The interaction of an electron beam with a relatively dense background plasma was examined through numerical experiments, where the beam velocity is much greater than the thermal velocities. It is shown that the initial growth of the unstable waves is described by the two-stream instability and that the phenomena can be separated into two regions, (high and low density) depending on whether or not merging of space-averaged velocity distributions occurs during the growth of the initially most unstable wave. The occurrence of these regions is shown to follow from energy and momentum considerations. The long-time behavior of the low-density regime, where the merging does not take place during the initial growth of the instability is shown to be described quite well by quasilinear theory.
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Kainer et al. (1972) studied this question.
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