Localized enhancements of energetic particles at oblique collisionless shocks

We investigate the spatial distribution of charged particles accelerated by non-relativistic oblique fast collisionless shocks using three-dimensional test-particle simulations. We find that the density of low-energy particles exhibits a localized enhancement at the shock, resembling the 'spike' measured at interplanetary shocks. In contrast to previous results based on numerical solutions to the focused transport equation, we find a shock spike for any magnetic obliquity, from quasi-perpendicular to parallel. We compare the pitch-angle distribution with respect to the local magnetic field and the momentum distribution far downstream and very near the shock within the spike; our findings are compatible with predictions from the scatter-free shock drift acceleration limit in these regions. The enhancement of low-energy particles measured by Voyager 1 at solar termination shock is comparable with our profiles. Our simulations allow for predictions of suprathermal protons at interplanetary shocks within 10 solar radii to be tested by Solar Probe mission. They also have implications for the interpretation of ions accelerated at supernova remnant shocks.