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Non-linear coupling of waves in a magnetized plasma with particle drift motions

Published online by Cambridge University Press:  13 March 2009

H. wilhelmsson
H. wilhelmsson
Affiliation:
Laboratori Gas lonizzati (Associazione EURATOM-CNEN) Frascati, Rome, Italy
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Abstract

We study non-linear interaction between three monochromatic waves which propagate parallel to the direction of a magnetic field in a plasma. The approach to the problem is hydromagnetic, including temperature effects, and the method of solution is that of coupled mode theory. In particular drift motions of the particles along the magnetic field are considered taking into account relativistic effects. The interaction of two transverse waves and one longitudinal wave is treated as well as that of three longitudinal waves. Besides, the case of two longitudinal waves and one perpendicular wave has been studied in some detail assuming the latter to have a long wavelength.

The present paper represents a generalization of the problem of three-wave interaction in a plasma to situations more complex than have been treated before. The most essential limitation consists in the assumptions made for the directions of propagation of the waves.

Type
Research Article
Information
Journal of Plasma Physics , Volume 3 , Issue 2 , May 1969 , pp. 215 - 226
Copyright
Copyright © Cambridge University Press 1969

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References

REFERENCES

Armstrong, J. A., Bloembergen, N., Ducuing, N. & Pershan, P. S. 1962 Phys. Rev. 127, 1918.CrossRefGoogle Scholar
Bogoliubov, N. & Mitropolskii, Y. A. 1961 Asymptotic Methods in the Theory of Nonlinear Oscillations. New York: Gordon and Breach.Google Scholar
Bornattici, M., Cavliere, A. & Engelmann, F. 1968 Report LGI 68/22, Laboratori Gas Ionizzati, Frascati, Rome.Google Scholar
Engelmann, F. & Wilhelmsson, H. 1969 Z. Naturforsch. 24 a, 206.Google Scholar
Frieman, E. A. 1963 J. Math. Phys. 4, 410.CrossRefGoogle Scholar
Hirshfield, J. L. 1968 (Private communication.)Google Scholar
Jarmén, A., Stenflo, L., Wilhelmsson, H. & Engelmann, F. 1969 Phys. Letters A (in press).Google Scholar
Knorr, G. 1968 Phys. Fluids, 11, 885.CrossRefGoogle Scholar
Krylov, N. & Bogoliubov, M. 1947 Introduction to Nonlinear Mechanics, translated by Lefshetz, S.. Princeton University Press.Google Scholar
Louisell, W. H. 1960 Coupled Mode and Parametric Electronics. New York: John Wiley and Sons, Inc.Google Scholar
Montgomery, D. 1965 Physica 31, 693.CrossRefGoogle Scholar
Ssgdeev, R. Z. & Galeev, A. A. 1966 Lectures on the Non-Linear Theory of Plasma. Trieste: Intern. Cen. f. Theor. Phys. (Unpublished lecture).Google Scholar
Sjölund, A. & Stenflo, L. 1967 J. Appl. Phys. 38, 2676; Physica 34, 567; Appl. Phys. Lett. 10, 201; Z. Phys. 204, 211.CrossRefGoogle Scholar
Stenflo, L. 1968 Plasma Phys. 10, 551.CrossRefGoogle Scholar
Stenflo, L. 1969 J. Atmosph. Terr. Phys. 31, 197.Google Scholar
Sugihara, R. 1968 Phys. Fluids 11, 178.Google Scholar
Tsytovich, V. N. 1967 Sov. Phys. Uspekhi 9, 805.CrossRefGoogle Scholar
Vedenov, A. A. 1966 Theory of Turbulent Plasma, translated by Lerman, Z., Jerusalem: Israel Program for Scientific translations.Google Scholar
Wilhelmsson, H. 1965 Proc. Int. Conf. London, I.E.E. Conf. Publ. no. 13; Report from Research Institute for National Defence Stockholm (FOA 2) A 2382–290.Google Scholar