Nonlinear decay and instability of a nonuniform finite-amplitude plasma wave

The effects of spatial nonuniformities in the amplitude of a decaying finite-amplitude plasma wave are examined. It is found that the usually neglected, but experimentally important, initial damping (or growth) of the finite-amplitude wave may have important consequences upon the decay process. The mode-coupling equations are solved for both forward-scattering and back-scattering type decay processes. The latter case is particularly interesting, since both amplification in space, and instability in time, of the perturbed waves may occur in the presence of damping mechanisms. Calculations are presented which show that longitudinal waves with frequencies in the vicinity of cyclotron harmonics may be subject to such instabilities.