The Density Transition Scale at Quasi-perpendicular Collisionless Shocks - Hybrid Simulations

The dependence of the shock thickness on the shock Mach number and the upstream proton beta have been subject of several studies. We carry out a parametric study of several numerical experiments of quasi-perpendicular shocks in two dimensions using standard hybrid code. Hybrid simulations treat ions as particles and electrons as a fluid. Having ions as particles allows ion kinetic behavior and waves to be included. We take the advantage of the fact, that in a numerical experiment whole shock front is available. A hyperbolic tangent is fitted to each density transition profile along the shock front to obtain a measure of the mean value of the shock thickness L and a the typical value of absolute error dL of this value caused by natural perturbations (ripples) of the accelerating shock front. Both parameters are scaled by both the upstream proton inertial lenght and by the ratio of the shock velocity and the inverse of the downstream proton gyrofrequency. Cluster II multispacecraft allows us to obtain an estimate of the mean value L and also a rough estimate of the absolute error dL. We find the dependency of the shock thickness L and the error dL on the wide range of shock's Mach number and and upstream proton beta in the numerical model and compare these results with Cluster II observations.