Fast Magnetic Reconnection: Secondary Tearing Instability and Role of the Hall Term

Magnetic reconnection provides the primary source for explosive energy release, plasma heating, and particle acceleration in many astrophysical environments. The last years witnessed a revival of interest in the MHD tearing instability as a driver for efficient reconnection. It has been established that, provided the current sheet aspect ratio becomes small enough (a/L∼S−1/3 for a given Lundquist number S?1), reconnection occurs on ideal Alfvén timescales and becomes independent of S. Here we investigate, by means of two-dimensional simulations, the ideal tearing instability in both the MHD and the Hall-MHD regime, which is appropriate when the width of the resistive layer δ becomes comparable to the ion inertial length di. Moreover, we study in detail the spontaneous development and reconnection of secondary current sheets, which for high S naturally adjust to the ideal aspect ratio and hence their evolution proceeds very rapidly. For moderate low S, the aspect ratio tends to the Sweet–Parker scaling (a/L∼S−1/2). When the Hall term is included, the reconnection rate of this secondary nonlinear phase is enhanced and, depending on the ratio di/δ, can be two times larger with respect to the pure MHD case, and up to 10 times larger than the linear phase. Therefore, the evolution of the tearing instability in thin current sheets in the Hall-MHD regime naturally leads to an explosive disruption of the reconnecting site and to energy release on super-Alfvénic timescales, as required to explain space and astrophysical observations.