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Lagrangian density for collisional plasma*

Published online by Cambridge University Press:  13 March 2009

Y. K. M. Peng
Y. K. M. Peng
Affiliation:
Institute for Plasma Research, Stanford University
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Abstract

For the purpose of deriving appropriate Lagrangians for equations in plasma physics that include effects of energy loss, the paper examines the inverse problem of the calculus of variations for systems of first and second order quasi- linear partial differential equations. This results in convenient forms of the sufficient conditions, under which the given differential equations are Euler Lagrange equations of a Lagrangian. These conditions are then applied, to determine the necessary transformation that converts equations, apparently not already in it, into Euler—Lagrange form. The appropriate Lagrangian for a warm collisional plasma is obtained. As an additional example, the Lagrangian is derived for a resistive transmission line.

Type
Research Article
Information
Journal of Plasma Physics , Volume 15 , Issue 1 , February 1976 , pp. 165 - 174
Copyright
Copyright © Cambridge University Press 1976

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