An Analytical Study of Electromagnetic Vector Field Propagation in a Nonlinear Electron Plasma

Citation

Tatoian, James Zareh (1983) An Analytical Study of Electromagnetic Vector Field Propagation in a Nonlinear Electron Plasma. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/hzt3-s585. https://resolver.caltech.edu/CaltechETD:etd-10312005-133116

Abstract

From the equations of hydrodynamics and electrodynamics, a system of a coupled nonlinear equations governing the propagation of plane electromagnetic waves in a collisionless electron plasma is obtained. It is shown that solitary wave solutions exist for both the longitudinal and transverse components of the electromagnetic field. It is found that the velocity of the electromagnetic vector solitary wave depends on the amplitudes of all components of the field linearly. The relations among the longitudinal and transverse components that support the solitary waves are determined for different values of plasma temperature. It is shown that while transverse solitary waves cannot exist, except when they are supported by longitudinal waves, the latter can exist by themselves. The dynamics of the plasma electrons during the passage of a longitudinal wave is analyzed and the interaction of such waves with each other is studied. An upper bound on the amplitudes of these waves is obtained. The uniqueness and stability of the longitudinal waves are demonstrated. A Lagrangian density function and two conservation laws for the longitudinal wave equation are found. Frequency spectra of the solitary waves are calculated and their low frequency content is emphasized.

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