THE NONLINEAR INTERACTION OF AN ELECTROMAGNETIC WAVE WITH A TIME-DEPENDENT PLASMA MEDIUM

Abstract

A one-dimensional, inhomogeneous model is used to describe the nonlinear interaction of a radio-frequency plane wave with a time-varying plasma medium. A monochromatic plane wave is normally incident upon an electron density profile where the electron density gradients are shallow compared to a wavelength. Changes in electron temperature and electron density are induced which continually alter the pattern of electromagnetic energy deposition into the medium. The electron energy relaxation time is much longer than the period of the electromagnetic wave, so that the electron temperature does not follow the rapid variations in the impressed field. A nonlinear constitutive relationship is derived relating the macroscopic current density to the impressed electric vector, assuming that the wave field is almost monochromatic in the medium. The time-dependent response of the plasma medium may be found by numerically solving the energy-balance equations and the continuity equation for the electron gas. The spread in frequency of the electromagnetic wave field due to the time-varying electrical conductivity may be computed by employing the WKB approximation as a solution to the wave equation for a time-varying medium. Graphs are presented which represent the time-dependent response of the electron temperature and electron density as a function of the incident r-f. field amplitude.