacts/i10_binding.yaml"

equilibrium:

psi: "/eq/psi.nc"

q: "/eq/q.nc"

waves:

n_eff: "/waves/n_eff.tbl"

rays: "/waves/rays.json"

alpha_abs: "/waves/alpha.tbl"

P_dep_Wm3: "/waves/Pdep.nc"

guiding_center:

D_nc_m2s: "/nc/Dnc.tbl"

chi_nc_m2s:"/nc/Chinc.tbl"

J_bs_Am2: "/nc/Jbs.tbl"

transport:

closure: "/closures/ql_mix.tbl"

Gamma_Q_Pi: "/flux/fluxes.nc"

edge_sol:

s_grid_m: "/edge/s.npy"

profiles_1D:"/edge/profiles.nc"

diagnostics:

H_blocks: [ "ECE_transfer", "Reflect_phase", "Mag_inversion", "IR_heatflux" ]

windows: "/diag/windows.yaml"

arrival:

form: "n_over_c"

gamma: "explicit"

measure: "d_ell"

c_ref: 299792458.0

Tarr_s: 3.1e-06

u_Tarr_s: 9.0e-08

delta_form: "n_over_c"

qa_gates: {check_dim:"pass", power_closure:"pass", topology:"pass", Tarr_dual:"pass"}

seed: 20250916

IX. Compliance Templates (APIs & snippets)

• API prototypes

api:

- id: "SimStackPlasma.build"

proto: "build(geometry, coils, binding_i10, options) -> sim_handle"

- id: "SimStackPlasma.forward"

proto: "forward(sim_handle, theta, grid) -> {equilibrium, stability, waves, gc, transport, edge, synth_obs}"

- id: "SimStackPlasma.invert"

proto: "invert(sim_handle, data, priors, sampler:'EnKF|4DVar') -> {posterior, logZ, summary}"

- id: "SimStackPlasma.ppc"

proto: "ppc(sim_handle, posterior, grid) -> {residual_spectrum, gates}"

- id: "SimStackPlasma.export"

proto: "export(sim_handle, format:'cards|json') -> artifacts[]"

• Power closure & arrival (pseudocode)

# Power closure

Pdep = integrate(P_dep_grid) # waves

assert abs(P_in - P_ref - P_rad - P_wall - Pdep) <= u_power

# Two-dialect arrival

Tarr1 = (1/c_ref) * trapz(n_eff(ω)*dℓ, ω)

Tarr2 = trapz((n_eff(ω)/c_ref)*dℓ, ω)

assert abs(Tarr1 - Tarr2) <= u_Tarr

• Stability & transport regression (pseudocode)

assert deltaW_min > 0 and DeltaPrime <= 0

R2_D = r2_score(log(D), log(D_GB))

R2_χ = r2_score(log(χ), log(χ_GB))

assert R2_D >= R2_gate and R2_χ >= R2_gate

X. Cross-Chapter Links & Closure

• Dependencies: Chapters 4 (S20- minimal equations), 5 (S30- equilibrium), 6 (S40- stability), 7 (S50- waves/deposition/arrival), 8 (S60- guiding center), 9 (S70- transport), 10 (S80- edge/wall), 11 (I10- binding), 12 (M10- assimilation).
• Downstream: Chapter 15 (Data & Repro—data/pipeline/env-lock & equivalence thresholds), Chapter 16 (Design Protocol & Checklist—integrate regression gates into sign-off).