SOME NONLINEAR PROBLEMS IN PARTIALLY IONIZED GASES.
UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES ENGINEERING CENTER
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The theoretical study of harmonics arising from nonlinear dissipation is the principal subject of this dissertation. The subjects treated fall into one of three overlapping topics 1 the kinetic theory of plasmas, 2 the development of accurate nonlinear macroscopic equations linking the important average quantities current, electron temperature, etc. together, and 3 application of the macroscopic equations to nonlinear problems involving harmonics. The first topic is primarily a review of the literature, interspersed with critical commentary, expanded discussion, and alternative and clearer derivations of important relations. The primary purpose in studying the kinetic theory is to examine the areas of difficulty and to resolve the conflicts. In the second topic, the macroscopic equations for the plasma, simple equations for the important quantities such as the electron current and electron temperature are developed directly from the kinetic theory. The principal purpose in studying this topic is to derive simple relations between the important average quantities in order to replace the virtually intractable kinetic theory approach. In the third topic, the macroscopic approach is applied to two nonlinear problems. The first is a study of the low frequency nonlinear current flow associated with the monochromatic electric field of arbitrary intensity. In the second nonlinear problem, a monochromatic field is incident upon a semi-infinite plasma slab and the back radiation from the interface, and the nature of the field within the plasma are sought.