Non linear 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. We solve theoretically this problem including the ballistic terms. We find that a new mode appears resulting from the nonlinear interaction between the Landau component and the ballistic perturbation. The amplitude of this mode is calculated as a function of distance and compared with experimental results in a plasma column