Parametric dependence of the density of specularly reflected ions at quasiperpendicular collisionless shocks

Abstract

We present and use two simple analytical models, based on the Rankine—Hugoniot conservation laws, to investigate the dependence of the number density of ions specularly reflected at quasi-perpendicular shocks upon four different upstream parameters. The fraction of incident ions reflected is found to increase with the angle between the direction of the upstream magnetic field and the shock normal, θ Bn, and with the upstream plasma beta, the increase being faster at the lowest values of θ Bn and beta. The effect of changing the plasma beta is less significant at higher Mach numbers. The fraction reflected is strongly dependent on the magnitude of the ratio of specific heat capacities, γ, chosen in the Rankine-Hugoniot relations. More importantly, we find that the number density of reflected ions reaches and remains at a maximum value in the high Mach number limit. Ion reflection can therefore always provide the amount of dissipation required by the Rankine-Hugoniot relations for quasi-perpendicular collisionless shocks.