Nonlinear behaviour of a finite amplitude electron plasma wave I. Electron trapping effects

Nonlinear effects in the propagation of longitudinal plasma waves due to trapped electrons are considered. The spatial evolution of a stable, finite amplitude wave is compared with theory and shown to be characterized by the ratio of the trapped electron oscillation frequency to the linear Landau damping rate. The ‘sideband’ instability which develops at larger amplitudes is examined in considerable detail experimentally, and comparison with theory enables the conclusion to be reached that trapped particles are essential to the mechanism of the instability. Regimes are defined in which these types of nonlinear behaviour occur, and the importance of the instability in the development of strong turbulence is discussed.