39-EFT.WP.Plasma.Confinement v1.0 | Chapter 12 — Diagnostics, Metrology Chain & Data Assimilation (M10-)

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Chapter 12 — Diagnostics, Metrology Chain & Data Assimilation (M10-)

I. Chapter Objectives & Structure

1. Objective: Establish an end-to-end metrology chain and data-assimilation dialect M10-PC-* from instruments → observables → physical fields/state vector, unifying calibration, spectral windows, arrival-time records, and uncertainty composition; specify observation operators—cost function—posteriors/assimilation release rules so Chapters 4/5/6/7/8/9/10/11 form a reproducible, falsifiable data loop.
2. Structure: Symbols & domain → M10-PC-1 diagnostics & observables → M10-PC-2 metrology chain & uncertainty → M10-PC-3 observation operators & assimilation → M10-PC-4 power/topology/arrival consistency → Implementation & records → Falsifiability → Cross-chapter closure.
3. Shared arrival-time dialect (two equivalent forms; record delta_form; explicit gamma(ell) & d ell):
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )

II. Symbols & Domain

1. Diagnostics/channels: ECE/CTS/interferometry/reflectometry/magnetics/bolometry/divertor heat flux/MSE/pinhole imaging, etc.
2. Observables: brightness T_b(ω), phase/group delay arg Z(ω), T_group(ω), polarization/scattering spectra S_obs(k,ω), magnetic Ḃ, Φ, target heat flux q_t.
3. State & parameters: x = {n_e,T_e,T_i, u_∥, B(ψ,θ,ζ), q(ψ), profiles, χ, D, P_dep, Γ, Q, Π_ψ, …}.
4. Observations & errors: y = H(x) + ε, ε ~ (0,R); background/prior x_b ~ 𝒩(μ_b, B).
5. Hard QA: check_dim=pass, two-dialect T_arr agreement, energy/power closure, topology consistency (LCFS/X/separatrix), versioned calibration & spectral windows.

M10-PC-1 | Diagnostics & Observables (Minimal)

6. RF/microwave:
   • ECE: T_b(ω) = 𝒜_E(ω) · T_e(ρ) (transfer matrix/visibility function).
   • Reflectometry: φ(ω), T_group(ω) → n_e(r) and asymptotic n_eff(ω).
   • CTS: spectral width/shift → T_i, u_∥.
7. Magnetics & beams: Ḃ/Φ → ψ(R,Z), q(ψ); MSE → q(ψ), B_θ/B_φ.
8. Power & wall: IR/thermography → q_t(s); bolometry/pinhole imaging → P_rad.
9. Arrival & phase correction:
10. arg Z_corr(ω) = arg Z_raw(ω) − ( ω · Δt_sync )

Fit T_group = d(arg Z)/dω within the coherence window (consistent with Chapters 6/7).

M10-PC-2 | Metrology Chain & Uncertainty Composition

11. Chain: instrument → calibration (AF/PF/efficiency) → geometry (LOS/antenna) → spectral windows & sampling → raw observable → physical variable → state-vector components.
12. Propagation (examples):
    • Arrival time:
    • u^2(T_arr) ≈ Σ_i ( (∂T_arr/∂n_eff)_i^2 u^2(n_eff_i) ) + u^2(Δt_sync)
    • Power closure:
    • u^2(P_in − P_ref − P_rad − P_wall − ∫ P_dep dV)
    • = u^2(P_in)+u^2(P_ref)+u^2(P_rad)+u^2(P_wall)+u^2(∫P_dep dV)
    • Topology: u(q) and u(ψ) from joint propagation of magnetics/geometry/solver (as in Chapter 5).
13. Composition rules: use covariance or linearized propagation; when needed, Monte Carlo sampling; version R/B (obs/background covariances).

M10-PC-3 | Observation Operators & Data Assimilation (H, J, K)

14. Observation operator: y = H(x) + ε, with H composed of ray/full-wave blocks, transfer matrices, magnetic/thermal inversions, etc.
15. Cost function (3D/4D-Var):
16. J(x) = 1/2 (y − Hx)^T R^{-1} (y − Hx) + 1/2 (x − x_b)^T B^{-1} (x − x_b)

Minimize → assimilated state x_a.

17. Kalman/EnKF (static form):
18. K = B H^T ( H B H^T + R )^{-1}
19. , x_a = x_b + K ( y − H x_b )
20. , P_a = (I − K H) B
21. Constraints & gates: energy/power closure, topology consistency, and two-dialect T_arr as priors or hard constraints in J(x) or via projection.

M10-PC-4 | Power, Topology & Arrival Consistency (Hard Gates)

22. Power closure (Ch. 7/10): P_in = P_ref + P_rad + P_wall + ∫ P_dep dV must close within u.
23. Topology (Ch. 5/11): assimilated ψ, q(ψ), LCFS/X consistent with magnetics/imaging/geometry.
24. Arrival (Ch. 7):
25. | T_arr^{(n_over_c)} − T_arr^{(one_over_c_times_n)} | ≤ u(T_arr)

VI. Implementation & Records (minimum execution dialect)

• Required fields:
  instruments:{type, model, cal_files}, windows:{band, bw, fs}, geometry:{LOS/antenna, coords},
  sync:{Δt_sync_s}, arrival:{form,gamma,measure,c_ref,Tarr,u_Tarr,delta_form},
  operators:{H_blocks, versions}, covariances:{R, B}, assimilation:{method, options},
  balances:{power, topology}, qa_gates:{check_dim, power_closure, topology_consistency, Tarr_dual}.
• Record template:
• m10_metrology_assim:
• instruments:
• - {type:"ECE", model:"...", cal:"/cal/ece_AF.yaml"}
• - {type:"magnetics", model:"...", cal:"/cal/mag.cfg"}
• - {type:"IR", model:"...", cal:"/cal/ir.yaml"}
• windows:
• ece_GHz: {band:[..., ...], bw_MHz:..., fs_Hz:...}
• refl_GHz: {band:[..., ...], bw_MHz:..., fs_Hz:...}
• geometry:
• LOS: "/geo/los.json"
• antennas: "/geo/ant.json"
• coords: "/eq/coords_boozer.nc"
• sync:
• dt_sync_s: 1.0e-08
• arrival:
• form: "n_over_c" # or "one_over_c_times_n"
• gamma: "explicit"
• measure: "d_ell"
• c_ref: 299792458.0
• Tarr_s: 3.2e-06
• u_Tarr_s: 1.0e-07
• delta_form: "n_over_c"
• operators:
• H_blocks: [ "ECE_transfer", "Reflectometry_phase", "Magnetic_inversion", "IR_heatflux" ]
• versions: {ece:"1.2", refl:"2.1", mag:"1.5", ir:"1.0"}
• covariances:
• R: "/cov/R_obs.h5"
• B: "/cov/B_bg.h5"
• assimilation:
• method: "EnKF"
• options: {ensemble: 64, inflation: 1.05}
• balances:
• power: {Pin_W:1.2e6, Pref_W:2.0e5, Prad_W:1.5e5, Pwall_W:1.0e5}
• topology:{LCFS:"/eq/lcfs.curve", Xpoints:[[R1,Z1],[R2,Z2]]}
• qa_gates:
• check_dim: "pass"
• power_closure: "pass"
• topology_consistency: "pass"
• Tarr_dual: {diff_s:2.0e-08, u_Tarr_s:1.0e-07, pass:true}

VII. Falsifiability (for M10-)

• J-M10-1 (Power closure failure): P_in − P_ref − P_rad − P_wall − ∫P_dep dV beyond u → reject power dialect or H blocks.
• J-M10-2 (Topology inconsistency): assimilated ψ, q(ψ), LCFS/X disagree with magnetics/imaging/geometry → reject boundary/coil/observation geometry.
• J-M10-3 (Arrival inconsistency): two-dialect T_arr exceeds u(T_arr) → reject arrival records or phase correction.
• J-M10-4 (Covariance/operator mismatch): mismatched R/B versions or dimensions produce decreasing J(x) with failed QA → reject covariances or H implementation.
• J-M10-5 (Assimilation degradation): PPC/cross-validation shows posterior x_a does not improve residuals/energy closure → reject assimilation configuration.

VIII. Cross-Chapter Links & Closure

• Dependencies: Chapters 2 (Terms & Symbols), 4 (S20-), 5 (S30-), 6 (S40-), 7 (S50-), 8 (S60-), 9 (S70-), 10/11 (S80-/I10-).
• Downstream: Chapter 13 (Experimental Design & Falsification—build H-matrices & power analysis), Chapter 14 (SimStack & benchmarks—operator & covariance baselines), Chapter 15 (Data & Repro—data/pipeline/env-lock & audit).