Wave Dynamics in Phase-Space and Ion Gyroresonant Absorption.

This thesis is a study of gyroresonance in a nonuniform magnetized plasma. In the first half of the thesis, we briefly review the Lagrangian formulation of the guiding center/oscillation center theory for the case of nonresonance, then we extend it to the gyroresonant particles. We use a Lagrangian variational principle, which naturally leads to the self-consistent Maxwell-Vlasov equations with the effects of gyroresonance included. The coupling equations for gyroresonance are the linearized Vlasov equation for the gyroresonant particles, and the wave equation for the electromagnetic perturbation driven by the current of the gyroresonant particles. We present a physical interpretation for the gyroresonance process, as the phase-space mode -conversion between the electromagnetic wave and a continuum of gyroresonant ballistic waves. A gyroresonant ballistic wave is an eigenfunction of the linearized Vlasov equation in the absence of electromagnetic perturbations, whose dispersion relation is the same as the local gyroresonance condition. The group velocity of a gyroresonant ballistic wave is the same as the drift velocity of a guiding center, but the wave carries phase information that is essential for its interaction with other waves. In the second half of this thesis, we apply our formalism to the one-dimensional model of ion gyroresonant absorption of a magnetosonic wave, which is an outstanding problem in the theory of tokamak heating. Two cases studied are the minority fundamental and the majority second harmonic gyroresonance. The mode conversions occurs at two separate places in wave phase-space, so correspondingly we make a two-step mode-conversion approximation. Explicit expressions are derived for the transmission and reflection coefficients. The gyroresonant ballistic waves are kinetic, and contain in them the ion-Bernstein wave, which in our heuristic model cannot escape from the resonance layer. We project out the ion-Bernstein wave right after the mode conversion(s), and obtain the "immediate" conversion and absorption coefficients. The conversion coefficient is defined as the fraction of action flux that goes into the ion-Bernstein wave.