Effects of collisions and thermal pressure on the nonlinear excitation of the upper hybrid resonance

Abstract

The nonlinear interaction of two ordinary modes (the pump wave and the idler or the scattered wave) and an extraordinary mode (the upper hybrid wave) propagating across the magnetostatic field in a uniform warm electron plasma is investigated. Using the parametric approximation, the threshold value of the pump wave electric field necessary for the excitation of the parametric instability near the upper hybrid resonance and the maximum growth rate of the instability are analyzed with respect to their dependence on the strength of the magnetostatic field and the relative directions of propagation. The choice of the physical parameters which will lead to the optimization of the energy transfer to the upper hybrid wave is examined. Omitting the damping of the waves, the time evolution of the amplitudes and the relative phase of the three interacting waves is determined. These amplitudes were found to vary periodically with the nonlinear period increasing with the increase in the strength of the magnetostatic field and the decrease in the amplitudes of the idler wave and the upper hybrid wave relative to that of the pump wave. The effect of the damping of the upper hybrid wave on the time evolution of the amplitudes of the three interacting waves in investigated. The amplitudes of the pump wave and the upper hybrid wave decrease to zero and that of the scattered wave increases to a saturation value either in an oscillatory or nonoscillatory manner according to whether the damping rate is below or above a critical value. The saturation amplitude of the scattered wave is found to decrease and that the coupling to the upper hybrid wave is found to increase if the extraordinary mode is excited slightly below the exact upper hybrid resonance.