Research Hub · Evidence
Equations
Each equation records its math, variables, units, assumptions, validity, source, implementation, tests and review. Sources are clickable.
| ID | Equation | Variables | Units | Assumptions | Validity | Source | Implementation | Tests | Review |
|---|---|---|---|---|---|---|---|---|---|
| EQ-DC-STAGE-BOUND | recovered ≤ q·V, with q·V ≤ E | q: charge (e); V: MV; E: MeV | MeV | ideal electrostatic collector | single-particle electrostatic collection | A Review of Direct Energy Conversion for Fusion Reactors | stages.py | DC-VAL-02 | draft |
| EQ-DC-ETA | η = ∫ p·A·O·qV dEdω / ∫ p·E dEdω | A: acceptance; O: orbit survival | – | separable losses at L1 | L0/L1 | Efficiency and Physical Limitations of Adiabatic Direct Energy Conversion; A Review of Direct Energy Conversion for Fusion Reactors | stages.py, models.py | DC-VAL-01/03 | draft |
| EQ-DC-BALANCE | balance = source − Σ(outputs+losses) | — | MeV | exact accounting | all levels | HBF accounting (ADR) | energy_balance.py | DC-VAL-01 | draft |
| EQ-P11B-REACTION | p + ¹¹B → 3α + Q, Q≈8.68 MeV | Q: Q-value | MeV | energetics only | aneutronic p-¹¹B | The AME 2020 atomic mass evaluation (II) | fusion_core/equations.py | fusion tests | draft |
| EQ-P11B-REACTIVITY | R = n_p n_B ⟨σv⟩(T_i) | n_p,n_B: densities; ⟨σv⟩: reactivity | m⁻³ s⁻¹ | Maxwellian ions; illustrative proxy | reduced model | Nevins & Swain (2000); EXFOR ¹¹B(p,α) | reactor3d_core/plasma.py | test_solver.py | draft |
| EQ-BREMS | P_b = C·Z_eff·n_e²·√T_e | n_e; T_e (keV) | W m⁻³ | non-rel. scaling; separate plasma diagnostic | illustrative | NRL Plasma Formulary (Huba) | reactor3d_core/plasma.py | test_solver.py | draft |
| EQ-BORIS | dp/dt = q(E + v×B) | q; E,B fields | SI | static fields per step; non-rel. | volume-preserving | Qin et al. (2013); orig. Boris 1970 | reactor3d_core/pusher.py | test_pusher.py | draft |
| EQ-ENERGY-LEDGER | alpha_source = deposited+detector+DC_rec+DC_loss+escaped+residual | residual: closure error | J | alpha budget separate from bremsstrahlung | L0/L1 | HBF reduced-model accounting | reactor3d_core/ledger.py | test_alpha_energy_conserved | draft |
| EQ-TOKAMAK-FIELD | B_φ=B₀R₀/R; q(a)=2πa²B₀/(μ₀IₚR₀) | R, r, Iₚ, q | T | circular; uniform current; no equilibrium | TOR-L0/L1 | Wesson & Campbell (OUP) | torus3d_core/field.py | test_torus.py | draft |
Promotion from draft requires a named review (review status).