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Lagrangian approach to non-linear wave interactions in a warm plasma

Published online by Cambridge University Press:  13 March 2009

J. J. Galloway  and
H. Kim
J. J. Galloway
Affiliation:
Institute for Plasma Research, Stanford University
H. Kim
Affiliation:
Institute for Plasma Research, Stanford University
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Extract

In this paper, the coupled-mode equations and coupling coefficients for three-wave interaction are derived by a Lagrangian approach for a general medium. A derivation of the Low Lagrangian for a warm plasma is then given, which avoids certain problems associated with the original analysis. An application of the Lagrangian method is made to interaction between collinearly-propagating electrostatic waves, and a coupling coefficient is derived which agrees with a previous result obtained by direct expansion of the non-linear equations. The paper serves primarily to present and demonstrate a conceptually useful and efficient theoretical approach to non-linear wave interactions.

Type
Articles
Information
Journal of Plasma Physics , Volume 6 , Issue 1 , August 1971 , pp. 53 - 72
Copyright
Copyright © Cambridge University Press 1971

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References

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