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 $δ$ is larger or smaller than the sound gyroradius $ρ_s$. The reconnection is slow or Sweet-Parker-like for $δ\gtrsim ρ_s$, and fast otherwise. In the fast regime, however, we find that ion viscosity $μ$ plays a critical role. In particular, for $δ< ρ_s$ the diffusion region thickness is proportional to $Ha^{-1}$ with $Ha \propto 1/\sqrt{ημ}$ the Hartmann number, and the reconnection rate is proportional to $Pr^{-1/2}$ with $Pr = μ/η$ the Prandtl number and $η$ the resistivity. If the perpendicular ion viscosity is employed for $μ$ the reconnection rate becomes independent of both plasma $β$ and collision frequencies and therefore potentially fast.

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