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.
Highlights
Critical behavior is ubiquitous in magnetic reconnection related phenomena, e.g., Ôflux transfer event at magnetopause [1, 2], solar flare, etc
We study the nonlinear dynamics of a current sheets (CSs) prior to the onset of fat reconnection
We show that under the joint interactions of the CDIA and CGDW, the CS can transmit into a rough state from a laminar state via subcritical bifurcation
Summary
Critical behavior is ubiquitous in magnetic reconnection related phenomena, e.g., Ôflux transfer event at magnetopause [1, 2], solar flare, etc. It has been found by Drake et al [6] that a thin CS can be broken into small scale vortices by whistler wave turbulence and facilitate the fast reconnection They showed that prior to breakup of the CS, the critical thickness of the CS is smaller than the electron skin depth. One approach to induce a fractal CS is via a series of macroscopic MHD instabilities, such as secondary tearing mode, Rayleigh-Taylor instability [11], etc It is a “top-down” process, cascading from macro-scales to micro-scales. Once the CS is narrower than a critical thickness, the order parameter of the CS will acquire a finite value via subcritical bifurcation, and the CS evolve into a rough state (but keep its topology).
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