ALADIN v0.6 – 2D Axisymmetric Resistive QMHD Exploratory Model with QED Pair Plasma Effects and Adaptive Timestep

This upload contains ALADIN v0.6, an exploratory 2D (r,z) axisymmetric numerical framework for resistive magnetohydrodynamics (MHD) coupled with quantum electrodynamic (QED) pair plasma effects. The model is designed to investigate emergent self-stabilization mechanisms in high-current plasma pinches via QED pair production and the resulting degenerate pair pressure. Key implemented features: - Full axisymmetric resistive MHD with flux-form induction equation - Constrained transport (CT) with additional parabolic ∇·B cleaning - QED pair production (Schwinger-like rate) + annihilation, synchrotron/inverse-Compton cooling, and annihilation heating - Degenerate pair pressure gradient force (radial only) - Adaptive CFL-controlled timestep - Multi-k_z Fourier mode tracking (axial harmonics at mid-radius) - Lundquist number S(t) evolution - Comprehensive 2D diagnostics: normalized plasma beta Π(r,z) map, div B monitor & heatmap, plasma density ρ(r,z) heatmap, pair density n_pair(r,z) heatmap - Benchmark comparison of mode growth rates against ideal MHD analytic limits (m=0 sausage, m=1 kink, m=2 flute) The code is written in Python using NumPy and Matplotlib, with tqdm progress visualization. It includes robust error handling, NaN/Inf checks, and axis-singularity regularization. Limitations and scope: - Toy/exploratory model only — no full conservative energy equation (heating only), approximate CT implementation, radial-only pair force, no azimuthal (m) modes - Extreme parameters are illustrative (magnetar-like regimes) and not intended for quantitative prediction or direct comparison to experiments - No rigorous validation against analytic theory or observational data — preliminary proof-of-concept for pair-stabilized pinch dynamics Future extensions planned: full 3D geometry, conservative form MHD, energy equation with pdV work, shock capturing, azimuthal mode analysis, and benchmark comparisons to known instabilities (Kruskal–Shafranov, tearing modes, Hall-driven reconnection).