Interaction of Test Waves and Trapped Particles in a Collisionless Electron Plasma

Theoretical studies are undertaken for effects of interaction between test waves and trapped particles in the presence of a large-amplitude monochromatic plasma wave of field amplitude E 0 and wave number k 0 . It is found that the oscillatory variation of the spatial average of the velocity distribution function due to electrons trapped in the wave troughs gives rise to an additional contribution to the plasma polarizability. Furthermore, the trapped electrons induce instabilities of side bands at frequencies ω k ±ω B , where ω k is the frequency of a test wave having wave number k and \(ωB{=}(√2eE₀k₀/m)1/2\) is the bounce frequency of electrons of charge - e and mass m in the wave troughs of the large-amplitude plasma wave.