Hostname: page-component-848d4c4894-cjp7w Total loading time: 0 Render date: 2024-06-28T00:06:41.856Z Has data issue: false hasContentIssue false
  • English
  • Français

Soliton formation in magnetized Vlasov plasmas

Published online by Cambridge University Press:  13 March 2009

J. G. Turner  and
T. J. M. Boyd
J. G. Turner
Affiliation:
School of Engineering and Science, Polytechnic of Central London, 115 New Cavendish Street, London W1M 8JS
T. J. M. Boyd
Affiliation:
University College of North Wales, University of Wales, Bangor LL57 2UW, Wales
Get access Rights & Permissions [Opens in a new window]

Abstract

Soliton formation at the upper hybrid frequency has been discussed recently on the basis of warm two-fluid theory. In this paper we report the results of a reductive perturbation theory analysis of the Vlasov equation describing the nonlinear modulation of electrostatic waves in a warm magnetized plasma. This approach allows a treatment of soliton formation with scale lengths of the order of, or less than, the electron Larmor radius rL for both upper hybrid and Bernstein waves. A three-dimensional generalized nonlinear Schrödinger equation has been found. Contributions to the nonlinear frequency shift derive from three distinct processes. One contribution describes the generation of the second harmonic governed by (ω + ω) → 2w where ω is the frequency of the electrostatic carrier; a second arises from the self-interaction between the high-frequency waves (ω + ω → ω + ω) while the third contribution describes the nonlinear coupling between the carrier and the slow background plasma motion.

Propagation orthogonal to the magnetic field is studied and leads to a simplified nonlinear Schrodinger equation with cubic nonlinearity, predicting soliton formation at the upper hybrid and cyclotron harmonic frequencies. Expressions for the nonlinear frequency shift coefficient are presented for the upper hybrid and Bernstein modes in the low temperature limit and the relative strengths of the three competing nonlinear processes are compared. For krL ≥ 1·0, numerical analysis shows the dominant nonlinearity to be that arising from the nonlinear wave-particle interaction. The stability of the soliton solution is determined by the relative signs of the dispersion and the nonlinear frequency shift coefficient. Some properties of upper hybrid and Bernstein solitons are examined. In particular the variation of the normalized dispersion and nonlinear frequency shift coefficient with the basic plasma parameters (krL)2 and (ωpe/Ω, is presented, where (ope, fi are the electron plasma frequency and electron gyrofrequency respectively. Regions of instability are identified for both upper hybrid and Bernstein modes. The connection between reductive perturbation theory and previous warm fluid theories is also established.

Type
Research Article
Information
Journal of Plasma Physics , Volume 22 , Issue 1 , August 1979 , pp. 121 - 147
Copyright
Copyright © Cambridge University Press 1979

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.)

References

REFERENCES

Asano, N., Taniuti, T. & Yajima, N. 1969 J. Math. Phys. 10, 2020.CrossRefGoogle Scholar
Boyn, T. J. M. & Turner, J. G. 1972 J. Phys. A 5, 881.Google Scholar
Buti, B. 1977 Phys. Rev. Lett. 38, 498.CrossRefGoogle Scholar
Dewar, R. L. 1972 J. Plasma Phys. 7, 267.CrossRefGoogle Scholar
Dysthe, K. B. & Pécseli, H. L. 1977 Plasma Phys. 19, 931.CrossRefGoogle Scholar
Evans-Jones, O. 1978 M.Sc. Thesis, University of Wales.Google Scholar
Fried, B. D. & Ichikawa, Y. H. 1973 J. Phys. Soc. (Japan), 34, 1073.CrossRefGoogle Scholar
Gibbons, J., Thornhill, S. G., Wardrop, M. J. & Ter, Haar D. 1977 J. Plasma Phys. 17, 153.CrossRefGoogle Scholar
Grek, B. & Porkolab, M. 1973 Phys. Rev. Lett. 30, 836.CrossRefGoogle Scholar
Ichikawa, Y. H., Imamura, T. & Taniuti, T. 1972 J. Phys. Soc. (Japan), 33, 189.CrossRefGoogle Scholar
Ichikawa, Y. H. & Kako, M. 1974 Supp. Prog. Theor. Phys. 55, 233.CrossRefGoogle Scholar
Kakutani, T. and & Sugimoto, N. 1974 Phys. Fluids, 17, 1617.CrossRefGoogle Scholar
Karpman, V. I. & Krushkal, E. M. 1969 Soviet Phys. JETP, 28, 277.Google Scholar
Kaufman, A. N. & Stenflo, L. 1975 Physica Scripta, 11, 269.CrossRefGoogle Scholar
Kono, M. & Sanuki, H. 1972 J. Phys. Soc. (Japan), 33, 1731.CrossRefGoogle Scholar
Morales, G. J. & Lee, Y. C. 1974 Phys. Rev. Lett. 33, 1016.CrossRefGoogle Scholar
Porkolab, M. & Goldman, M. V. 1976 Phys. Fluids, 19, 872.CrossRefGoogle Scholar
Raven, A., Willi, O. & Rumsby, P. T. 1978 Phys. Rev. Lett. 41, 554.CrossRefGoogle Scholar
Shimizu, K. & Ichikawa, Y. H. 1972 J. Phys. Soc. (Japan), 33, 789.CrossRefGoogle Scholar
Stamper, J. A. & Ripin, B. H. 1975 Phys. Rev. Lett. 34, 138.CrossRefGoogle Scholar
Stamper, J. A., McLean, E. A. & Ripin, B. H. 1978 Phys. Rev. Lett. 40, 1177.CrossRefGoogle Scholar
Taniuti, T. & Yajima, N. 1969 J. Math. Phys. 10, 1369.CrossRefGoogle Scholar
Turner, J. G. & Boyd, T. J. M. 1977 Paper presented at Third International Congress on Waves and Instabilities in Plasmas, Palaiseau.Google Scholar
Yajima, N. & Outi, A. 1971 Prog. Theor. Phys. 45, 1997.CrossRefGoogle Scholar
Yu, M. Y. & Shukla, P. K. 1977 Plasma Phys. 19, 889.CrossRefGoogle Scholar
Zakharov, V. E. & Shabat, A. B. 1972 Soviet Phys. JETP, 34, 62.Google Scholar