A study of one-dimensional nonlinear hydromagnetic waves and collisionless shocks

Abstract

A variety of nonlinear hydromagnetic waves have been observed in the collisionless solar wind plasma. A comprehensive theoretical study of nonlinear hydromagnetic waves, including rotational discontinuities and collisionless shocks, is carried out in this thesis by means of both analytical solutions and numerical simulations. Nonlinear hydromagnetic waves are governed by the interplay of the dispersion process, the collisionless dissipation process and the nonlinear steepening process. The purpose of this thesis is to understand the nonlinear behavior of hydromagnetic waves in terms of these fundamental processes. It is shown that the rotational discontinuity structures observed in the solar wind and at the magnetopause are nonlinear Alfven wave solutions of the collisionless two-fluid plasma equations. In these nonlinear wave solutions, nonlinear steepening is self-consistently balanced by dispersion. Collisionless viscous dissipation is the dominant dissipation in high Mach number shocks, which converts the flow energy into thermal energy. Hybrid simulations show that the collisionless viscous dissipation can result from the reflection and pitch-angle scattering of incoming ions flowing through the magnetic structures in the shock transition region. Collisionless dissipations in hydromagnetic shocks is governed by the magnetic structures in the shock transition region. The dissipation in turn can modify the wave structures and balance the nonlinear steepening. However, such delicate balance of the dispersion, dissipation, and nonlinear steepening has been observed to break down momentarily in high Mach number quasi-parallel shocks. This leads to the so-called cyclic shock front reformation seen in the hybrid simulations. The shock front reformation can be explained in terms of momentary off-balance between the dispersion-dissipation on the one hand and the nonlinear steepening on the other hand. The off-balance occurs after a significant fraction of incoming ions are reflected. Each off-balance lasts a few ion gyro periods, which governs the shock front reformation time scale.