Sweet-Parker Reconnection with Anomalous Resistivity — A Toy Model
Magnetic reconnection is a common phenomenon in astrophysical contexts. The conventional Sweet-Parker model describes magnetic reconnection due resistivity. However, microscopic resistivity appears too small to reproduce the observed rate of reconnection. In this report, we describe the basic idea of anomalous resistivity in non-relativistic collisionless ion-electron plasma. We build a one-dimensional model along the direction of current in the current sheet. When the ion temperature is much less than the electron temperature, ion-acoustic instability develops when current density is sufficiently large so that the electron drift speed exceeds a few times the sound speed. The instability generates ion-acoustic waves, which are damped by non-linear wave-particle interaction. Anomalous resistivity arises due to the momentum exchange between waves and particles. The calculated anomalous resistivity strongly depends on the current density in the current sheet, and is typically much larger than the microscopic resistivity. However, matching the anomalous resistivity to the Sweet-Parker model, the resulting reconnection rate still falls off the observed rate by a large factor.