Parametric Excitation and Mode Coupling

Abstract

We have described simple examples of nonlinear wave propagation in Sects.5.6 and 6.6. There we were mainly concerned with a single nonlinear wave mode. In many cases of interest, nonlinear coupling of different linear wave modes can also be important Such couplings typically occur as a result of periodic modulation of a plasma parameter characterizing the dispersion relation of the wave. The modulation is due to the presence of another wave, therefore it can be considered as a mode coupling process. Such a mode coupling often causes an unstable beat wave, that is, a beat between the original wave and the modulation. This instability is called the parametric instability [8.1.2]. In this chapter, we first discuss some general properties of parametric instabilities by using model equations and then specifically discuss the case of the excitation of an electron plasma wave and an ion acoustic wave in an isotropic plasma. We further discuss the nonlinear wave-particle interaction for the case of the electron plasma wave and finally discuss the Langmuir wave turbulence with particular attention to the condensation and collapse of the wave.