A macro-kinetic description of parametric instabilities

Summary form only given. Parametric instability is a very important phenomenon in the study of nonlinear plasma physics. The instability can be analyzed either within the framework of fluid or kinetic equations. The former reveals a clear physical picture of the coupling processes (beating current, ponderomotive and thermal pressure forces) involved, and the analysis is usually less complicated. The latter requires more extensive analytical work (especially in the magnetized plasma case), but its result also contains the kinetic effect of the plasma that is lost in the fluid approach. Therefore, a hybrid approach which takes the advantages of both approaches is desirable. A difficulty in the formulation of a rigorous hybrid approach is that, in the analysis of parametric instabilities, the nonlinear terms (beating current and ponderomotive force) in the fluid equations have their common root ascribed to the convective term (v/spl middot//spl nabla/f) of the Vlasov equation, while it is the E/spl middot//spl nabla//sub v/f term that provides the nonlinear coupling in the kinetic analysis. In the present work, a moment expansion procedure is applied to the perturbed distribution function in the nonlinear coupling term in the kinetic analysis of parametric instabilities. Since the proposed theory incorporates fluid variables into the kinetic framework, it is termed macro-kinetic theory (MKT). This macro-kinetic formulation is, in principal, exact if all the moments in the expansion are taken into account. Moreover, the fluid description for parametric coupling can be retrieved from the kinetic framework. Therefore, the macro-kinetic coupling terms contain fluid insights as well as the kinetic information, while greatly simplify the kinetic analysis of parametric instabilities.