Reconnection in a Weakly Stochastic Field

We examine the eeect of weak, small scale magnetic eld structure on the rate of reconnection in a strongly magnetized plasma. This aaects the rate of reconnection by reducing the transverse scale for reconnection ows, and by allowing many independent ux reconnection events to occur simultaneously. Allowing only for the rst eeect and using Goldreich and Sridhar's model of strong turbulence in a magnetized plasma with negligible intermittency, we nd a lower limit for the reconnection speed V A R ?3=16 L M 3=4 , where V A is the Alfv en speed, R L is the Lundquist number, and M is the large scale magnetic Mach number of the turbulence. We derive an upper limit of V A M 2 by invoking both eeects. 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=5 L M 8=5 , and the thickness of the current sheet scales as R ?3=5 L M ?2=5. A signiicant fraction of the magnetic energy goes into high frequency Alfv en waves. The angle between adjacent eld lines on the same side of the reconnection layer is R ?1=5 L M 6=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.