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An investigation is made into the stabilization of 'explosive' instabilities in beam-plasma systems. The stabilizing mechanism is a non-linear frequency shift. The interaction of the waves is studied in the fixed phase approximation using second order perturbation theory. The correct mathematical procedure is established for obtaining the second order equations for the wave amplitudes using a multiple time scale formalism. For the beam-plasma system considered here, the maximum amplitude values and the characteristic times between 'flashes' in the interacting wave amplitudes are obtained. The theory which is developed is applied to a wide range of parameter values for the plasma and the electron beam.
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Davydova et al. (1975) studied this question.
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