Catastrophe Model for Fast Magnetic Reconnection Onset

A catastrophe model for the onset of fast magnetic reconnection is presented that suggests why plasma systems with magnetic free energy remain apparently stable for long times and then suddenly release their energy. For a given set of plasma parameters there are generally two stable reconnection solutions: a slow (Sweet-Parker) solution and a fast (Alfvénic) Hall reconnection solution. Below a critical resistivity the slow solution disappears and fast reconnection dominates. Scaling arguments predicting the two solutions and the critical resistivity are confirmed with two-fluid simulations.

Figure 1

Normalized reconnection rate, $E^{\prime }$, as a function of island width, $w$, for the two sets of simulations described in the text. The vertical dotted lines show when the added effects were enabled. Note that the final parameters of the two solid line simulations are identical.

Figure 2

Out of plane current density, $J_z$, for late times from the two solid lines of Fig. 1. The top plot corresponds to the thick solid line (Hall reconnection). The bottom plot corresponds to the thin solid line (SP reconnection).

Figure 3

(a) Steady state normalized reconnection rate, $E^{\prime }$, as a function of normalized resistivity, ${\eta }^{\prime }$ for runs analogous to those in Fig. 1 as described in the text. (b) Current sheet width, $\delta$, as a function of ${\eta }^{\prime }$ for the simulations in (a).

Figure 4

Normalized reconnection rate, $E^{\prime }$, as a function of time $t$ (in units of ${\Omega }_{ci}^{-1}$) for the simulation which is started at ${\eta }^{\prime }=0.015$, reduced to 0.007, then increased back to 0.015.