VARIATIONAL APPROACH TO PARAMETRIC-INSTABILITIES IN INHOMOGENEOUS PLASMAS .1. 2 MODEL PROBLEMS

A variational formalism is introduced in the theory of three-wave para metric instabilities in inhomogeneous plasmas. This minimum pump stren gth principle (MPSP) is then applied to two model problems, the first being the Rosenbluth model equations [Phys. Rev. Lett. 29, 565 (1972)] . By choosing appropriate trial functions, the MPSP is used to solve f or the complex eigenfrequency of the most unstable mode. The wave vect or mismatch is assumed to be of the form kappa(x)=kappa((n))(0)x(n)/n! , where n is any positive integer. The results are compared to numeric al solutions of the same eigenvalue problem. The second problem is the Liu, Rosenbluth, and White Raman sidescattering model [Phys. Fluids 1 7, 1211 (1974)], which is treated for any positive-integer power law d ensity profile. The choice of trial functions, the role of symmetry, a nd various useful approximations are discussed.