| The parametric instabilities in magnetized plasmas play a role in experiments which berelevant to radio-frequency heating of fusion devices and it has special emphasis onradio-frequency heating of tokamaks. Currently, kinetic description has been used mostly inlarge number of researches of the parametric instabilities in magnetized plasmas.Another method, the hydrodynamical fluid description, is chosen in this paper.Departure from the generality equation of the electric field of waves, and analysis thenonlinear parts in wave equations, which can be used to derive a wave equation to describenon-linear effects of both electromagnetic waves and electrostatic waves. From the nonlinearterms in this equation can make out a variety of parametric process of three-wave orfour-wave interaction relevant to electromagnetic waves or electrostatic waves (or bothelectromagnetic and electrostatic waves). In this article, the parametric processes of anordinary electromagnetic wave into two ordinary electromagnetic waves, an extraordinaryelectromagnetic wave into two extraordinary electromagnetic waves, and an electrostaticwave into two electrostatic waves, have been used as examples, to introduce how to use thewave equation to obtain the coupled-mode equations which can describe a parametricprocess, and ultimately obtained the corresponding nonlinear coupling coefficients and ratesof growth. |
