Magnetohydrodynamic Shocks in and above Post-flare Loops: Two-dimensional Simulation and a Simplified Model

Solar flares are an explosive phenomenon where super-sonic flows and shocks are expected in and above the post-flare loops. To understand the dynamics of post-flare loops, a two-dimensional magnetohydrodynamic (2D MHD) simulation of a solar flare has been carried out. We found new shock structures in and above the post-flare loops, which were not resolved in the previous work by Yokoyama & Shibata. To study the dynamics of flows along the reconnected magnetic field, the kinematics and energetics of the plasma are investigated along selected field lines. It is found that shocks are crucial to determine the thermal and flow structures in the post-flare loops. On the basis of the 2D MHD simulation, we developed a new post-flare loop model, which we defined as the pseudo-2D MHD model. The model is based on the one-dimensional (1D) MHD equations, where all variables depend on one space dimension, and all the three components of the magnetic and velocity fields are considered. Our pseudo-2D model includes many features of the multi-dimensional MHD processes related to magnetic reconnection (particularly MHD shocks), which the previous 1D hydrodynamic models are not able to include. We compared the shock formation and energetics of a specific field line in the 2D calculation with those in our pseudo-2D MHD model, and found that they give similar results. This model will allow us to study the evolution of the post-flare loops in a wide parameter space without expensive computational cost or neglecting important physics associated with magnetic reconnection.