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=ℏk,ɛ=ℏω). Numerical simulations unveil three distinct stages: initial transient growth, a linear stage (γ_{m}∝|m|), and nonlinear evolution and saturation. Harmonic interactions display a growth mechanism governed by energy and momentum conservation (γ_{m}=γ_{m^{'}}+γ_{m^{''}},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.