Abstract
The basic equations and numerical results which describe the non-linear interaction of a weak, modulated electron beam with a single, stationary one-dimensional wave, excited in a cold, magnetic field-free plasma, are presented and discussed. The effect of all possible irreversible processes (e.g. plasma turbulence) accompanying this interaction is simulated by a constant, effective collision frequency nu eff of plasma electrons. Starting from the non-linear Poisson equation, expressions for the amplitude and phase of the beam-excited wave are derived and then solved numerically, together with the equations of motion of the beam electrons. The results are compared with those of the time-dependent model. Considerable differences which can be detected experimentally are established.