Test particle simulations of ion acceleration at perpendicular collisionless shocks

Test particle simulations are performed to investigate ion acceleration at perpendicular collisionless shocks. The dependence of the ion energy gain on some key ion parameters (i. e., initial gyro-phase angle, position, and average upstream kinetic energy) is first explored for an ideal shock profile given by the Rankine-Hugoniot relations. The shock profile is then switched to more realistic ones given by a self-consistent one-dimensional hybrid shock simulation, in order to examine the influence of small scale, internal electric and magnetic shock structures on the ion acceleration. The results show that, when the ion initial energy is relatively low (with the ion gyroradius comparable or shorter than the shock transition thickness), the presence of the electric cross-shock potential and the magnetic shock overshoot enhances the ion energy gain. However, when the ion initial energy becomes higher, the influence of the small scale, internal shock structures diminishes and becomes negligible. In addition, the ion energy gain increases with the strength of the magnetic shock overshoot. The influence of the magnetic overshoot strength on the ion energy gain dominates that of the electric cross-shock potential. Their individual contributions do not simply add up and can cancel each other at times. One such example is presented to demonstrate how the bipolar shock normal electric field structure may reduce the ion energy gain.