Electron distributions in quasi-perpendicular shocks: Simulations

One of the outstanding problems of collisionless shock physics is the microphysical description of electron thermalization and associated wave processes. Observations at the Earth's bow shock have shown various features in the electron velocity distribution such as a loss-cone, temperature anisotropies, and beams before a thermalized, flat-topped distribution is reached downstream. It is generally believed that in addition to the macroscopic fields, which determine the overall mapping of the distribution function, electromagnetic whistler waves and lower hybrid waves are responsible for the pitch-angle scattering and thermalization of the electrons. However, a genuine physical explanation requires analysis of the evolution of the electron distribution in the self-consistent wave fields. Particle simulations are ideally suited to do this, and include processes in which both electrons and ions are involved, such as cross-field streaming instabilities. We show results from l-D and 2-D simulations using an implicit code, which allows time steps large compared to the inverse electron plasma frequency. It is shown that in order to capture the correct propagation characteristics of the waves, a large mass ratio between the protons and electrons is generally necessary. Detailed diagnostics of the waves as well as the evolution of the electron velocity distribution will be presented and will be discussed in the frame work of satellite observations.