Suprathermal Proton Spectra at Interplanetary Shocks in Hybrid Simulations

Interplanetary shocks are one of the proposed sources of suprathermal ion populations -- that is, ions with energies of a few times the solar wind energy. Here, we present results from a series of three-dimensional hybrid simulations of collisionless shocks in the solar wind. We focus on the influence of the shock-normal angle, $\theta_{Bn}$, and the shock speed by considering seven values of $\theta_{Bn}$ and two values of the shock speed. The 14 combinations of $\theta_{Bn}$ and $V_1$ result in shocks with Alfv{\'e}n Mach numbers in the range 3.0 to 6.0, or fast magnetosonic Mach numbers in the range 2.5 to 5.0, representing moderate to strong interplanetary shocks. We find that $\theta_{Bn}$ largely organizes the shape of proton energy spectra while shock speed controls acceleration efficiency. All shocks accelerate protons at the shock front. Shocks with $\theta_{Bn} \geq 60^\circ$ produce isolated bursts of suprathermal protons at the shock front while shocks with $\theta_{Bn} \leq 45^\circ$ create suprathermal beams upstream of the shock. Downstream proton energy spectra have exponential or smoothed broken power-law forms when $\theta_{Bn} \geq 45^\circ$, and a single power-law form when $\theta_{Bn} \leq 30^\circ$. The set of stronger shocks produce protons with energies at least 100 times the local thermal energy (10 times the local thermal speed) downstream of the shock, with $\theta_{Bn} \leq 30^\circ$ shocks producing the highest energy protons.