Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-29T18:00:51.617Z Has data issue: false hasContentIssue false
  • English
  • Français

Lagrangian methods in plasma dynamics. I. General theory of the method of the averaged Lagrangian

Published online by Cambridge University Press:  13 March 2009

J. P. Dougherty
J. P. Dougherty
Affiliation:
Department of Applied Physics and Information Science, University of California, San Diego, La Jolla, California 92037, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

Whitham's averaged Lagrangian method is used to yield a relativistically covariant formalism for wave packets in a weakly inhomogeneous (and time dependent) medium. Provided the physics of the medium can be based on a Lagrangian density, a procedure of expansion and averaging is available which gives separate Lagrangians for the dynamics of the background and of the waves. The Euler—Lagrange equations then give immediately the equations of motion for the background, including non-linear reaction of the waves, and the dispersion relation, equations for ray tracing, conservation of wave action and non-linear coupling coefficients, for the waves. Many of these results can be interpreted in an illuminating way by considering the corresponding expansion of the canonical four-dimensional stress tensor.

Type
Research Article
Information
Journal of Plasma Physics , Volume 4 , Issue 4 , December 1970 , pp. 761 - 785
Copyright
Copyright © Cambridge University Press 1970

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

Budden, K. G. 1961 Radio waves in the ionosphere. Cambridge University Press.Google Scholar
Cole, J. D. 1908 Perturbation Methods in Applied Mathematics. Blaisdell Publishing Company.Google Scholar
Harris, E. G. 1970 Classical plasma phenomena from a quantum mechanical viewpoint in Advances in Plasma Physics, Vol. III, Ed. Simon, A. and Thompson, W. B.. Wiley.Google Scholar
Kadomtsev, B. B. 1965 Plasma Turbulence. Academic Press.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1962 The Classical Theory of Fields, 2nd ed.Pergamon Press.Google Scholar
Sagdeev, R. Z. & Galeev, A. A. 1969 Non-Linear Plasma Theory. Benjamin, Inc.Google Scholar
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic Press.Google Scholar