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The method of the averaged Hamiltonian and the two-stream explosive instability

Published online by Cambridge University Press:  13 March 2009

Z. Sedláček
Z. Sedláček
Affiliation:
Institute of Plasma Physics, Czechoslovak Academy of Sciences, Prague
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Abstract

Second-order perturbation calculation shows that an explosive instability of three resonantly interacting coherent electrostatic waves can be limited, and converted into a multiple-periodic process by nonlinear terms of the same order as those that destabilize the waves in the first-order approximation. No higher- order nonlinearities are necessary. The method used is purely classical, and consists in transforming the Hamiltonian of the waves into angle-action variables, and canonical averaging of the Hamiltonian over the proper angles. The number of degrees of freedom is thus reduced to one, which permits one to analyse the wave interaction in the phase plane without using the usual equations for the complex wave amplitudes.

Type
Research Article
Information
Journal of Plasma Physics , Volume 15 , Issue 1 , February 1976 , pp. 1 - 14
Copyright
Copyright © Cambridge University Press 1976

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