Trajectories of ions specularly reflected from non-planar collisionless shocks

An important contribution to the thermalization of the solar wind ions at the Earth's bow shock for high Mach numbers comes from the reflection of a fraction of these ions from the shock. Previous studies have examined the trajectories of the reflected ions assuming the shock to be an infinite plane. In this paper a model is developed to describe the trajectories of particles after reflection for a variety of shock geometries. Of particular interest are the initial conditions which allow the particle to return to the shock with a greater normal velocity than at first encounter, or to return to the shock at all. The effects of the magnetic field direction and the curvature of the shock on particle trajectories are discussed for cylindrical and spherical shock geometries and compared to those for a planar shock.