Analysis of Collisionless Magnetic Reconnection Through Truncated 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 relative importance of all of the eigenmodes (as determined by their amplitudes), we find the unstable/stable pair to contribute dominantly to the overall system dynamics, while the marginal modes are of minimal importance. Importantly, the stable eigenmode is not negligible as linear theory would predict, but grows to be of comparable importance to the unstable mode. We explore a simplified computational model for collisionless tearing consisting only of this stable/unstable pair. The effectiveness of this model is determined by calculating the percent error between this expansion and full nonlinear evolution. We use this truncated expansion to calculate the magnetic reconnection rate and compare with expectations from nonlinear models.

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