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Re-normalized quasi-linear approximation of plasma turbulence: Part 1. Modification of the Weinstock weak-coupling limit

Published online by Cambridge University Press:  13 March 2009

J. H. Misguich  and
R. Balescu
J. H. Misguich
Affiliation:
Association Euratom – CEA sur la Fusion Département de Physique du Plasma et de la Fusion Contrôlée Centre d'Etudes Nucléaires, Boîte Postale no. 6, 92260 Fontenay-aux-Roses, France
R. Balescu
Affiliation:
Association Euratom-Etat Beige, Faculté des Sciences, Université Libre de Bruxelles, 1050 Bruxelles
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Abstract

A re-normalized expansion is presented for the solution of the fluctuating Vlasov equation for turbulent plasmas. Its first term can be identified with the Weinstock result in the weak-coupling approximation. The use of time-ordering operators allows one to solve the Weinstock UA evolution operator explicitly. Detailed results are given for the weak-coupling approximation, presented here as a simple re-normalization of the quasi-linear theory. Results of Weinstock and Birmingham & Bornatici, concerning the frequency shift, resonance broadening and Dupree damping appear to be deeply modified by similar corrective terms. These arise from a consistent handling of expressions involving non-commuting operators.

Type
Research Article
Information
Journal of Plasma Physics , Volume 13 , Issue 3 , June 1975 , pp. 385 - 417
Copyright
Copyright © Cambridge University Press 1975

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References

REFERENCES

Backus, G. 1960 J. Math. Phys. 1, 178.CrossRefGoogle Scholar
Baker, H. F. 1901 Proc. London Math. Soc. 34, 91.CrossRefGoogle Scholar
Baker, H. F. 1905 Proc. London Math. Soc. 3, 24.CrossRefGoogle Scholar
Balescu, R. 1963 Statistical Mechanics of Charged Particles. Interscience.Google Scholar
Balescu, R. & Misguich, J. H. 1973 a Rep. EUR. CEA. FC, 691.Google Scholar
Balescu, R. & Misguicu, J. H. 1973 b Rep. EUR. CEA. FC, 718.Google Scholar
Balescu, R. & Misguich, J. H. 1975 a J. Plasma Phys. 13, 33.CrossRefGoogle Scholar
Balescu, R. & Misguich, J. H. 1975 b J. Plasma Phys. 13, 53.CrossRefGoogle Scholar
Benford, G. & Thomson, J. J. 1972 Phys. Fluids, 15, 1496.CrossRefGoogle Scholar
Birmingham, T. J. & Bornatici, M. 1972 a Phys. Fluids, 15, 1778.CrossRefGoogle Scholar
Birmingham, T. J. & Bornatici, M. 1972 b Phys. Fluids, 15, 1785.CrossRefGoogle Scholar
Campbell, J. E. 1901 Proc. London Math. Soc. 33, 285.Google Scholar
Davidson, R. C. 1972 Methods in Nonlinear Plasma Theory. Academic.Google Scholar
Dupree, T. H. 1966 Phys. Fluids, 9, 1773.CrossRefGoogle Scholar
Fer, F. 1958 Bull. C1asse des Sci. Acad. Roy. Belgique, 44, 818.Google Scholar
Frisch, U. 1966 Annales d'Astrophysique, 29, 645.Google Scholar
Hausdorff, F. 1906. Ber. Verh. Saechs. Akad. Wiss. Leipsig, Math. Phys. Kl. 58, 19.Google Scholar
Kadomtsev, B. B. 1965 Plasma Turbulence. Academic.Google Scholar
Kono, M. & Ichikawa, Y. H. 1973 Prog. Theor. Phys. 49, 754.CrossRefGoogle Scholar
Kraichnan, R. H. 1972 Proc. 6th IUPAP Conf. on Stat. Mech. Chicago (ed. Rice, S. A., Freed, K. F. and Light, J. C.), p. 201. University of Chicago Press.Google Scholar
Magnus, W. 1954 Comm. Pure Appl. Math. 7, 649.CrossRefGoogle Scholar
Mima, K. 1973 J. Phys. Soc. Japan, 34, 1620.CrossRefGoogle Scholar
Misguich, J. H. & Balescu, R. 1975 a J. Plasma Phys. (To be published.)Google Scholar
Misguich, J. H. & Balescu, R. 1975 b J. Plasma Phys. (To be published.)Google Scholar
Nishikawa, K. 1966 Prog. Theor. Phys. 36, 193.CrossRefGoogle Scholar
Orszag, S. A. & Kraichnan, R. H. 1967 Phys. Fluids, 10, 1720.CrossRefGoogle Scholar
Pelletier, G. & Pomot, C. 1974 Colloque Ondes Sté Française de Physique, Grenoble.Google Scholar
Peyraud, N. & Coste, J. 1974 J. Plasma Phys. 12, 177.CrossRefGoogle Scholar
Rudakov, L. I. & Tsytovich, V. N. 1971 Plasma Phys. 13, 213.CrossRefGoogle Scholar
Tsytovich, V. N. 1973 Soviet Phys. Uspekhi, 15, 632.CrossRefGoogle Scholar
Thomson, J. J. & Benford, G. 1973a J. Math. Phys. 14, 531.CrossRefGoogle Scholar
Thomson, J. J. & Benford, G. 1973b Phys. Fluids, 16, 1505.CrossRefGoogle Scholar
Weinstock, J. 1969 Phys. Fluids, 12, 1045.CrossRefGoogle Scholar
Weinstock, J. 1970 Phys. Fluids, 13, 2308.CrossRefGoogle Scholar
Weinstock, J. 1972 Phys. Fluids, 15, 454.CrossRefGoogle Scholar
Wilcox, R. J. 1967 J. Math. Phys. 8, 962.CrossRefGoogle Scholar