Computer simulation of nonlinear interaction between a cold beam and a weakly collisional plasma

The spatial growth of the instability and the nonlinear interaction between a small cold beam and a warm background plasma are examined by means of particle simulation. Up to the first maximum in the amplitude oscillation of the wave, quantitative measurements confirm the predictions based on the single wave model: the magnitude of the growth rate, monochromaticity of the unstable mode, the maximum wave amplitude, and the phase space orbits of the beam electrons. After the first maximum of the wave amplitude, the spatial dependence of the wave amplitude cannot be explained by the single wave model predictions and the wave power is anomalously overdamped by a factor of 0.1 smaller than the predicted value in the first minimum. The extended single wave model equations suggest that this anomalous phenomenon is caused by weak collisions of the order of ν/ωp~10-3 within the background plasma