The quasilinear theory is revised analytically and its consequences are tested by a numerical simulation for a one-dimensional periodic electron plasma with discrete electrostatic modes. The theory is formulated for unstable and damped modes and a series of constants of motion derived. The numerical model is a Vlasov-Poisson system where the mode-mode coupling terms have been omitted. The result is that the predictions of our analytical theory are confirmed by simulation. For all cases considered there are always several modes which are initially unstable, but become damped at a later time so that an inclusion of damped modes in the theory is absolutely necessary.
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Burns et al. (1972) studied this question.
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