Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-27T20:52:08.440Z Has data issue: false hasContentIssue false
  • English
  • Français

Propagation of nonlinear waves in a plasma in a magnetic field

Published online by Cambridge University Press:  13 March 2009

Jeffrey P. Freidberg
Jeffrey P. Freidberg
Affiliation:
Courant Institute of Mathematical Sciences, New York University
Get access Rights & Permissions [Opens in a new window]

Abstract

The propagation of nonlinear electromagnetic waves in a plasma is investigated by seeking travelling wave solutions to the macroscopic plasma equations. The model considered is that of a warm, anisotropic electron plasma in a magnetic field, in which the waves are allowed to propagate at any angle with respect to the magnetic field. A nonlinear dispersion relation is obtained which is valid for frequencies sufficiently close to the resonant frequencies. Travelling wave solutions are found for all amplitudes for which the local density remains positive. Also in sufficiently anisotropic plasmas the nature (i.e. propagating or cut-off) of one of the resonant waves can depend upon the amplitude.

Type
Research Article
Information
Journal of Plasma Physics , Volume 2 , Issue 2 , June 1968 , pp. 105 - 118
Copyright
Copyright © Cambridge University Press 1968

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

Alloucherie, Y. J. 1967 J. Plasma Physics 1, 55.Google Scholar
Bernstein, I. B., Greene, J. M. & Kruskal, M. D. 1957 Phys. Rev. 103, 546.CrossRefGoogle Scholar
Bernstein, I. B. & Trehan, S. K. 1960 Nucl. Fusion 1, 3.CrossRefGoogle Scholar
Bogoliusov, N. & Mitropolskii, Y. A. 1961 Asymptotic Methods in the Theory of Nonlinear Oscillations. New York: Gordon and Breach.Google Scholar
Briggs, R. J. 1964 Electron Stream Interaction with Plasmas. Cambridge, Mass.: MIT Press.Google Scholar
Buneman, O. 1959 Phys. Rev. 115, 503.Google Scholar
Dawson, J. M. 1959 Phys. Rev. 113, 383.Google Scholar
Fried, B. D. & Ossakow, S. 1966 Bull. Am. Phys. Soc. 11, 716.Google Scholar
Freidberg, J. P. 1967 Phys. Fluids 10, 176.Google Scholar
Gibbons, J.J. & Hartle, R. E. 1967 Phys. Fluids 10, 189.Google Scholar
Kalman, G. 1960 Ann. Phys. 10, 29.CrossRefGoogle Scholar
Krylov, N. & Bogoliubov, N. 1947 Introduction to Nonlinear Mechanics, trans. by Lefshetz., S.Princeton University Press.Google Scholar
Lutomirski, R. F. & Sudan, R. N. 1966 Phys. Rev. 147, 156.Google Scholar
Minorsky, N. 1962 Nonlinear Oscillations. Princeton, New Jersey: D. Van Nostrand.Google Scholar
Nekrasov, F. M. 1963 Sov. Phys. Tech. Phys. 8, 581.Google Scholar
Stix, T. 1962 Theory of Plasma Waves. New York: McGraw-Hill.Google Scholar