Electrostatic, beam-target and hybrid explorer
The closed-form relations of this family, live: a spherical cathode grid's combinatorics, transparency and pass bound; the Duane cross-section fit at a stationary-target and a colliding-beam energy; and the four figures of merit of a fusion–fission hybrid with the ORNL blankets as presets.
computational_prototype maturity: the printed geometry of a grid, a printed cross-section fit, printed figures of merit. No potential well, sheath, space charge, beam stopping, target density, blanket neutronics or criticality is computed anywhere in these cores; no fusion rate, yield, gain or breakeven statement is made, and the beam-target core states that no energy-gain claim of any kind is made or implied for its family; no value describes or validates any real machine.IEC — spherical cathode grid (Wulfkühler et al. 2024; Radel 2007)
\(\alpha = \arctan(t/D)\); \(N_{\mathrm{globe}} = 2n_{\mathrm{long}}(n_{\mathrm{lat}}+1)\); symmetric grids 3/6/9/15 rings → 8/24/48/120 apertures at \(360^\circ/2n\); passes \(\le \eta/((1-\eta)(1+\eta))\). Radel prints no transparency for the Wisconsin grids; 0.95 is declared. The pass bound is set by geometry alone and is never a predicted pass count.
Beam target — Duane cross section with the frame stated (NRL Plasma Formulary 2019, p. 44)
\(\sigma(E)\) in barn at the equivalent stationary-target energy (\(4E_{\mathrm{beam}}\) for equal-mass colliding beams); \(\dot N = I/Ze\); \(P = E_{\mathrm{keV}}I_{\mathrm{mA}}/Z\) W; the D–T \(\langle\sigma v\rangle\) at \(kT\) by quadrature against the formulary's printed table (e.g. 1.1×10⁻¹⁶ cm³/s at 10 keV). No beam stopping, target density or thickness is modelled; no reaction rate, yield or gain follows.
Fusion–fission hybrid — four figures of merit (ORNL/PPA-79/3)
\(P_T/P_F = 1/Q' + 1 + f_n(M-1)\); \(\eta_{\mathrm{hybrid}} = \eta_H - (1/Q')/(P_T/P_F)\); \(R_o = (200/E_{\mathrm{fus}})\,F/((1-C)(1+\alpha))\); \(N = R_o/(P_T/P_F)\); on-line \(R\) in both printed forms; neutron multiplication \(1/(1-k_{\mathrm{eff}})\) reported beside \(M\) and derived from it in neither direction. A conversion ratio of one or more is refused: a reactor that needs no fissile makeup supports no hybrid.