Modeling Coherent Injections Produced by Substorm Dipolarizations

In the inner magnetosphere, processes affecting the dynamics of energetic particles can be broadly categorized as either stochastic processes, which describe the random dynamics of individual particles in a quasilinear approximation; or coherent processes, whereby particles are collectively driven in one direction in energy or space. This study focuses on the coherent injections produced by substorm dipolarizations propagating Earthward from the tail. These injections are defined as simultaneous enhancements in the fluxes of particles of different energies which is typically observed near or inside geosynchronous orbit. We model the coherent injection by computationally tracking the motion of test particles in magnetic and electric fields computed analytically. By tracking the particles, we calculate advection coefficients that are applied to the Fokker-Planck equation with an advection term and solved for phase space density time evolution. We present the resultant phase space density to show the effects of the coherent injection of energetic particles from interaction with model substorm fields and their overall effect relative to stochastic processes.