Eigenmode Decomposition Analysis of Resistive Magnetic Reconnection

Recent work demonstrates that specific aspects of nonlinear magnetic reconnection in a collisionless regime are directly attributable to linearly damped eigenmodes (Stolnicki et al. 2024). In this work, we apply similar eigenmode analysis tools to create a linear sum which equals nonlinear magnetic reconnection driven by resistivity. In contrast to the collisionless case which contains a single unstable eigenmode and a single stable eigenmode, the resistive case contains an unstable eigenmode and a wide spectrum of stable modes. Calculating eigenmode amplitudes allows for a determination of the significance of each individual mode in the nonlinearly-evolved resistive reconnection. Linearly stable modes, while often neglected in quasilinear models, are found to be important in determining properties of nonlinear systems. We discuss how energy is transferred between magnetic, kinetic, and resistive channels. This analysis is conducted locally in wavenumber space, suggestive of significant energy transfer at large scales in contrast to energy transferred via a cascade as is commonly considered.