Two-dimensional hybrid models of ion dynamics in collisionless quasi-perpendicular shocks

Spacecraft observations show that collisionless shocks are ubiquitous in the heliosphere from CME shock fronts to the heliospheric termination shock with broad range of Mach numbers. Evidently, quasi-perpendicular collisionless shocks undergo structural changes with the increase of the Mach number. These changes are related to the increasing role of the reflected ions, which have a highly non-gyrotropic distribution. Eventually, it is expected that the shock front becomes non-stationary and rippled. At low and moderate Mach numbers the fraction of reflected ions is small, yet recent observations show existence of a well-pronounced structure of the post-shock magnetic field in the close vicinity of the transition layer. Here we show, using 2D hybrid simulations, that the gyration of the directly transmitted ions downstream of the ramp produces spatial pressure variations, accompanied with the observed magnetic oscillations due to the momentum conservation. In a wide range of the upstream ion temperatures the low and moderate Mach number shocks remain stationary and one-dimensional (on smaller scale than the variation of the global magnetic field), so that the magnetic and electric field depend only on the coordinate along the shock normal. The downstream ion distributions gradually gyrotropize due to the collisionless mixing of gyrophases of the ion velocity distributions. Non-stationary effects in these shocks do not affect noticeably the ion dynamics. However, we find that with the increase of the Mach number rippled fronts are formed in the low-beta and moderate-beta regimes.