Analytical Model of Fast Magnetic Reconnection with a Large Guide Field

TL;DR

This paper develops an analytical model for fast magnetic reconnection with a large guide field, revealing two regimes based on diffusion region thickness and highlighting ion viscosity's role in enabling potentially fast reconnection.

Contribution

It presents the first analytical theory of fast magnetic reconnection with a large guide field, identifying conditions for fast versus slow regimes and the influence of ion viscosity.

Findings

Reconnection regimes depend on diffusion region thickness relative to sound gyroradius.

Ion viscosity critically affects the reconnection rate in the fast regime.

Using perpendicular ion viscosity makes the reconnection rate independent of plasma beta and collision frequency.

Abstract

Analytical theory of fast magnetic reconnection with a large guide field is presented for the first time. We confirm that two distinct reconnection regimes are possible depending on whether the diffusion region thickness $\delta$ is larger or smaller than the sound gyroradius $\rho_s$. The reconnection is slow or Sweet-Parker-like for $\delta \gtrsim \rho_s$, and fast otherwise. In the fast regime, however, we find that ion viscosity $\mu$ plays a critical role. In particular, for $\delta < \rho_s$ the diffusion region thickness is proportional to $Ha^{-1}$ with $Ha \propto 1/\sqrt{\eta \mu}$ the Hartmann number, and the reconnection rate is proportional to $Pr^{-1/2}$ with $Pr = \mu/\eta$ the Prandtl number and $\eta$ the resistivity. If the perpendicular ion viscosity is employed for $\mu$ the reconnection rate becomes independent of both plasma $\beta$ and collision frequencies and therefore potentially fast.