THe relationship between the particle injection rate and the dispersion of the scattering angular distribution

Although non-linear diffusive shock acceleration could be simulated by some well-established models, the particle injection rate is a priori assumed to proceed from thermal particles to the superthermal population in some models that use numerical simulations. In order to investigate the effect of anisotropy in particle scattering on the particle injection rate, we present a dynamical Monte Carlo simulation of a bow shock from Earth with different dispersions in the pitch-angle scattering. Since the particle injection rate is intrinsically defined by the prescribed scattering law in a Monte Carlo approach, we can directly study the relationship between the particle injection rate and the dispersion of the particle scattering angular distribution. As a result, we find that the particle injection rate increases as the dispersion of the scattering angular distribution increases. The shock energy spectrum also becomes harder as the scattering angular distribution varies from a situation with anisotropy to one with isotropy. If the particle injection rate can dominate the shock strength, that may imply that a low-speed coronal mass ejection (CME) could drive a strong shock and a high-speed CME could drive a weak shock.