Interaction of energetic ring current protons with magnetospheric hydromagnetic waves

This thesis describes a theoretical study of the interaction of energetic (;A set of gyrokinetic eigenmode equations which describe the linear stability of antisymmetric (with respect to the geomagnetic equator) coupled transverse and compressional magnetic perturbations in an isotropic ;In order to study the effect of the waves on the resonant particles we have used the phase-space Lagrangian Lie transform perturbation methods to derive Hamiltonian gyrophase-independent test-particle equations of motion which include finite gyroradius effects. Analysis and numerical solutions of these equations for the drift-bounce resonance protons yield the following main results: (i) The expected phase-space island structure is obtained. (ii) The observed wave amplitudes exceed the Chirikov overlap criterion by roughly two orders of magnitude. (iii) The motion in a wave packet consisting of more than about 10 azimuthal mode numbers is well approximated by a quasilinear diffusion coefficient. (iv) The observed wave amplitudes are consistent with nonlinear saturation by quasilinear diffusion from the free-energy source region.