Analytical Model of Fast Magnetic Reconnection with a Large Guide Field

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.