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Bifurcation of BGK waves in a plasma of cold ions and electrons

Published online by Cambridge University Press:  13 March 2009

L. Hannibal ,
E. Rebhan  and
C. Kielhorn
L. Hannibal
Affiliation:
Institut für Theoretisehe Physik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany
E. Rebhan
Affiliation:
Institut für Theoretisehe Physik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany
C. Kielhorn
Affiliation:
Institut für Theoretisehe Physik, Heinrich-Heine-Universität Düsseldorf, Universitätsstr. 1, D-40225 Düsseldorf, Germany
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Abstract

For the simple model of cold electrons streaming against cold ions the complete set of nonlinear stationary waves is expressed in terms of elliptic functions. The conditions for their dynamical connection to a uniform neutral plasma state are taken into account, and the conditions for the neglect of the magnetic field are analysed. The range of existence of stationary waves is found to be confined to the stable regime of the two-stream instability, but covers only part of it. All nonlinear BGK waves that are found within the limits of the model can be shown to bifurcate from the two-stream instability, some of them also exhibiting secondary and further bifurcations. As an exceptional case, all bifurcations can be treated exactly. Close to the linear regime, all nonlinear modes turn out to be unstable. The corresponding instability is caused by a wave decay that transports energy from low to high wavenumbers of the Fourier modes constituting the wave. From the two-stream solutions four- stream solutions with exactly vanishing magnetic field are derived.

Type
Research Article
Information
Journal of Plasma Physics , Volume 52 , Issue 1 , August 1994 , pp. 1 - 22
Copyright
Copyright © Cambridge University Press 1994

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References

REFERENCES

Akheizer, A. I. & Lyubarskizs, G. YA. 1951 Dokl. Akad. Nauk SSSR 80, 193.Google Scholar
Bernstein, I. B., Greene, J. M. & Kruskal, M. D. 1957 Phys. Rev. 108, 546.CrossRefGoogle Scholar
Bohm, D. & Gross, E. P. 1949 Phys. Rev. 75, 1851, 1864.CrossRefGoogle Scholar
Davidson, R. C. 1960 Methods in Nonlinear Plasma Theory. Academic.Google Scholar
Dawson, J. M. 1959 Phys. Rev. 113, 383.CrossRefGoogle Scholar
Holloway, J. P. & Dorning, J. J. 1991 Phys. Rev. A 44, 3856.CrossRefGoogle Scholar
Jackson, E. A. 1960 Phys. Fluids 3, 786.CrossRefGoogle Scholar
Leven, R. & Müller, W. F. 1974 Wiss. Zeitschr. Ernst-Moritz-Arndt-Universität.Google Scholar
Pierce, J. R. 1948 J. Appl. Phys. 19, 231.CrossRefGoogle Scholar
Rebhan, E. 1983 Proceedings of 16th Conference on Phenomena in Ionized Gases, Düsseldorf (ed. W. Bötticher, H. Wenk & E. Schulz-Guide), p. 688. Organising Committee ICPIG XVI.Google Scholar
Schamel, H. 1986 Phys. Rep. 140, 161.CrossRefGoogle Scholar