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The Hamiltonian structure of the Maxwell-Vlasov equations

Marsden, Jerrold E. and Weinstein, Alan J. (1982) The Hamiltonian structure of the Maxwell-Vlasov equations. Physica D, 4 (3). pp. 394-406. ISSN 0167-2789. doi:10.1016/0167-2789(82)90043-4.

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Morrison [25] has observed that the Maxwell-Vlasov and Poisson-Vlasov equations for a collisionless plasma can be written in Hamiltonian form relative to a certain Poisson bracket. We derive another Poisson structure for these equations by using general methods of symplectic geometry. The main ingredients in our construction are the symplectic structure on the co-adjoint orbits for the group of canonical transformations, and the symplectic structure for the phase space of the electromagnetic field regarded as a gauge theory. Our Poisson bracket satisfies the Jacobi identity, whereas Morrison's does not [37]. Our construction also shows where canonical variables can be found and can be applied to the Yang-Mills-Vlasov equations and to electromagnetic fluid dynamics.

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Additional Information:© 1982 North-Holland. Received 11 August 1981. Available online 25 September 2002. Research partially supported by NSF grant MCS-81-07086, ARO contract DAAG-29-79-C-0086 and the Miller Institute. Research partially supported by NSF grants MCS 77-23579 and MCS 80-23356 and the Miller Institute. We are grateful to Allan Kaufman for showing us Morrison's paper and for his continuing encouragement. We also thank Iwo Bialynicki-Birula, Robert Glassey, Darryl Holm, John Hubbard, Bertram Konstant, Robert Littlejohn, Henry McKean, Philip Morrison, Paul Rabinowitz, Tudor Ratiu, Rudolf Schmid and Richard Spencer for their interest and comments.
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Army Research Office (ARO)DAAG-29-79-C-0086
NSFMCS 77-23579
NSFMCS 80-23356
Miller InstituteUNSPECIFIED
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Record Number:CaltechAUTHORS:20100910-112829181
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ID Code:19870
Deposited By: Ruth Sustaita
Deposited On:10 Sep 2010 20:30
Last Modified:08 Nov 2021 23:55

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