Suprathermal Proton Spectra at Interplanetary Shocks in 3D Hybrid Simulations

Interplanetary shocks are one of the proposed sources of suprathermal ion populations (i.e., ions with energies of a few times the solar-wind energy). Here we present results from a series of 3D hybrid simulations of collisionless shocks in the solar wind. We focus on the influence of the shock-normal angle, θBn, and the shock speed, Vs, on producing protons with energies a few to hundreds of times the thermal energy of the upstream plasma. The combined effects of θBn and Vs result in shocks with Alfvén Mach numbers in the range 3.0-6.0 and fast magnetosonic Mach numbers in the range 2.5-5.0, representing moderate to strong interplanetary shocks. We find that θBn largely organizes the shape of proton energy spectra, while shock speed controls acceleration efficiency. All shocks accelerate protons at the shock front, but the spectral evolution depends on θBn. Shocks with θBn ≥ 60° produce isolated bursts of suprathermal protons at the shock front, while shocks with θBn ≤ 45° create suprathermal beams upstream of the shock. Downstream proton energy spectra have exponential or smoothed broken power-law forms when θBn ≥ 45° and a single power-law form when θBn ≤ 30°. Protons downstream of the strongest shocks have energies at least 100 times the upstream thermal energy, with θBn ≤ 30° shocks producing the highest-energy protons and θBn ≥ 60° shocks producing the largest number of protons with energies at least a few times the thermal energy.