| Summary: | The thesis investigates ion behaviour at collisionless shocks, with a focus on two areas of interest. The first area concerns the reflection of particles from collisionless shocks, a necessary mechanism for thermalization at a shock at sufficiently high Mach numbers such as ordinarily prevail at the Earth's bow shock. Previous studies have examined the trajectories of reflected ions with the assumption of a planar shock. In this study, a general framework is developed to describe the trajectory of an ion after reflection, with application to a variety of shock geometries. The conditions allowing an ion to return to the shock after reflection and to return with an increased normal velocity are studied, with three primary parameters considered: the radius of curvature, the magnetic field orientation, and the incident velocity in the shock normal direction. Each of these parameters depends on the shape of the shock and the location of incidence. Results are reported for cylindrical, spherical, and parabolic shock geometries, over ranges of shock curvatures, magnetic field orientations, and incident velocities. Second, we consider the thermalization of the ion distribution initially transmitted through the shock under low Mach number conditions, where reflection is a less significant contributor to thermalization. Previous work has considered the phase area invariant in an exactly perpendicular case. This is generalized to a quasi-perpendicular shock, and invariants of the flow are determined for a Hamiltonian formulation. The evolution of the distribution through the shock is then studied analytically and numerically. Results regarding the shape of phase shells of constant probability, the phase volume within these shells, and the temperature of the distribution are given.
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