Interaction between a Langmuir wave and a ballistic perturbation

The theoretical solutions of the Landau--Vlasov initial value problem giving mode-mode coupling usually neglect the free-streaming contribution. The problem is solved theoretically including the ballistic terms. A mode, resulting from the interaction between the ballistic perturbation of the frequency ω' associated with a launched wave and the Landau component of frequency ω'' of a second launched wave, appears only if ω''>ω'. Its frequency is ω=ω''-ω' and its phase velocity is identical to that of the Landau mode ω/k=ω''/k''. The amplitude of this mode is calculated as a function of distance from the launching probe and this is compared with the amplitude measured experimentally in a plasma column