Plasma Instabilities: Non-Linear Effects

This lecture delves into the study of a system of three non-linearly coupled waves, exploring the effective energy transfer between them and the concepts of action amplitude and action density. The lecture covers wave energy in dispersive media, deriving solutions for the time evolution of the amplitudes of three resonantly coupled waves. Analytic solutions are expressed in terms of elliptic functions, illustrating saturation mechanisms of parametric instabilities. The closely related topic of Stimulated Raman Scattering (SRS) is carefully examined, providing exercises to derive wave energy related to Transverse Electromagnetic Waves (TEMWs) and Electron Plasma Waves (EPWs).