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 ω_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, ω_S and the mixed frequencies ω₀±ω_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, ω_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.