Time-dependent magnetic reconnection in two-dimensional periodic geometry

Abstract

We compare the predictions of incompressible, analytic reconnection theory with numerical simulations performed using a time-dependent, doubly periodic code. The properties of the simulated current sheets are shown to be in good quantitative agreement with recent planar analytic reconnection solutions based on X-point merging driven by sheared incompressible flows. We conclude that the analytic treatment is not seriously compromised by assuming an open flow geometry and a one-dimensional current layer. The analytic models, when augmented by nonlinear saturation arguments, are also shown to provide resistive scaling laws that accord well with computed merging rates. By way of contrast, we have found no computational evidence for the osculation of separatrices in current sheets, even for the case of classical head-on reconnection in which all shearing flows are absent. We attribute this to the dynamic nature of the simulated current sheet. Our simulations provide some evidence that dynamic current sheets can break up into magnetic islands, but whether this fragmentation can be attributed to the tearing mode instability remains unclear.