A saddle-node bifurcation model of magnetic reconnection onset

It was recently shown that magnetic reconnection exhibits bistability, where the Sweet Parker (collisional) and Hall (collisionless) reconnection solutions are both attainable for the same set of system parameters. Here, a dynamical model based on saddle-node bifurcations is presented which reproduces the slow to fast transition. It is argued that the properties of the dynamical model are a result of the Hall effect and the dispersive physics associated with it. Evidence from resistive two-fluid and Hall magnetohydrodynamics simulations are presented that show that the time evolution agrees with the dynamical model, the outflow speed is correlated with the dispersive physics due to the Hall effect, and bistability persists in the absence of electron inertia. (C) 2010 American Institute of Physics. [doi:10.1063/1.3435269]