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An action principle for the Vlasov equation and associated Lie perturbation equations. Part 2. The Vlasov–Maxwell system

Published online by Cambridge University Press:  13 March 2009

Jonas Larsson
Jonas Larsson
Affiliation:
Department of Plasma Physics, Umeå University, S-901 87 Umeå, Sweden, and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720, U.S.A.
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Abstract

An action principle for the Vlasov–Maxwell system in Eulerian field variables is presented. Thus the (extended) particle distribution function appears as one of the fields to be freely varied in the action. The Hamiltonian structures of the Vlasov–Maxwell equations and of the reduced systems associated with small-ampliltude perturbation calculations are easily obtained. Previous results for the linearized Vlasov–Maxwell system are generalized. We find the Hermitian structure also when the background is time-dependent, and furthermore we may now also include the case of non-Hamiltonian perturbations within the Hamiltonian-Hermitian context. The action principle for the Vlasov–Maxwell system appears to be suitable for the derivation of reduced dynamical equations by expanding the action in various small parameters.

Type
Research Article
Information
Journal of Plasma Physics , Volume 49 , Issue 2 , April 1993 , pp. 255 - 270
Copyright
Copyright © Cambridge University Press 1993

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References

REFERENCES

Brizard, A. 1992 Phys. Lett. 168A, 357.CrossRefGoogle Scholar
Brizard, A. J., Cook, D. R. & Kaufman, A. N. 1993 Phys. Rev. Lett. 70, 521.CrossRefGoogle Scholar
ElvsÉn, R. & Larsson, J. 1992 Physica Scripta 46, 365.CrossRefGoogle Scholar
ElvsÉn, R. & Larsson, J. 1993 An action principle for the relativistic Vlasov–Maxwell system. Physica Scripta. 47, 571.Google Scholar
Iwinski, R. & Turski, L. A. 1976 Lett. Appl. Engng Sci. 4, 179.Google Scholar
Kaufman, A. N. 1991 Nonlinear and Chaotic Phenomena in Plasmas, Solids and Fluids (ed. Rozmus, W. & Tuszynski, J. A.). World Scientific.Google Scholar
Larsson, J. 1991 Phys. Rev. Lett. 66, 1466.CrossRefGoogle Scholar
Larsson, J. 1992 J. Plasma Phys. 48, 13.CrossRefGoogle Scholar
Marsden, J. E. & Weinstein, A. 1982 D 4, 394.Google Scholar
Morrison, P. J. 1980 Phys. Lett. 80A, 383.CrossRefGoogle Scholar
Morrison, P. J. & Pfirsch, D. 1990 Phys. Fluids 10, 1105.CrossRefGoogle Scholar
Weinstein, A. & Morrison, P. J. 1981 Phys. Lett. 86A, 235.CrossRefGoogle Scholar
Ye, H. & Morrison, P. J. 1992 Phys. Fluids B 4, 771.CrossRefGoogle Scholar
Ye, H., Morrison, P. J. & Crawford, J. D. 1991 Phys. Lett. 156A, 96.CrossRefGoogle Scholar