Hostname: page-component-5f56664f6-w4vgn Total loading time: 0 Render date: 2025-05-07T09:35:08.283Z Has data issue: false hasContentIssue false
  • English
  • Français

On the theory of Langmuir solitons†

Published online by Cambridge University Press:  13 March 2009

J. Gibbons ,
S. G. Thornhill ,
M. J. Wardrop  and
D. Ter Haar
J. Gibbons
Affiliation:
Department of Theoretical Physics, 12 Parks Road, Oxford OX1 3PQ, Great Britain
S. G. Thornhill
Affiliation:
Department of Theoretical Physics, 12 Parks Road, Oxford OX1 3PQ, Great Britain
M. J. Wardrop
Affiliation:
Department of Theoretical Physics, 12 Parks Road, Oxford OX1 3PQ, Great Britain
D. Ter Haar
Affiliation:
Department of Theoretical Physics, 12 Parks Road, Oxford OX1 3PQ, Great Britain
Get access Rights & Permissions [Opens in a new window]

Abstract

We find a Lagrangian density from which the equations of motion for the Lang-muir solitons follow in the usual way. We show how this Lagrangian leads to the usual conservation laws. For the one-dimensional case we discuss how a consideration of these conservation laws can help us to understand some of the results obtained in numerical experiments on the behaviour of a strongly turbulent plasma. We point out that the situation in the three-dimensional case may be fundamentally different, and we discuss near-sonic perturbations and Karpman's treatment of these.

Type
Research Article
Information
Journal of Plasma Physics , Volume 17 , Issue 2 , April 1977 , pp. 153 - 170
Copyright
Copyright © Cambridge University Press 1977

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Abdulloev, Kh. D., Bogolyubskij, I. L. & Makhan'kov, V. G. 1975 Nucl. Fusion, 15, 21.CrossRefGoogle Scholar
Bogolyubskij, I. L. & Makhan'kov, V. G. 1975 Dubna preprint E4–9425.Google Scholar
Degtyarev, L. M., Makhan'kov, V. G. & Rudakov, L. I. 1975 Sov. Phys. JETP, 40,264.Google Scholar
Gelfand, I. M. & Fomin, S. V. 1963 Calculus of Variations. Prentice-Hall.Google Scholar
Gibbons, J. & Ter Haar, D. 1976 Oxford preprint 12/76.Google Scholar
Ter Haar, D. 1971 Elements of Hamiltonian Mechanics. Pergamon.Google Scholar
Ter Haar, D. 1975 Contribution to the MHD Instabilities Meeting, Bilthoven, Nether. lands, May 1975; Oxford preprint 53/75.Google Scholar
Kaplan, S. A. & Tsytovich, V. N. 1973 Plasma Astrophysics. Pergamon.Google Scholar
Karpman, V. I. 1975 a Non-Linear Waves in Dispersive Media. Pergamon.CrossRefGoogle Scholar
Karpman, V. I. 1975 b Physica Scripta, 11, 263.CrossRefGoogle Scholar
Kingsep, A. S., Rudakov, L. I. & Sudan, R. N. 1973 Phys. Rev. Lett. 31, 1482.CrossRefGoogle Scholar
Makhn'kov, V. G. 1974 Dubna preprint E5–8389.CrossRefGoogle Scholar
Petviashvili, V. I. 1975 Sov. J. Plasma Phys. 1, 15.Google Scholar
Scott, A. C., Chu, F. Y. F. & McLaughlin, D. W. 1973 Proc. IEEE, 61, 1443.CrossRefGoogle Scholar
Thornhill, S. G. & Ter Haar, D. 1975 Oxford preprrnt 80/75.Google Scholar
Tsytovich, V. N. 1976 Physica, 82BC, 141, 191.Google Scholar
Vedenov, A. A., Gordeev, A. V. & Rudakov, L. I. 1966 Plasma Phys. 9, 719.CrossRefGoogle Scholar
Vedenov, A. A. & Rudakov, L. I. 1965 Sov. Phys. Doklady, 9, 1073.Google Scholar
Wilcox, J. Z. & Wilcox, T. J. 1975 Phys. Rev. Let. 34, 1160.CrossRefGoogle Scholar
Yajima, N. & Oikawa, M. 1976 Formation and interaction of sonic-Langmuir solitons. Inverse scattering method. Preprint. Research Institute for Applied Mechanics, Kyushu University, Fukuoka, Japan.CrossRefGoogle Scholar
Zakharov, V. E. 1972 Sov. Phys. JETP, 35, 908.Google Scholar
Zakharov, V. E. & Synakh, V. S. 1976 Soy. Phys. JETP, 41, 465.Google Scholar