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Lifting of the Vlasov–Maxwell bracket by Lie-transform method

Published online by Cambridge University Press:  14 December 2016

A. J. Brizard ,
P. J. Morrison ,
J. W. Burby ,
L. de Guillebon  and
M. Vittot
A. J. Brizard*
Affiliation:
Department of Physics, Saint Michael’s College, Colchester, VT 05439, USA
P. J. Morrison
Affiliation:
Department of Physics and Institute for Fusion Studies, University of Texas at Austin, Austin, TX 78712, USA
J. W. Burby
Affiliation:
Courant Institute of Mathematical Sciences, New York, NY 10012, USA
L. de Guillebon
Affiliation:
Aix Marseille Univ., Univ. Toulon, CNRS, CPT, Marseille, France
M. Vittot
Affiliation:
Aix Marseille Univ., Univ. Toulon, CNRS, CPT, Marseille, France
*
†Email address for correspondence: abrizard@smcvt.edu
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Abstract

The Vlasov–Maxwell equations possess a Hamiltonian structure expressed in terms of a Hamiltonian functional and a functional bracket. In the present paper, the transformation (‘lift’) of the Vlasov–Maxwell bracket induced by the dynamical reduction of single-particle dynamics is investigated when the reduction is carried out by Lie-transform perturbation methods. The ultimate goal of this work is to provide an explicit pathway to the Hamiltonian formulations for the guiding-centre and gyrokinetic Vlasov–Maxwell equations, which have found important applications in our understanding of turbulent magnetized plasmas. Here, it is shown that the general form of the reduced Vlasov–Maxwell equations possesses a Hamiltonian structure defined in terms of a reduced Hamiltonian functional and a reduced bracket that automatically satisfies the standard bracket properties.

Keywords

magnetized plasmasplasma dynamics
Type
Research Article
Information
Journal of Plasma Physics , Volume 82 , Issue 6 , December 2016 , 905820608
Copyright
© Cambridge University Press 2016 

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