A nonlinear multiwave model that describes the interaction of an electron beam, plasma waves, and electromagnetic waves in a cold plasma is derived and studied. The derivation, which is based on slow amplitude and phase change approximations, begins with the electromagnetic Lagrangian coupled to an electron beam, a background plasma, and electrostatic and electromagnetic waves. The model obtained is finite dimensional, and allows for efficient computational and analytical study. Numerical computations demonstrate that with the inclusion of an electromagnetic wave with the plasma wave, the beam-plasma instability is suppressed. If two electromagnetic waves that satisfy a beat-wave matching condition are included, the plasma wave is seen to be amplified provided the beat-wave amplitude exceeds a certain threshold.
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Evstatiev et al. (2005) studied this question.
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