The Physics of Particle Acceleration From Thermal to Suprathermal Energies at Collisionless Shocks

We discuss the physics of the formation of high-energy tails in the distributions of charged particles accelerated by collisionless shocks. We utilize self-consistent hybrid simulations to study the dependence of the injection energy - the energy at which the high-energy tail of the distribution begins - on shock parameters such as Mach number and shock-normal angle. One the one hand, we find that the ratio of the injection energy to plasma-ram energy is remarkably independent of many shock parameters, including the average shock-normal angle. We note that our simulations include large-scale, pre-existing magnetic turbulence - known to exist in solar, heliospheric, and astrophysical plasmas - that plays a critical role in the injection and acceleration process and cannot be ignored. Pre-existing turbulence also plays a vital role in the acceleration of electrons at shocks, previously thought to be a problem, which will also be discussed. On the other hand, we also find that the number of injected particles, which is related to the efficiency of the injection and acceleration can depend on a number of factors, most notably on the nature of the incident particle distribution. When there is significant energy density in pre-existing suprathermal particles, then the efficiency of accelerating thermal plasma by the shock is much reduced compared to a case when there is little, or no energy, in pre-existing suprathermal particles. Consequences for understanding and interpreting spacecraft observations will be discussed.