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Renormalization method and singularities in the theory of Langmuir turbulence

Published online by Cambridge University Press:  13 March 2009

G. Pelletier
G. Pelletier
Affiliation:
Laboratoire de Physique des Plasmas, Equipe de Recherche Associée au C.N.R.S., Université de Grenoble I
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Abstract

The method of renormalization, using propagators and diagrams, is recalled with enough mathematical details to be read and used by a non-specialist. The Markovian models are discussed and applied to plasma turbulence. The physical meaning of the diagrams is exhibited. In addition to the usual resonance broadening, an improved renormalization is set out, including broadening of the nonlinear resonance with a beat wave by induced scattering. We emphasize this improved renormalization. In the case of Langmuir turbulence, it removes difficulties arising at the group velocity, and enhances large-scale induced-scattering diffusion.

Type
Research Article
Information
Journal of Plasma Physics , Volume 18 , Issue 1 , August 1977 , pp. 49 - 76
Copyright
Copyright © Cambridge University Press 1977

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References

REFERENCES

Abrikosov, A. A., Gorkov, L. P. & Dyaloshinski, I. E. 1963 Methods of Quantum Field Theory in Statistical Physics, p. 48. Prentice-Hall.Google Scholar
Balescu, R. 1963 Statistical Mechanics of Charged Particles. Interscience.Google Scholar
Birmingham, T. J. & Bornatici, M. 1972 Phys. Fluids, 15, 1778.CrossRefGoogle Scholar
Davidson, R. 1972 Methods in Nonlinear Plasma Theory. Academic.Google Scholar
Duk-in-choi, , & Horton, W. 1974 Phys. Fluids, 17, 2048.CrossRefGoogle Scholar
Dupree, Th. 1966 Phys. Fluids, 9, 1773.CrossRefGoogle Scholar
Dupree, Th. 1972 Phys. Fluids, 15, 334.CrossRefGoogle Scholar
Engleman, F. & Zampaglione, V. 1969 Il Nuovo Cimento, 62 B, 43.CrossRefGoogle Scholar
Fisch, N. J. & Bers, A. 1975 Phys. Rev. Lett. 35, 373.CrossRefGoogle Scholar
Fox, R. F. 1974 J. Math. Phys. 15, 1479.CrossRefGoogle Scholar
Frisch, U. 1966 Annales d'Astrophysique, 29, 645.Google Scholar
Gervais, F., Olivain, J., Quemeneur, A. & Matthieussent, G. 1976 Phys. Fluids. (To be published.)Google Scholar
Hasegawa, A. 1975 Plasma Instabilities and Non linear Effects. Springer.CrossRefGoogle Scholar
Hinton, F. L. & Oberman, C. 1968 Phys. Fluids, 11, 1982.CrossRefGoogle Scholar
Jones, F. C. & Birmingham, T. J. 1975 Plasma Phys. 17, 15.CrossRefGoogle Scholar
Kadomtsev, B. B. 1965 Plasma Turbulence. Academic.Google Scholar
Kono, M. & Ichikawa, Y. H. 1973 Prog. Theor. Phys. 49, 754.CrossRefGoogle Scholar
Kubo, R. 1962 J. Phys. Soc. Japan, 17, 1100.CrossRefGoogle Scholar
Kubo, R. 1963 J. Math. Phys. 4, 174.CrossRefGoogle Scholar
Misguisch, J. H. & Balescu, R. 1975 J. Plasma Phys. 13, 385.CrossRefGoogle Scholar
Mori, H. 1965 Prog. Theor. Phys. 33, 423.CrossRefGoogle Scholar
Pelletier, G. & Pomot, C. 1975 a J. Plasma Phys. 14, 153.CrossRefGoogle Scholar
Pelletier, .G & Pomot, C. 1975 b J. Plasma Phys. 14, 491.CrossRefGoogle Scholar
Rolland, P. 1976 J. Plasma Phys. 15, 57CrossRefGoogle Scholar
Rogister, A. & Oberman, C. 1968 J. Plasma Phys. 2, 33.CrossRefGoogle Scholar
Rudakov, L. I. & Tsytovich, V. N. 1971 Plasma Phys. 13, 213.CrossRefGoogle Scholar
Thompson, J. J. & Benford, G. 1973 a J. Math. Phys. 14, 531.CrossRefGoogle Scholar
Thompson, J. J. & Benford, G. 1973 b Phys. Fluids, 16, 1505.CrossRefGoogle Scholar
Tsytovich, V. N. 1972 An Introduction to the Theory of Plasma Turbulence. Pergamon.Google Scholar
Vaclavik, J. 1975 J. Plasma Phys. 14, 315.CrossRefGoogle Scholar
Wax, N. 1954 Noise and Stochastic Processes. Dover.Google Scholar
Weinstock, J. 1969 Phys. Fluids, 12, 1045.CrossRefGoogle Scholar
Wong, E. 1971 Stochastic Processes in Information and Dynamical Systems. McGraw Hill.Google Scholar
Yosida, K. 1965 Functional Analysis. Springer.Google Scholar
Zwanzig, R. 1964 Physica, 30, 1109.CrossRefGoogle Scholar