The Cerenkov interaction of a weak electron beam with a plasma is studied numerically. Three parts of the nonlinear evolution of the convective instability are discussed. In the first part the understanding of the saturation amplitude of the initial wave and its harmonics is extended. In the second part it is shown that a quasi-linear-like cascade process is responsible for the simutaneous appearance of beam particles and waves which move slower than the original beam velocity. These modes destroy the trapped particle oscillations of the initial wave. The third part of the instability is the development of fast waves whose phase velocities are greater than the original velocity of the beam. It is shown that these waves arise due to a mode coupling mechanism.
Plasma simulation models have been developed which replicate the fundamental features of the convective and oscillating instability in the nonlinear weak beam regime. The oscillating instability is characterized in this regime by a randomly fluctuating electric field which is caused by the presence of a fresh, strong beam in a region of space in which the electric field is large. Nonlinear behavior of the background plasma need not be present during the production of the oscillating instability. The convective instability develops into a quasilinear quiescent state during its nonlinear evolution because the nonlinear behavior of the system is confined to a diffused beam.
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