Nonlinear tearing mode instability studied using Galerkin spectral method

This study investigates the nonlinear evolution of tearing mode instabilities utilizing a quasiparticle framework integrated with spectral methods. By reformulating the resistive magnetohydrodynamic (MHD) equations via Galerkin spectral decomposition, a direct connection between MHD and quasiparticle statistics is established, where the wave-number--frequency relationship reflects the de Broglie duality (p=k,4pt0exε=ω). Numerical simulations unveil three distinct stages: initial transient growth, a linear stage (γₘ∝|m|), and nonlinear evolution and saturation. Harmonic interactions display a growth mechanism governed by energy and momentum conservation (${{γ}}ₘ={{γ}}_{{m}^{{'}}}+{{γ}}_{{m}^{{'}{'}}},{{4pt}{0ex}}m={m}^{{'}}+{m}^{{'}{'}}$). Statistical analysis indicates that the spectral energy distribution follows Maxwell-Boltzmann statistics, with the temperaturelike parameter ${β}$ evolving linearly during the linear stage. Comparisons with HL-2A experimental spectra validate the predictive capability of the model for the evolution of magnetic islands. This study bridges turbulence theory and statistical physics, offering a general mechanism for analyzing magnetic reconnection and nonlinear tearing mode instabilities in magnetized plasmas.