A variational approach to parametric instabilities in inhomogeneous plasmas I: Two model problems
- University of California, Davis---Livermore, Livermore, California 94550 (United States)
- Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)
A variational formalism is introduced in the theory of three-wave parametric instabilities in inhomogeneous plasmas. This minimum pump strength principle (MPSP) is then applied to two model problems, the first being the Rosenbluth model equations [Phys. Rev. Lett. {bold 29}, 565 (1972)]. By choosing appropriate trial functions, the MPSP is used to solve for the complex eigenfrequency of the most unstable mode. The wave vector mismatch is assumed to be of the form {kappa}(x)={kappa}{sup (n)}(0)x{sup n}/n!, where n is any positive integer. The results are compared to numerical solutions of the same eigenvalue problem. The second problem is the Liu, Rosenbluth, and White Raman sidescattering model [Phys. Fluids {bold 17}, 1211 (1974)], which is treated for any positive-integer power law density profile. The choice of trial functions, the role of symmetry, and various useful approximations are discussed.
- OSTI ID:
- 544839
- Journal Information:
- Physics of Plasmas, Vol. 4, Issue 11; Other Information: PBD: Nov 1997
- Country of Publication:
- United States
- Language:
- English
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