This record presents v0. 4 of the ALADIN Plasma Stability Law — a first-principles criterion for self-stabilization in current-driven Z-pinch plasmas. The law is anchored to a single measured parameter: the axial current density J₀ = 1. 000 × 10¹⁸ A/m². Core Law Statement A current-driven plasma column with uniform axial current density J₀ is stable against sausage (m=0) and kink (m=1) instabilities if and only if ! (Bᵦ{B_) ², ; Sₘ 1 } with exact definitions: • B_θ = μ₀ J₀ a / 2 • γₘ = vA / a • vA = B_θ / √ (μ₀ ρₑff) • ρₑff = μ₀ J₀² a² / (8 c²) • Π = μ₀ J₀² a² / (ρₑff c²) = 8 at the magnetic-rest energy balance point QMHD Extensions The law incorporates quantum magnetohydrodynamic effects: Schwinger pair production (induced Eᵦ from Faraday during collapse), quantum degeneracy pressure Pq, and effective density ρₑffQMHD = ρₑff + ρₚair + Pq / c². Falsification The law is falsified if Π 0. 5 or q 10 a / vA). Regime of Validity Ideal/low-resistivity MHD, β ≲ 1, approximate axial symmetry, resistive diffusion time ≫ instability growth time, subdominant reconnection during collapse phase. Scope This is the frozen core law. The included script demonstrates 1D collapse with emergent Bᵦ dynamo ramp, axial shear S, and QMHD back-reaction. Plots illustrate stability evolution (Π (t), growth rates, pair density, vA/c). Previous versions v0. 2: 10. 5281/zenodo. 18306470v0. 3: 10. 5281/zenodo. 18313105
Mihai Alexandru Bucurenciu (Tue,) studied this question.