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Noncanonical Hamiltonian field theory and reduced MHD

Marsden, Jerrold E. and Morrison , Philip J. (1984) Noncanonical Hamiltonian field theory and reduced MHD. In: Fluids and plasmas : geometry and dynamics. Contemporary Mathematics. No.28. American Mathematical Society , Providence, R.I, pp. 133-150. ISBN 0821850288 http://resolver.caltech.edu/CaltechAUTHORS:20100901-112223214

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Abstract

Aspects of noncanonical Hamiltonian field theory are reviewed. Many systems are Hamiltonian in the sense of possessing Poisson bracket structures, yet the equations are not in canonical form. A particular system of this type is considered, namely reduced magnetohydrodynamics (RMHD) which was derived for tokamak modelling. The notion of a lie Poisson bracket is reviewed; these are special Poisson brackets associated to Lie groups. The RMHD equations are shown to be Hamiltonian for brackets closely related to the Poisson bracket of a semi-direct product group. The process by which this bracket may be derived from a canonical Lagrangian description by reduction is described.


Item Type:Book Section
Additional Information:© 1984 American Mathematical Society. lResearch partially supported by DOE contract DE-AT03-82ER-12097. 2Research partially supported by DOE contract DE-FGOS-BOETS3088.
Funders:
Funding AgencyGrant Number
Department of EnergyDE-AT03-82ER-12097
Department of EnergyDE-FGOS-BOETS3088
Record Number:CaltechAUTHORS:20100901-112223214
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100901-112223214
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19756
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:01 Sep 2010 19:39
Last Modified:26 Dec 2012 12:23

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