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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

REFERENCES

Benney, D. J. & Newell, A. C. 1969 Studies in Appl. Math. 48, 29.CrossRefGoogle Scholar
Benney, D. J, & Saffman, P. G. 1966 Proc. Roy. Soc. A 289, 301.Google Scholar
Bogoljubov, N. N. & Mitropoloski, Y. A. 1961 Asymptotic Methods in the Theory of Non-linear Oscillations. India: Hindustan Publishing Corp.Google Scholar
Davidson, R. C. 1967 J. Plasma Phys. 1, 341.CrossRefGoogle Scholar
Elsässer, K. 1969 MPI-PAE/Astro 24.Google Scholar
Frieman, E. A. 1963 J. Math. Phys. 4, 410.CrossRefGoogle Scholar
Frieman, E. A. & Rutherford, P. H. 1964 Ann. Phys. 28, 134.CrossRefGoogle Scholar
Galeev, A. A. & Karpman, V. I. 1963 Soviet Phys. JETP 17, 403.Google Scholar
Hasselmann, .K. 1962 J. Fluid Mech. 12, 481.CrossRefGoogle Scholar
Litvak, M. M. 1960 Avco Everett Research Rep. no. 92.Google Scholar
Newell, A. C. 1968 Rev. Geophys. 6, 1.CrossRefGoogle Scholar
Sandri, G. 1963 Ann. Phys. 24, 332, 380.CrossRefGoogle Scholar
Sandri, G. 1965 Nuovo Cimento 36, 67.CrossRefGoogle Scholar