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Oscillation centres and mode coupling in non-uniform Vlasov plasma

Published online by Cambridge University Press:  13 March 2009

Shayne Johnston  and
Allan N. Kaufman
Shayne Johnston
Affiliation:
Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
Allan N. Kaufman
Affiliation:
Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720
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Abstract

The general coupling coefficient for three electromagnetic linear modes of an inhomogeneous and relativistic plasma is derived from the oscillation-centre viewpoint. A concise and manifestly symmetric formula is obtained; it is cast in terms of Poisson brackets of the single-particle perturbation Hamiltonian and its convective time-integral along unperturbed orbits. The simplicity of the compact expression obtained is shown to lead to a new insight into the essence of three-wave coupling and of the Manley–Rowe relations governing such interactions. Thus, the interaction Hamiltonian of the three waves is identified as simply the trilinear contribution to the single-particle (new) Hamiltonian, summed over all non-resonant particles. The relation between this work and the Lie-transform approach to Hamiltonian perturbation theory is discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 22 , Issue 1 , August 1979 , pp. 105 - 119
Copyright
Copyright © Cambridge University Press 1979

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