NONLINEAR INTERACTIONS OF POSITIVE AND NEGATIVE ENERGY WAVES

Nonlinear resonant three-wave interactions are examined for a number of weakly inhomogeneous plasmas with available free energy. It is shown that for some resonant interactions the necessary and sufficient conditions for the existence of unbounded solutions to the interaction equations reduce to simple criteria. For a number of different realizations of electron and ion beams these criteria indicate that the longitudinal modes in these systems lead to large fluctuations even for wavelengths and beam velocities for which the modes are linearly stable.