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. We recover lower and upper limits on the reconnection rate, depending on the reaction of the magnetic field to stresses exerted from within the reconnection layer. Using Goldreich and Sridhar's model of strong turbulence in a magnetized plasma with negligible intermittency, we find that the lower limit for the reconnection speed is the Alfven speed times the magnetic Reynolds number to the power (-3/16). The upper limit on the reconnection speed is typically a large fraction of Alfven speed. 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 magnetic Reynolds number to the power (-2/5) and the thickness of the current sheet scales as Rm to the power (-3/5). A large fraction of the magnetic energy goes into high frequency Alfven waves. We claim 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.