Spatial Distribution and Anisotropy of Energetic Particles Accelerated by Shock Waves: Focused Transport Model

The focused transport equation (FTE) contains the necessary physics of shock acceleration but avoids the limitation of small pitch-angle anisotropy inherent in the cosmic ray transport equation. We present a focused transport model based on FTE to investigate the spatial distribution and anisotropy of energetic particles accelerated by shock waves from pickup ions. It is found that in the upstream of the shock, the accelerated particles are highly anisotropic, but in the downstream it is approximately isotropic. An intensity spike is formed across the shock. These simulation results are qualitatively consistent with the observations of the termination shock particles by two Voyager spacecraft in the vicinity of the termination shock.