Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-28T12:37:39.634Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

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, N. I. 1962 The Calculus of Variations. Blaisdell.Google Scholar
Atherton, R. W., & Homsy, G. M. 1975 Stud. Appl. Math. 54, 31.CrossRefGoogle Scholar
Courant, R., & Hilbert, D. 1953 Methods of Mathematical Physics, vol. 1. Interscience.Google Scholar
Davis, D. R. 1929 Bull. Amer. Math. Soc. 35, 371.CrossRefGoogle Scholar
Dorman, G. 1969 J. Plasma Phys. 3, 387.Google Scholar
Douglas, J. 1941 Trans. Amer. Math. Soc. 50, 71.CrossRefGoogle Scholar
Funk, P. 1970 Variationsrechnung und ihre Anwendung in Physik und Technik (2nd edn). Springer.Google Scholar
Galloway, J. J., & Crawford, F. W. 1970 Proc. 4th European Conf. on Controlled Fusion and Plasma Physics, Rome (CNEN), p. 161.Google Scholar
Goldstein, H. 1950 Classical Mechanics. Addison-Wesley.Google Scholar
Jacobi, C. G. J. 1837 J. Math. 17, 63.Google Scholar
Kürsohák, J. 1906 Mathematische Annalen, 60, 157.CrossRefGoogle Scholar
LaPaz, L. 1930 Trans. Amer. Math. Soc. 32, 509.Google Scholar
Lamb, H. 1930 Hydrodynamics (5th edn). Cambridge University Press.Google Scholar
Parker, J. V., Nickel, J. C., & Gould, R. W. 1964 Phys. Fluids, 7, 1489.Google Scholar
Penfield, P., & Haus, H. A. 1967 Electromagnetics of Moving Media. M.I.T.Google Scholar
Peng, Y. M., & Crawford, F. W. 1975 J. Plasma Phys. 13, 283.CrossRefGoogle Scholar
Tonti, E. 1969a Acad. Roy. Belg. Bull. Cl. Sciences, 55, 137.Google Scholar
Tonti, E. 1969b Acad. Roy. Belg. Bull. Cl. Sciences, 55, 262.Google Scholar
Van der Vaart, H. R. 1967 Amer. J. Phys. 35, 419.Google Scholar
Vainberg, M. M. 1964 Variational Methods for the Study of Nonlinear Operators. Holden Day.Google Scholar
Whitham, G. B. 1965 J. Fluid Mech. 22, 273.CrossRefGoogle Scholar