The "ideal" tearing mode: theory and resistive MHD simulations

TL;DR

This paper combines theoretical analysis and resistive MHD simulations to demonstrate that fast magnetic reconnection occurs when current sheets reach a critical thickness, challenging classical models and explaining explosive solar phenomena.

Contribution

It confirms the critical threshold for fast tearing mode onset through simulations and reveals a cascading plasmoid instability leading to explosive reconnection.

Findings

Critical current sheet thickness triggers fast tearing modes.

Simulations validate the linear analysis predictions.

Secondary plasmoid instability causes cascading explosive reconnection.

Abstract

Classical MHD reconnection theories, both the stationary Sweet-Parker model and the tearing instability, are known to provide rates which are too slow to explain the observations. However, a recent analysis has shown that there exists a critical threshold on current sheet's thickness, namely a/L~S^(-1/3), beyond which the tearing modes evolve on fast macroscopic Alfvenic timescales, provided the Lunquist number S is high enough, as invariably found in solar and astrophysical plasmas. Therefore, the classical Sweet-Parker scenario, for which the diffusive region scales as a/L~S^(-1/2) and thus can be up to ~100 times thinner than the critical value, is likely to be never realized in nature, as the current sheet itself disrupts in the elongation process. We present here two-dimensional, compressible, resistive MHD simulations, with S ranging from 10^5 to 10^7, that fully confirm the linear analysis. Moreover, we show that a secondary plasmoid instability always occurs when the same critical scaling is reached on the local, smaller scale, leading to a cascading explosive process, reminiscent of the flaring activity.