Injection and acceleration of thermal protons at quasi-parallel shocks: A hybrid simulation parameter survey

Collisionless shocks that propagate along the mean magnetic field are known to accelerate some fi action of the incident charged particles directly from the thermal pool to energies that are considerably higher than the energy at which the plasma rams into the shock. Using hybrid simulations, we address two issues: (1) the dependence of the injection/acceleration of thermal protons to energies much higher than the plasma ram energy on various shock parameters such as Mach number, plasma beta, etc., and (2) the effect of the high-energy particles, accelerated directly from the thermal population by the shock, on the macroscopic Properties of the shock, most notably, on the density compression. We find that for supercritical Mach numbers the acceleration of the thermal plasma is efficient enough that the back pressure due to the energetic particles can significantly increase the density compression across the shock, above the value expected from the simple Rankine-Hugoniot prediction. Additionally, at low Alfven Mach number, where the acceleration of the thermal plasma is inefficient, the density compression is smaller than the simple Rankine-Hugoniot prediction owing to the nonresonant fire hose instability. The acceleration efficiency increases with Mach number except at very high Alfven Mach numbers, where it begins to decrease for Mach numbers greater than similar to 10. This is due to the presence of a fixed, free-escape boundary that limits the size of the foreshock region measured in units of the mean-free paths of the accelerated particles. Additionally we find that regardless of the upstream plasma parameters,the acceleration efficiency increases with both the density compression ratio across the shock and the distance to the free-escape boundary measured in units of the mean-free path of the energetic particles. Both of these are consistent with analytic theory and numerical models that use a phenomenological scattering law.