Nonlinearized Theory of Transverse Plasma Oscillations

Abstract

Exact, nonlinearized, solutions of the Vlasov equation for a homogeneous, neutral plasma with infinitely heavy ions in the presence of transverse electromagnetic waves are found. The dispersion relation is developed both for stationary waves and for the general initial value problem. For stationary waves the result is analogous to that obtained by Van Kampen in his linearized treatment of the longitudinal plasma oscillations. The initial-value problem approach yields results similar to those of Landau but, for nonrelativistic plasmas, damping exists only for phase velocities much smaller than the velocity of light. It is proved that no growing-wave solutions exist. A distribution function which is consistent with a single-wave-packet solution of the wave equation, and which propagates subject to an arbitrary root of the dispersion relation, is constructed. The intimate relationship between the initial electron distribution function and the dispersion relation is discussed.