Stationary nonlinear interaction between high- and low-frequency waves and the generation of density cavities in a plasma

The nonlinear interaction of a high-frequency wave (transverse or longitudinal) and an ion-acoustic wave in a homogeneous plasma is investigated. The waves are assumed to be simultaneously excited by two localized external sinusoidal disturbances with frequencies ω0 and ωsub(s) in the plasma. From the coupled wave equations a system of ordinary differential equations for the spatial change of the amplitudes of the interacting waves (including the primary frequencies ω0, ωsub(s) and the mixed frequencies ω0 +- ωsub(s)) and a zero-frequency density disturbance is derived. The spatial development of the high-frequency amplitudes is characterized by localized regions of high intensities, coupled with local depressions of the plasma density. The influence of the initial amplitudes and the frequencies ω0, ωsub(s) on the maximum of the primary high-frequency amplitude and the 'cavity' depth is shown. The numerical results are compared with conclusions from a simplified model of three resonantly interacting normal modes. (author)