Date of Award

Winter 2006

Project Type


Program or Major


Degree Name

Doctor of Philosophy

First Advisor

Martin A Lee


It has been well documented that the plasma immediately downstream of Earth's quasi-perpendicular bow shock, which consists of reflected protons and directly transmitted ions with large temperature anisotropies, is unstable to the excitation of ion-cyclotron waves. These waves in turn scatter the protons and ions to marginal stability. A quasilinear theory is presented for the relaxation of the proton and helium distribution functions and the associated excitation of ion cyclotron waves, downstream of the low-Mach-number quasi-perpendicular Earth's bow shock. For a plasma with low density of He 2+ ions, the theory predicts the wave polarization, power and peak frequency, and the proton bulk velocity and temperature anisotropy, sufficiently far downstream of the shock that the ions and waves have relaxed to a quasi-equilibrium, and the time scale for the relaxation. The results except for the time scale are compared with the AMPTE/IRM crossings of the marginally supercritical bow shock documented by Sckopke et al. [1990], for which the number of "reflected" protons is small and the quasilinear approximation is expected to be valid and He2+ ions are negligible. The agreement with the observations except for the total wave power is generally very good if the contribution of the transmitted core protons is included.

Some of He2+ ions in the downstream plasma diffuse in v1 (velocity in the direction perpendicular to the ambient magnetic field) due to stochastic scattering. The second part of the theory predicts the time evolution of temperature anisotropy for the relaxation of the He2+ ions downstream of the shock and estimates the waves spectrum excited by the protons and He2+ ions.

We also present Cluster data following the inbound shock crossing at 17:17:48 on 31 March 2001, which is an event with higher concentration of He2+ ions. The observed results show that some of the alpha particles are heated perpendicular to the magnetic field as predicted. The predicted evolution of temperature anisotropy, the general shape of wave spectrum, and the time scale match the observed quantities remarkably well though some of the detailed feature for the evolution of the wave spectrum needs further work.