Three-dimensional non-linear instability of spontaneous fast magnetic reconnection

Three-dimensional instability of spontaneous fast magnetic reconnection is studied using MHD (magnetohydro- dynamic) simulation. Previous two-dimensional MHD studies have demonstrated that, if a current-driven anomalous resistivity is assumed, two-dimensional fast magnetic reconnection occurs and two-dimensional largescale magnetic loops, i.e., plasmoids, are ejected from the reconnection region. In most two-dimensional MHD studies, the structure of the current sheet is initially one-dimensinal. On the other hand, in recent space plasma observations, fully three-dimensional magnetic loops frequently appear even in the almost one-dimensional current sheet. This suggests that the classical two-dimensional fast magnetic reconnection may be unstable to any three-dimensional perturbation, resulting in three-dimensional fast magnetic reconnection. In this paper, we show that a three-dimensional resistive perturbation destabilizes two-dimensional fast magnetic reconnection and results in three-dimensional fast magnetic reconnection. The resulting three-dimensional fast reconnection repeatedly ejects three-dimensional magnetic loops downstream. The obtained numerical results are similar to the pulsating downflows observed in solar flares. According to the Fourier analysis of the ejected magnetic loops, the time evolution of this three-dimensional instability is fully non-linear.