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Time asymptotic perturbation theory in weak plasma turbulence I. Macroscopic description

Published online by Cambridge University Press:  13 March 2009

Klaus Elsässer
Klaus Elsässer
Affiliation:
Max-Planok-Institut für Physik und Astrophysik, 8 München 23, Föhringer Ring 6, Germany
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Abstract

The time asymptotic method of non-linear mechanics (Bogoljubov & Mitropoiski 1961) is used to solve the hierarchy equations of low-amplitude wave correlations. We start with a formal description of individual dispersive and undamped waves and derive the usual kinetic equation for the energy spectrum and the three-wave correlation in the lowest order (three-wave processes). We show that the equations are automatically closed (‘Quasi-Gaussian’) even in the case where the correlations have the same order of magnitude as the corresponding moments. This approach parallels the multiple-time formalism of Sandri and Frieman, but it represents an alternate systematic and unique method (without ‘extension’ in the sense of Sandri).

Type
Articles
Information
Journal of Plasma Physics , Volume 5 , Issue 1 , January 1971 , pp. 31 - 37
Copyright
Copyright © Cambridge University Press 1971

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References

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