ALADIN Plasma Stability Law v0.5 — Invariant Threshold for Causal Self-Stabilization in Current-Driven Plasmas

This release presents v0.5 of the ALADIN Plasma Stability Law — a first-principles force-balance criterion for self-stabilization in current-driven plasma columns (Z-pinches) against sausage (m=0) and kink (m=1) instabilities. The law is anchored to a single experimentally accessible parameter — the axial current density J_0 = 1.000 × 10¹⁸,A/m^2 — and an invariant threshold Π = 8 that arises from relativistic causality constraints on Alfvénic signal propagation (v_Aʳᵉˡ ≤ c / √2). The threshold Π = 8 is derived exactly from the magnetic-rest energy balance point (Pmag = ρeff c^2), where the classical Alfvén speed formally reaches v_A = √2\, c, signaling the breakdown of non-relativistic MHD. The physical (causal) Alfvén speed is bounded by v_Aʳᵉˡ ≤ c / √2. Stabilization emerges naturally when QMHD back-reaction (Schwinger pair production and quantum degeneracy pressure), relativistic flow corrections, Kerr-like GR effects (phenomenological), turbulence damping, reconnection feedback, and multi-mode tracking increase ρeff(t) to enforce Π(t) ≥ 8 — without any imposed suppression terms. The included script demonstrates 1D time-dependent collapse with pure force-balance dynamics. A separate falsification grid verifies runaway collapse for initial Π < 8 in the absence of stabilizing mechanisms. Previous versions v0.2: 10.5281/zenodo.18306470 v0.3: 10.5281/zenodo.18313105 v0.4: 10.5281/zenodo.18319371 Repository https://github.