Reconnection in a Weakly Stochastic Field

We examine the effect of weak, small-scale magnetic field structure on the rate of reconnection in a strongly magnetized plasma. This affects the rate of reconnection by reducing the transverse scale for reconnection flows and by allowing many independent flux reconnection events to occur simultaneously. Allowing only for the first effect and using Goldreich & Sridhar's model of strong turbulence in a magnetized plasma with negligible intermittency, we find a lower limit for the reconnection speed ~VAℛ-3/16Lℳ3/4, where VA is the Alfvén speed, ℛL is the Lundquist number, and ℳ is the large-scale magnetic Mach number of the turbulence. We derive an upper limit of ~VAℳ2 by invoking both effects. We argue that generic reconnection in turbulent plasmas will normally occur at close to this upper limit. The fraction of magnetic energy that goes directly into electron heating scales as ℛ-2/5Lℳ8/5, and the thickness of the current sheet scales as ℛ-3/5Lℳ-2/5. A significant fraction of the magnetic energy goes into high-frequency Alfvén waves. The angle between adjacent field lines on the same side of the reconnection layer is ~ℛ-1/5Lℳ6/5 on the scale of the current sheet thickness. We claim that the qualitative sense of these conclusions, that reconnection is fast even though current sheets are narrow, is almost independent of the local physics of reconnection and the nature of the turbulent cascade. As the consequence of this the Galactic and solar dynamos are generically fast, i.e., do not depend on the plasma resistivity.