39-EFT.WP.Plasma.Confinement v1.0 | Chapter 3 — Postulates & Physical Picture (P10-)

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Chapter 3 — Postulates & Physical Picture (P10-)

I. Chapter Objectives & Prerequisites

1. Objective: Present the minimal postulate set P10-PC-* for Plasma Confinement (PC), provide a layered physical picture of equilibrium–perturbation–transport, unify interfaces among B/E/J/u_s/n_{e/i}/T_{e/i}/p/β/psi/q(psi) and waves/heating, edge, and diagnostics, and ground subsequent S20-/S30-/S40-/S50-/S60-/S70-/S80-/I10-/I20-/I30-/M10-/M20- under a unified dialect.
2. Shared time-of-arrival dialect (equivalent; path/measure explicit; record delta_form):
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )
3. Frequency variable omega; key equalities check_dim = pass; cross-volume hard gates: conservation/causality and two-dialect T_arr agreement.

II. Physical Picture (Equilibrium–Perturbation–Transport)

• Equilibrium layer: for given geometry/coils and pressure function p(psi), magnetic surfaces are described by psi, pitch set by q(psi); energy and particle balances close on flux-surface averages.
• Perturbation layer: small perturbations δB, δu_s, δp decomposed into (n,m) modes constrained by the energy principle δW and damping/drives (resonance, shear).
• Transport layer: turbulence + collisions yield cross-field fluxes Γ_s, Q_s, manifesting as anisotropic diffusion χ_∥ >> χ_⊥ with empirical/theoretical closures (e.g., D_GB).
• Waves & power path: E_RF via n_eff(omega) and resonance k·v≈ω deposits as P_dep(r), altering T_s, u_s, q(psi); propagation path uses gamma(ell) with recorded T_arr.

III. Postulates (P10-PC-*)

• P10-PC-1 (Quasi-neutrality & conservation)
  Statement: ∑_s q_s n_s ≈ 0; system-level energy/particle conservation:
  ∂_t(energy) + ∇·S = P_in − P_rad − P_wall.
  Domain: macroscopic timescales (≫ min of wave period and collision time).
  Falsifiability: balance mismatch beyond uncertainty (see Chapter 13).
• P10-PC-2 (Scale separation & anisotropy)
  Statement: ρ_L << L_B; separable λ_mfp and wave/drift times enable guiding-center & flux-surface averaging; transport tensor satisfies χ_∥ >> χ_⊥.
  Domain: strongly magnetized, weak-gradient regions.
  Falsifiability: diagnostics show χ_⊥ comparable to χ_∥ with weak shear dependence.
• P10-PC-3 (Flux surfaces & safety factor)
  Statement: nested flux surfaces with well-defined q(psi); islands/stochastic layers are exceptions handled in edge models.
  Domain: core & well-confined regions.
  Falsifiability: q(psi) from magnetics/inversion incompatible with boundary conditions.
• P10-PC-4 (Wave–particle resonance & effective index)
  Statement: absorption at k·v ≈ ω dominates deposition; n_eff(omega) is definable on given density/temperature backgrounds for ray tracing.
  Domain: bands where cold/warm plasma approximations hold.
  Falsifiability: systematic discrepancies between P_dep(r) peaks/widths and predictions from n_eff, k_∥/k_⊥.
• P10-PC-5 (Edge/SOL sheath compatibility)
  Statement: edge & sheath satisfy potential drop and mass/energy flux matching; outward flux and wall power close.
  Domain: Ω_edge/Ω_SOL.
  Falsifiability: divertor heat flux fails to close with volumetric sources/deposition.

IV. Minimal Mappings & Interface Anchors (S/I/M)

• Equilibrium & topology (S30-/I20-): geometry, coils, p(psi) -> {psi, q(psi), J_∥}; mesh/coordinates consistent with diagnostics.
• Stability (S40-): energy principle δW and spectral methods yield mode criteria, mapped to measurable lines.
• Waves & heating (S50-/I30-): {E_RF, n_eff(ω), gamma(ell)} -> {T_arr, α_abs, P_dep(r)}; record delta_form for T_arr.
• Transport & closures (S70-): {S_k(ω), shear} -> {Γ_s, Q_s, χ_⊥} (closures/scalings).
• Diagnostics & metrology (M10-): state -> observables mapping with uncertainties.
• Experimental design & falsification (M20-): controls & gates targeting P10-PC-*.

V. Implementation & Records (minimum execution dialect)

• Mandatory records: binding_ref (geometry/coils/boundary binding), equilibrium{psi,q(psi)}, transport/closure, rf{freq,n_eff,α_abs,P_dep}, diagnostics{AF/PF,cal}, arrival{form,gamma,measure,c_ref,Tarr,u_Tarr,delta_form}, qa_gates{check_dim,conservation,stability}.
• Phase correction: arg Z_corr(omega) = arg Z_raw(omega) − ( omega · Δt_sync ) (if phase fitting used).
• Record template:
• pc_postulates_record:
• equilibrium: {solver:"GS", p_of_psi:"poly3", F_of_psi:"tab"}
• stability: {method:"energy_principle", modes:[{n:1,m:2}, {n:2,m:1}]}
• rf:
• freq_GHz: 170
• n_eff_model: "cold_plasma"
• rays: [{gamma:"explicit", nodes:[...]}]
• transport: {closure:"gyroBohm", chi_perp_m2s: 0.6}
• arrival:
• form: "n_over_c"
• gamma: "explicit"
• measure: "d_ell"
• c_ref: 299792458.0
• Tarr_s: 2.31e-06
• u_Tarr_s: 8.0e-08
• delta_form: "n_over_c"
• qa_gates: {check_dim:"pass", conservation:"pass", stability:"pass"}

VI. Baselines & Reference Scenarios (reproducible)

• EQ-GS: equilibrium regression aligning psi/q(psi) with magnetics/bound constraints.
• RF-DEP: window-consistency among T_arr/α_abs and P_dep(r) peaks.
• MHD-MODE: δW criterion & eigenfrequency mapping to ECE/magnetic channels.
• TRAN-GB: Γ_s/Q_s vs D_GB scaling verification.

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

VII. Falsifiability (chapter-specific)

• J-PC-1 (Conservation break): energy/particle balances deviate beyond uncertainty → reject P10-PC-1 closure/source settings.
• J-PC-2 (Topology mismatch): inverted vs solved q(psi) disagree → reject P10-PC-3 geometry/current settings.
• J-PC-3 (Resonance/deposition mismatch): P_dep(r) vs n_eff, k_∥/k_⊥ predictions disagree → reject P10-PC-4 propagation dialect.
• J-PC-4 (Anisotropy failure): diagnostics show χ_⊥ ~ χ_∥ with weak shear dependence → reject P10-PC-2.
• J-PC-5 (Two-dialect arrival): |T_arr^{(1)}−T_arr^{(2)}| > u(T_arr) → no release.

VIII. Cross-Chapter Links & Closure

• Dependencies: Chapter 2 (Terms & Symbols), Chapter 5 (Equilibrium & Topology), Chapter 6 (Stability), Chapter 7 (Waves & Heating), Chapter 9 (Transport), Chapter 12 (Diagnostics & Metrology).
• Downstream: Chapter 4 (S20-* Minimal Equations), Chapter 13 (Experimental Design & Falsification), Chapter 14 (SimStack & Benchmark Cases), Chapter 16 (Design Protocol & Checklist).