Comparison of Full-Wave and Ray-Tracing Analysis of Mode Conversion in Plasmas.

摘要

This dissertation reports on the first direct comparison between the results of ray-based and full-wave calculations for mode conversion in plasma. This study was motivated by the modular method originally developed by Ye and Kaufman to treat a magnetosonic wave crossing a cold minority-ion gyroresonance layer. We start with the cold plasma fluid model and introduce a system of evolution equations for electrons and two ion species: deuterium and hydrogen. We first study this system of equations for uniform plasma by Fourier methods, which gives the dispersion relations. We discuss how the traditional approach---which eliminates all other dynamical variables in terms of the electric field---leads to singular denominators at the resonances. We then introduce the Kaufman & Ye approach, which retains the ion velocities as dynamical variables. In this formulation, the ion resonances appear as 'avoided crossings' between the familiar 'fast wave' and a zero-group-velocity ion 'mode' associated with the particle velocities. We then extend our problem to nonuniform plasma where the resonance is localized in space. Away from the resonance, WKB methods apply, but they break down in the vicinity of the resonance. In this region, we introduce the notion of 'uncoupled modes' and discuss how to use them to systematically carry out a simplification of the problem. This leads directly to the modular method of Kaufman & Ye in the mode conversion region, and provides the connection coefficients for the WKB solutions across the resonance layer. We specialize to an incoming wave packet and use the full-wave equations and the reduced 2x2 form to numerically study the wave packet conversion. This allows us to observe the emission of the reflected wave packet after a time delay (the linear 'ion-cyclotron echo'). We calculate the incoming, transmitted and reflected wave packet energies. We compare them to the transmission and reflection coefficients predicted by the S matrix approach of Kaufman and Ye for a wide range of ion density ratios and find good agreement.