A variational approach to parametric instabilities in inhomogeneous plasmas I: Two model problems

Journal Article · Sat Nov 01 04:00:00 EST 1997 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.872504· OSTI ID:544839

Afeyan, B B ^[1]; Williams, E A ^[2]

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1. University of California, Davis---Livermore, Livermore, California 94550 (United States)
2. 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, Journal Name: Physics of Plasmas Journal Issue: 11 Vol. 4; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
INHOMOGENEOUS PLASMA
PARAMETRIC INSTABILITIES
PLASMA INSTABILITY
RESONANCE
VARIATIONAL METHODS