Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-02-06T04:24:07.193Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear waves in a cold plasma by Lorentz transformation

Published online by Cambridge University Press:  13 March 2009

P. C. Clemmow
P. C. Clemmow
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

Wave propagation in a cold, collisionless, two-component plasma is analyzed by considering, first, the frame of reference in which the field has no space dependence, and then applying a Lorentz transformation to obtain a wave whose space-time dependence is a function of t — nz / c only, where n is a constant. Exact (nonlinear, relativistic) results for known special cases, and some others, are given; and it is shown that, when there is no ambient magnetic field, the general problem in essence reduces to the solution of one second-order, nonlinear differential equation. The desirabifity of introducing a free parameter representing a stream velocity in the direction of wave propagation is emphasized; and the significance of the choice of this parameter is discussed.

Type
Research Article
Information
Journal of Plasma Physics , Volume 12 , Issue 2 , October 1974 , pp. 297 - 317
Copyright
Copyright © Cambridge University Press 1974

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

Akhiezer, A. I. & Polovin, R. V. 1956 Soviet Phys. JETP, 3, 696.Google Scholar
Clemmow, P. C. & Dougherty, J. P. 1969 Electrodynamics of particles and plasmas. Addison-Wesley.Google Scholar
Kalman, G. 1960 Ann. Phys. (N.Y.) 10, 1.CrossRefGoogle Scholar
Lünow, W. 1968 Plasma Phys. 10, 973.CrossRefGoogle Scholar
Max, C. E. 1973 Phys. Fluids, 16, 1277.CrossRefGoogle Scholar
Sterger, A. D. & Woods, C. H. 1972 Phys. Rev. A 5, 1467.CrossRefGoogle Scholar
Stewart, P. 1973 Lettere al Nuovo Cimento, 7, 310.CrossRefGoogle Scholar
Winkles, B. B. & Eldridge, O. 1972 Phys. Fluids, 15, 1790.CrossRefGoogle Scholar