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 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 Lundquist 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 Lundquist number to the power (-2/5) and the thickness of the current sheet scales as the Lundquist number to the power (-3/5). A significant fraction of the magnetic energy goes into high frequency Alfven waves. 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.Comment: Extended version accepted to ApJ, 44pages, 2 figure

We perform direct three-dimensional numerical simulations for magnetohydrodynamic (MHD) turbulence in a periodic box of size 2n threaded by strong uniform magnetic Ðelds. We use a pseudospectral code with hyperviscosity and hyperdi †usivity to solve the incompressible MHD equations. We analyze the structure of the eddies as a function of scale. A straightforward calculation of anisotropy in wavevector space shows that the anisotropy is scale independent. We discuss why this is not the true scaling law and how the curvature of large-scale magnetic Ðelds a †ects the power spectrum and leads to the wrong conclusion. When we correct for this e †ect, we Ðnd that the anisotropy of eddies depends on their size : smaller eddies are more elongated than larger ones along local magnetic Ðeld lines. The results are consistent with the scaling law recently proposed by Goldreich & Sridhar. Here (and arewavenumbers measured relative to the local magnetic Ðeld direction. However, we see some systematic deviations that may be a sign of limitations to the model or our inability to fully resolve the inertial range of turbulence in our simulations.

We study the effects of turbulence on magnetic reconnection using three-dimensional direct numerical simulations. This is the first attempt to test a model of fast magnetic reconnection in the presence of weak turbulence proposed by . This model predicts that weak turbulence, which is generically present in most of astrophysical systems, enhances the rate of reconnection by reducing the transverse scale for reconnection events and by allowing many independent flux reconnection events to occur simultaneously. As a result the reconnection speed becomes independent of Ohmic resistivity and is determined by the magnetic field wandering induced by turbulence. We test the dependence of the reconnection speed on turbulent power, the energy injection scale and resistivity.We study the reconnection model with the open and experiment with the outflow boundary conditions and discuss the advantages and drawbacks of various setups. To test our results, we also perform simulations of turbulence with the same outflow boundaries but without a large scale field reversal, thus without large scale reconnection. To quantify the reconnection speed we use both an intuitive definition, i.e. the speed of the reconnected flux inflow, as well as a more sophisticated definition based on a formally derived analytical expression. Our results confirm the predictions of the Lazarian & Vishniac model. In particular, we find that the reconnection speed is proportional to the square root of the injected power, as predicted by the model. The dependence on the injection scale for some of our models is a bit weaker than expected, i.e. l 3/4 inj , compared to the predicted linear dependence on the injection scale, which may require some refinement of the model or may be due to the effects like finite size of the excitation region, which are not a part of the model. The reconnection speed was found to depend on the expected rate of magnetic field wandering and not on the magnitude of the guide field. In our models, we see no dependence on the guide field when its strength is comparable to the reconnected component. More importantly, while in the absence of turbulence we successfully reproduce the Sweet-Parker scaling of reconnection, in the presence of turbulence we do not observe any dependence on Ohmic resistivity, confirming that the reconnection of weakly stochastic field is fast. We also do not observe a dependence on anomalous resistivity, which suggests that the presence of anomalous effects, e.g. Hall MHD effects, may be irrelevant for astrophysical systems with weakly stochastic magnetic fields.

We analyze three-dimensional numerical simulations of driven incompressible magnetohydrodynamic (MHD) turbulence in a periodic box threaded by a moderately strong external magnetic Ðeld. We sum over nonlinear interactions within Fourier wave bands and Ðnd that the timescale for the energy cascade is consistent with the Goldreich-Sridhar model of strong MHD turbulence. Using higher order longitudinal structure functions, we show that the turbulent motions in the plane perpendicular to the local mean magnetic Ðeld are similar to ordinary hydrodynamic turbulence, while motions parallel to the Ðeld are consistent with a scaling correction that arises from the eddy anisotropy. We present the structure tensor describing velocity statistics of and turbulence. Finally, we conÐrm that an Alfve nic pseudo-Alfve nic imbalance of energy moving up and down magnetic Ðeld lines leads to a slow decay of turbulent motions, and speculate that this imbalance is common in the interstellar medium, where injection of energy is intermittent both in time and space.

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