Pinch explorer
The closed-form relations of this family, live: a Bennett Z-pinch column with its instability estimates and the Pease–Braginskii current, the sharp-boundary theta-pinch of the Scyllac review, and the Lee model's normalised circuit and snowplow with the four machines the plasma-focus core anchors on.
computational_prototype maturity. No equilibrium, stability, compression or transport equation is solved and no eigenvalue problem exists in the cores; the anchors reproduce numbers the sources print, which for the plasma focus are themselves outputs of the source's fitted code, and are not correlations with experimental data. No reactivity, yield, gain, breakeven or confinement-time statement is made; no value describes or validates any real machine.Z-pinch — Bennett column, stability, Pease–Braginskii
Profiles of \(n/n_0\), \(B_\theta/B_\theta(a)\) and \(I(r)/I\) across \(r/a\) from 0 to 4. The temperature is the equal-species Bennett temperature \(T = \mu_0 I^2/(16\pi N k_B)\).
Theta-pinch — sharp-boundary state, Scyllac sector, end loss
The equilibrium ratio is unity when \(\delta_1\delta_0\) equals \(-2/((3-2\beta)h^2aR)\); in field ratios \(B_1B_{0l}/B_0^2 = 4(1-\beta/2)(1-\beta)/((3-2\beta)hR)\), and the anchor point of Fig. 2 requires 0.0059 against the measured 0.0064. The \(m = 1\) growth rate is an order-of-magnitude estimate by design; the wall condition is the reduced eq. 6.
Dense plasma focus — bank normalisation, snowplow, rule-of-thumb geometry, neutron instruments
\(t_{\mathrm{rise}} = (\pi/2)\sqrt{L_0C_0}\) against the table's rise-time column; \(v_\infty\) at the peak current overestimates the table's \(v_a\) column by 7–14 % on every row, by design of the closed form; the empirical \(Y_n\) law is refused outside 0.1–1 MA. Fill: \(N_0 = p/k_BT_0\) at 300 K, \(\rho_0 = N_0 \cdot 4 m_p\).