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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.
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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

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References

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