The ideal tearing mode: theory and resistive MHD simulations. (May 2016) - Zanna, L. Del; Landi, S.; Papini, E.; Pucci, F.; Velli, M.
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 Alfvénic 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.