Nonlinear wave optics of parametric pump radiation in an inhomogeneous plasma

The nonlinear propagation of an intense (pump) beam of electromagnetic radiation that excites a parametric decay instability in an inhomogeneous plasma is calculated self-consistently. A generalization to an inhomogeneous plasma of the nonlinear absorptive conductivity calculated according to several recent theories for the saturated electron-ion decay instability in a homogeneous plasma is added to the linear absorptive conductivity in the wave equation. A model is introduced for the qualitative change in the pump dependence of the nonlinear conductivity in the strong pumping limit. The resulting nonlinear wave equation for radiation propagating into a stratified plasma is integrated numerically. Application is made to the anomalous absorption of the modified radiation in ionosphere modification experiments and to absorption of laser radiation in laser-produced plasmas. The reflection coefficient is computed as a function of incident power. Also computed are waveforms, the Poynting flux, and the ponderomotive force. These are displayed as functions of position in the plasma. A distinct standing-wave pattern is shown to persist very near the reflection point even in cases of nearly total absorption.