Catastrophe Model for the Onset of Fast Magnetic Reconnection

Abstract

Solar flares, magnetic substorms and sawtooth crashes in fusion devices are explosive events in which magnetic reconnection facilitates the rapid release of energy stored in stressed magnetic fields into the surrounding plasma. Much effort has gone into understanding how the energy is released so fast. Collisional (Sweet-Parker) reconnection, based on resistive magnetohydrodynamics (MHD), is a successful physical model but is far too slow to explain observed energy release rates. In collisionless (Hall) reconnection, dispersive waves introduced by the Hall effect lead to energy release rates fast enough to explain observations. However, the steady-state description does not address why reconnection is explosive. We present a fully nonlinear model for the dynamics of magnetic reconnection. Using scaling arguments and resistive Hall-MHD numerical simulations, we show that the Sweet-Parker solution only exists when the current sheet is thick enough, while the Hall solution only exists when the resistivity is small enough. Furthermore, we show that reconnection is bistable, i.e., both the Sweet-Parker and Hall solutions can exist for the same set of control parameters. The disappearance of steady-state solutions as a control parameter varies is interpreted as a saddle-node bifurcation. Three signatures of this model are verified with numerical simulations, including the existence of a heretofore unidentified unstable steady-state reconnection solution. We present a theoretical model motivating that the existence of saddle-node bifurcations is intimately related to the presence of dispersive waves caused by the Hall effect.

This result has a potentially profound impact on the long-standing ``Onset Problem'', i.e., explaining how large amounts of free magnetic energy can be stored for a long time before being explosively released. During Sweet-Parker reconnection, magnetic energy accumulates because the energy release is very slow. When the thickness of the current sheet decreases past a critical value, the Sweet-Parker solution catastrophically disappears, causing a sudden transition to Hall reconnection which begins the fast release of the stored energy. We delineate scenarios for the catastrophic onset of Hall reconnection and discuss the impact of this model on observations of magnetic explosions, showing in particular that it is consistent with observations of reconnection events in the solar corona.