Onset of fast magnetic reconnection via subcritical bifurcation

Abstract

We report a phase transition model for the onset of fast magnetic reconnection. By investigating the joint dynamics of streaming instability(i.e., current driven ion acoustic in this paper) and current gradient driven whistler wave {\color{blue} {prior to the onset of fast reconnection}}, we show that the nonlinear evolution of current sheet(CS) can be described by a Landau-Ginzburg equation. The phase transition from slow reconnection to fast reconnection occurs at a critical thickness, $\Delta_c\simeq \frac{2}{\sqrt{\pi}}\left|\frac{v_{the}}{v_c}\right|d_e$, where $v_{the}$ is electron thermal velocity and $v_c$ is the velocity threshold of the streaming instability. For current driven ion acoustic, $\Delta_c$ is $\leq10d_e$. If the thickness of the CS is narrower than $\Delta_c$, the CS subcritically bifurcates into a rough state, which facilitates breakage of the CS, and consequently initiates fast reconnection.