Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T06:40:42.848Z Has data issue: false hasContentIssue false
  • English
  • Français

Relativistic effects on non-linear waves in a cold collisionless plasma

Published online by Cambridge University Press:  13 March 2009

Yoshinori Inoue
Yoshinori Inoue
Affiliation:
Faculty of Engineering Science, Osaka University, Toyonaka, Osaka
Get access Rights & Permissions [Opens in a new window]

Abstract

Non-linear periodic waves propagating across a magnetic field are investigated, taking relativistic effects into account. The governing equations of the phenomena are taken to be the relativistic two-fluid plasma equations for a cold plasma together with Maxwell's equations. The analytical solution in the non-relativistic case was obtained by Adlam and Allen and others, a case where the quasi- neutral approximation is a good one and the inertia of the electrons plays an essential role in the dispersion effect of the plasma.

In contrast, the analysis of the relativistic waves shows that the quasi- neutral approximation becomes invalid and that the charge separation plays an essential role in the dispersion effect while the inertia of the electrons plays minor role only. Therefore the phenomena to be investigated have a length scale of the appropriately defined Debye distance (the ion Larmor radius), while in the non-relativistic case the width of the wave is of the order of the geometric mean of the Larmor radii of the electrons and of the ions. In the present case where the electron mass may be neglected, there exists an exact solution which is a good approximation for a real plasma. The solitary wave solution is found as the limiting case of infinite periodicity.

Type
Research Article
Information
Journal of Plasma Physics , Volume 3 , Issue 4 , December 1969 , pp. 661 - 671
Copyright
Copyright © Cambridge University Press 1969

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

Adlam, J. H. & Allen, J. E. 1958 Phil. Mag. 3, 448.CrossRefGoogle Scholar
Byrd, P. E. & Friedman, M. D. 1954 Handbook of Elliptic Integrals for Engineers and Physicists. Berlin: Springer Verlag.CrossRefGoogle Scholar
Davis, L., Lüst, R. & Schlüter, A. 1958 Z. Naturforsch. 13a, 916.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1961 The Classical Theory of Fields. New York: Pergamon Press.Google Scholar
Polovin, R. V. 1964 Nuclear Fusion 4.CrossRefGoogle Scholar