Theory of Parametric Coupling in Plasmas

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Abstract
Based on a simple fluid approach, the theory of the instability due to the nonlinear coupling of an electron plasma oscillation and an ion acoustic oscillation to a driving transverse field is worked out and extended to the case in which the driving field is a longitudinal field. It is shown that the effects of transverse and longitudinal driving fields on the instability are the same in the limit of long wavelength as one would expect physically. In addition, the effect of an electron drift velocity on the nonlinearity-induced instability mentioned above is also examined. It is found that the electron plasma oscillation can be greatly enhanced when the drift velocity approaches the ion wave velocity. Derivation of the above results by the Vlasov equation is indicated in an Appendix.