An examination of nonlinear collisionless magnetic reconnection through eigenmode decomposition

Collisionless magnetic reconnection is examined through the evolution of the tearing instability described using a two-fluid model (Ottaviani and Porcelli, 1995). In contrast to standard modeling approaches, we examine these processes via a weighted eigenmode decomposition. The eigenspectrum for this system is characterized by a single unstable/stable mode pair and a large set of marginally stable modes. In assessing the contribution of all of the eigenmodes (as determined by their amplitudes), we find the unstable/stable pair to contribute dominantly to the overall system dynamics. Importantly, the stable eigenmode is not negligible as linear theory would predict, but grows to be of comparable importance to the unstable mode. In addition, the stable mode is observed to be connected to an enhanced rate of reconnection. This is suggested by the lack of the 'quasi-explosive growth' upon the removal of the stable mode. We explore a simplified computational model for collisionless tearing consisting only of this stable/unstable pair. It is found to be most accurate during the linear state of the system but decreases in effectiveness during the nonlinear evolution. This suggests that the stable/unstable pair alone is insufficient in describing the nonlinear phase and the marginally stable modes have a nontrivial contribution.