Closed-confinement explorer
The closed-form relations of this family, live: the tokamak's geometry and consistency instruments, the reversed-field pinch's Bessel-function relaxed state, the spheromak's flux-conserver eigenvalue and formation disposition, and the FRC's pressure balance. The presets are the anchor fixtures the cores test against.
computational_prototype maturity: exact geometry, a vacuum field, empirical consistency instruments, and the fully relaxed states of an ideal cylinder. No equilibrium, stability, transport or current-drive equation is solved; the relaxed states are identities of a model that real devices depart from; no confinement, fusion power, gain or breakeven statement is made; no value describes or validates any real machine.Tokamak — geometry, vacuum field, instruments
Relations: \(V = 2\pi^2 R_0 a^2 \kappa\); \(B(R) = B_0 R_0/R\) at \(R_0 \mp a\); \(I_N = I_p/(aB_0)\) against the printed ceiling of about 7; \(n_G = I_p/(\pi a^2)\) in \(10^{20}\,\mathrm{m^{-3}}\); \(q_{\mathrm{cyl}} = 5a^2 B_0 (1+\kappa^2)/(2 R_0 I_p)\). Neither filed source prints a machine's absolute dimensions; every absolute value here is declared.
Reversed-field pinch — the Bessel-function relaxed state
Profiles of \(B_\phi/B_0 = J_0(2\Theta\,r/a)\), \(B_\theta/B_0 = J_1(2\Theta\,r/a)\) and \(q(r)\,R_0/a\) across the minor radius; the reversal surface is marked where \(B_\phi\) crosses zero. The edge field of the declared current, \(\mu_0 I_p/(2\pi a)\), is compared with the model's \(B_\theta(a) = \langle B_\phi\rangle\Theta\) as the configuration's own cross-check.
Spheromak — flux-conserver eigenvalue and formation
\(\lambda_{\mathrm{fc}} = \sqrt{(j_{1,1}/R)^2 + (\pi/L)^2}\); \(\lambda_{\mathrm{gun}} = \mu_0 I_{\mathrm{gun}}/\psi_{\mathrm{gun}}\); midplane profiles \(B_z/B_0 = J_0(k_r r)\), \(B_\theta/B_0 = (\lambda/k_r) J_1(k_r r)\). The printed 9.9 m⁻¹ of SSPX is reproduced within one per cent; nothing here reconstructs an equilibrium or evaluates tilt, helicity balance or decay.
FRC — pressure balance and kinetic scale
\(p_{\max} = B_e^2/2\mu_0\), \(x_s = r_s/r_c\), \(\langle\beta\rangle = 1 - x_s^2/2\), \(T_e + T_i = \langle\beta\rangle p_{\max}/(n k_B)\), \(\delta_i = c/\omega_{pi}\), \(S^* = r_s/\delta_i\), \(E = l_s/2r_s\), bound \(S^*/E < 3.5\), \(v_A = B_e/\sqrt{\mu_0 n m_i}\).