Current Sheet Statistics in Three-Dimensional Simulations of Coronal Heating

Abstract: In a recent numerical study [Ng et al., Astrophys. J. {\bf 747}, 109, 2012], with a three-dimensional model of coronal heating using reduced magnetohydrodynamics (RMHD), we have obtained scaling results of heating rate versus Lundquist number based on a series of runs in which random photospheric motions are imposed for hundreds to thousands of \al time in order to obtain converged statistical values. The heating rate found in these simulations saturate to a level that is independent of the Lundquist number. This scaling result was also supported by an analysis with the assumption of the Sweet-Parker scaling of the current sheets, as well as how the width, length and number of current sheets scale with Lundquist number. In order to test these assumptions, we have implemented an automated routine to analyze thousands of current sheets in these simulations and return statistical scalings for these quantities. It is found that the Sweet-Parker scaling is justified. However, some discrepancies are also found and require further study.