NUMERICAL SIMULATIONS OF PLASMA DYNAMICS IN THE VICINITY OF A RETRACTING FLUX TUBE
In a previous paper, we presented an analytical, zero- β model for supra-arcade downflows in which a retracting flux tube deforms the surrounding magnetic field, constricting the flow of plasma along affected field lines and, in some cases, forcing the plasma to exhibit collimated shocks. Here we present a numerical simulation based on the same model construction—a retracting flux tube is treated as a rigid boundary around which the plasma is forced to flow and the magnetic field and plasma evolve according to the governing equations of magnetohydrodynamics. We find that the collimated shocks described in our previous study are recovered for plasma β in the range of 0 ≤ β ≲ 1, while for 1 ≲ β the behavior is similar to the simpler hydrodynamic case, with classical bow shocks forming when the acoustic Mach number approaches or exceeds unity. Furthermore, we find that while the plasma β is important for identifying the various types of behaviors, more important still is the Alfvén Mach number, which, if large, implies that the bulk kinetic energy of the fluid exceeds the internal energy of the magnetic field, thereby leading to the formation of unconfined, fast-mode magnetosonic shocks, even in the limit of small β .