Suprathermal Proton Spectra at Interplanetary Shocks in 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 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, $V_s$, on producing protons with energies a few to hundreds of times the thermal energy of the upstream plasma. The combined effects of $\theta_{Bn}$ and $V_s$ result in shocks with Alfv\'en Mach numbers in the range 3.0 to 6.0 and 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 but the spectral evolution depends on $\theta_{Bn}$. 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 $\theta_{Bn} \leq 30^\circ$. Protons downstream of the strongest shocks have energies at least 100 times the upstream thermal energy, with $\theta_{Bn} \leq 30^\circ$ shocks producing the highest energy protons and $\theta_{Bn} \geq 60^\circ$ shocks producing the largest number of protons with energies at least a few times the thermal energy.