39-EFT.WP.Plasma.Confinement v1.0 | Chapter 10 — Edge Layer, Scrape-Off Layer & Wall Interactions (S80-)

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Chapter 10 — Edge Layer, Scrape-Off Layer & Wall Interactions (S80-)

I. Chapter Objectives & Structure

1. Objective: On Chapters 5 (S30-) equilibrium/topology, 8 (S60-) guiding-center & neoclassical, and 9 (S70-) turbulence/transport closures, present an integrated dialect S80-PC-* for Edge/SOL—sheath—wall interactions, unifying along-field conservation of mass/momentum/energy, sheath matching, recycling & impurity sources, detachment/attached criteria, and engineering acceptance metrics.
2. Structure: Symbols & domain → S80-PC-1 1D SOL minimal equations → S80-PC-2 sheath matching & Bohm criterion → S80-PC-3 recycling/impurity & radiation → S80-PC-4 heat loads, detachment & operating windows → Implementation & records → Falsifiability → Cross-chapter closure.
3. Shared arrival-time dialect (two equivalent forms; explicit gamma(ell) & d ell; record delta_form if arrival/phase diagnostics are used in this chapter):
   • Constant-factored: T_arr = ( 1 / c_ref ) * ( ∫ n_eff d ell )
   • General: T_arr = ( ∫ ( n_eff / c_ref ) d ell )

II. Symbols & Domain

1. Geometry & regions: Ω_edge (edge), Ω_SOL (scrape-off layer), saddle/separatrix & targets; along-field coordinate s (s=0 upstream, s=L_∥ target).
2. Plasma quantities: n(s), T_e(s), T_i(s), parallel flow u_∥(s), sound speed c_s = √( (T_e+γ_i T_i)/m_i ).
3. Fluxes & power: parallel particle flux Γ_∥ = n u_∥, heat flux q_∥ = - κ_∥ ∂_s T - κ_⊥ ∂_⊥ T + …, injected power P_in, radiation P_rad, wall work P_wall.
4. Recycling & impurities: recycling coefficient R, sputtering yield Y, neutral source S_n^0, impurity radiation function L_z(n,T).
5. Sheath parameters: Bohm criterion, sheath drop Δφ_sheath, sheath heat-flux factor γ_q (typically ~7–10).

S80-PC-1 | 1D SOL Minimal Equations (along B)

Conservation (steady-state approximation)

1. Mass:
2. ∂_s ( n u_∥ ) = S_n(s) # includes recycled-neutral ionization, volumetric sources/deposition
3. Momentum (minimal, higher-order viscosity neglected):
4. m_i n u_∥ ∂_s u_∥ = - ∂_s p - m_i n ν_∥ ( u_∥ - u_∥,neutral ) + S_m
5. Energy (electron/ion; electrons shown):
6. ∂_s q_{e,∥} + p_e ∂_s u_∥ = P_{e,src} - C_{ei} - P_{rad,e}
7. , q_{e,∥} = - κ_{e,∥} ∂_s T_e
8. Cross-field supply & closures (aligned with S70-): Γ_⊥, Q_⊥ enter as boundary or volumetric terms in S_n, P_{src}.

Energy closure (hard gate)

P_in = ∑_legs ∫ q_∥(s) ds + P_rad + P_wall

Must close within uncertainty for release.

S80-PC-2 | Sheath Matching & Bohm Criterion (wall boundary conditions)

Bohm entrance at target/wall

u_∥(L_∥) ≥ c_s , Γ_∥(L_∥) = n_s c_s

Sheath heat flux

q_∥(L_∥) = γ_q n_s T_s c_s

with γ_q dependent on material/surface state and secondary emission—recorded in dataset cards.
Sheath drop & secondary emission: include Δφ_sheath and electron secondary-emission coefficient δ to correct electron heat flux and target-temperature estimates.

S80-PC-3 | Recycling/Impurity Sources & Radiation

1. Recycling model: at target, Γ_REC ≈ R · Γ_∥(L_∥); upstream neutral source S_n^0(s) is provided by neutral transport (or tabulations).
2. Impurity source: physical/chemical sputtering Γ_Z = Y(E_i,T_s) · Γ_∥; partition between core and SOL.
3. Radiation closure:
4. P_rad(s) = n_e(s) n_Z(s) L_z( T_e(s) )

Version L_z (species/charge-state dependent) in records.

S80-PC-4 | Heat Loads, Detachment & Operating Windows

5. Target heat-flux density: q_t = q_∥ B_t/B_p (geometric amplification); engineering gate q_t ≤ q_gate.
6. Detachment criteria (minimal):
   • Momentum/energy sink drive T_e(L_∥) → O(1–5 eV) with rising n_e(L_∥);
   • Anomalous slope ∂ q_t / ∂ P_in < 0.
7. Operating windows: joint windows in P_in, R, fuelling, B, and geometry (magnetic inclination/aperture); tabulate gates for attached/semi-detached/detached regimes.

VI. Implementation & Records (minimum execution dialect)

• Required fields:
  geometry:{L_∥, B_t/B_p, target_angle}, profiles:{n,T_e,T_i,u_∥}(s), sources:{S_n,S_m,P_src},
  sheath:{gamma_q, Δφ_sheath, material}, recycling:{R, S_n^0}, impurity:{Y(E_i,T), L_z(T)},
  power_balance:{P_in,P_rad,P_wall}, targets:{q_t_gate},
  qa_gates:{check_dim, bohm_entry, energy_closure}.
• Record template:
• s80_edge_sol:
• geometry:
• L_parallel_m: 25.0
• Bt_over_Bp: 7.5
• target_angle_deg: 2.0
• profiles_1D:
• s_grid_m: [ ... ]
• ne_m3: [ ... ]
• Te_eV: [ ... ]
• Ti_eV: [ ... ]
• upar_ms: [ ... ]
• sources:
• Sn_m3s: "table:/edge/Sn.tbl"
• Psrc_Wm3: "table:/edge/Psrc.tbl"
• sheath:
• gamma_q: 8.0
• delta_phi_V: 3.0
• material: "W"
• recycling:
• R: 0.95
• S0_neutral: "mc:/neutrals/S0.nc"
• impurity:
• sputter_Y: "table:/impurity/Y.tbl"
• Lz_Wm3: "table:/impurity/Lz.tbl"
• power_balance:
• Pin_W: 6.0e6
• Prad_W: 2.1e6
• Pwall_W: 3.6e5
• targets:
• q_t_gate_MWm2: 10.0
• qa_gates: {check_dim:"pass", bohm_entry:"pass", energy_closure:"pass"}

VII. Falsifiability (for S80-)

• J-S80-1 (Bohm-entry failure): u_∥(L_∥) < c_s or Γ_∥ ≠ n_s c_s → reject sheath matching or boundary conditions.
• J-S80-2 (Energy/power non-closure): P_in ≠ ∑∫ q_∥ ds + P_rad + P_wall beyond uncertainty → reject source/radiation/wall-power dialect.
• J-S80-3 (Heat-load over gate / trend anomaly): q_t > q_gate or ∂ q_t/∂P_in contradicts detachment-window criteria → reject operating window or geometry.
• J-S80-4 (Recycling/impurity inconsistency): densities from R, Y, L_z disagree with diagnostic inversions → reject recycling/sputtering models or calibration.
• J-S80-5 (Two-dialect arrival): if arrival diagnostics are used and two T_arr dialects disagree beyond u(T_arr), no release.

VIII. Cross-Chapter Links & Closure

• Dependencies: Chapter 2 (Terms), Chapter 4 (S20- minimal equations), Chapter 5 (S30- equilibrium & topology), Chapter 8 (S60- guiding center), Chapter 9 (S70- transport closures).
• Downstream: Chapter 12 (Diagnostics & Metrology—divertor heat load/radiation/neutrals & impurities), Chapter 13 (Experimental Design & Falsification—detachment & heat-load gates), Chapter 14 (SimStack & benchmarks—Edge/SOL regression).