Particle acceleration in step function shear flows: A microscopic analysis

We present a discussion of the transport of energetic particles in a moving, scattering fluid, which has a large shear in its velocity over a distance small compared with the scattering mean free path. The analysis is complementary to an earlier paper by Earl, Jokipii, and Morfill, which considered effects of more-gradual shear in the diffusion approximation. In the present paper we consider the case in which the scattering fluid undergoes a step function change in velocity, in the direction normal to the flow. We present both an analytical, approximate calculation and a Monte Carlo analysis of particle motion. We find that particles gain energy at a rate proportional to the square of the magnitude of the velocity change. Application to the boundary of a magnetosphere suggests significant acceleration of the particles.