Invariant QMHD Threshold for Self-Stabilization in Current-Driven Plasma Columns

The ALADIN Plasma Stability Law provides a first-principles criterion for self-stabilization in current-driven plasma columns (Z-pinches, astrophysical jets, magnetized outflows) against sausage (m=0) and kink (m=1) magnetohydrodynamic instabilities. The law is anchored to a single measured parameter — the axial current density J₀ = 1.000 × 10¹⁸ A/m² — and the dimensionless threshold Π = μ₀ J₀² a² / (ρ_eff c²) ≥ 8, where ρ_eff is the effective inertial density (classical + relativistic + QMHD contributions). At Π = 8, the Alfvén speed reaches v_A = c/√2, marking the relativistic equipartition point beyond which classical MHD dynamics become acausal unless stabilizing back-reaction mechanisms increase ρ_eff. The threshold is invariant under microphysical closures (shear flow, emergent axial B_z, Schwinger pair production, quantum degeneracy pressure, etc.). The law is falsifiable: a column with Π < 4 must exhibit exponential instability growth (γ a / v_A > 0.5) in the long-wavelength limit. Pure force-balance simulation (no artificial suppression) shows Π decreasing during compression leads to unbounded implosion — verifying the necessity of maintaining Π ≥ 8 for bounded dynamics. This upload contains: • Main simulation code (pure force-balance collapse) • Stability evolution plot (Π(t), r(t), v_A(t)/c, acc_r(t)) • PDF law statement with derivation, falsification condition, and scope Previous baseline work: • https://doi.org/10.5281/zenodo.18306470 • https://doi.org/10.5281/zenodo.18313105 Repository: https://github.com/aladinibz/AladinEquationVinfinity License: MIT Programming language: Python