Effects of trapped electrons on ion reflection in an oblique shock wave

A magnetosonic shock wave propagating obliquely to an external magnetic field can trap electrons and accelerate them to ultrarelativistic energies. The trapped electrons excite two-dimensional (2D) electromagnetic fluctuations with finite wavenumbers along the shock front. We study effects of the trapped electrons on ion motions through the 2D fluctuations. It is analytically shown that the fraction of ions reflected from the shock front is enhanced by the 2D fluctuations. This is confirmed by 2D (two space coordinates and three velocities) relativistic, electromagnetic particle simulations with full ion and electron dynamics and calculation of test ions in the electromagnetic fields averaged along the shock front. A comparison between 2D and one-dimensional electromagnetic particle simulations is also shown