On the Rates of Steady, Quasi-steady and Impulsive Magnetic Reconnection

Abstract

Magnetic reconnection (MR) is considered as a major source of particle energization in astrophysical plasma. In the past, analysis of MR often assumes the magnetostatic condition, i.e. $\partial_t = 0$. We show that under the Sweet-Parker-Petschek framework, steady state is an over-constraint and is not achievable. On the other hand, the quasi-steady state defined as $\partial_t \mathbf{E} = 0$ but $\partial_t \mathbf{B} \neq 0$ or equivalently $\partial_t\mathbf{j}\neq 0$ better describes the asymptotic behaviour of MR without turbulence. The upper limit of MR rate for quasi-steady MR is found to be $\sim 1/3\sqrt{3} \sim 0.19$. The limit does not apply to impulsive or turbulent MR of which $\partial_t\mathbf{B} \neq 0$ and $\partial_t\mathbf{E} \neq 0$. In impulsive MR the rate can be higher or lower than 0.19 depending on the state of the turbulence. Our results may explain the apparent discrepancy in observations of solar flare MR rates. The analysis is independent of mass ratio and thus the results are applicable to pair plasma.