Ion reflection at the shock front revisited

We study the process of ion reflection at the structured perpendicular shock front, in which ions cross the ramp, proceed to the overshoot, turn back to the ramp, and cross it again, being observed in the upstream region as reflected-gyrating ions. We derive analytically the reflection condition which depends on the potential, magnetic compression ratio and increase of the vector potential across the foot and ramp. The theoretical developments are illustrated by direct numerical analysis of ion trajectories in a model structured shock front. The parameters of the model shock are chosen close to the parameters of the observed high-Mach number supercritical shock with beta(i) similar to 1. The analysis shows that the foot length differs substantially from the value predicted by the specular reflection model and depends on beta(i) as well. The foot length found for the model shock with beta(i) similar to 1 is in a good agreement with observations and simulations of shocks with similar parameters. It is also shown that the reflected ion velocities at the outer edge of the foot and downstream agree with measurements within the limits of the observational errors.