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

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.

Authors:
; ; ; ;
Publication Date:
Research Org.:
New York Univ. (NYU), NY (United States); Univ. of Texas, Austin, TX (United States); Saint Michael's College, Colchester, VT (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1534395
DOE Contract Number:  
FG02-86ER53223; FG02-04ER54742; SC0006721; SC0014032
Resource Type:
Journal Article
Journal Name:
Journal of Plasma Physics
Additional Journal Information:
Journal Volume: 82; Journal Issue: 6; Journal ID: ISSN 0022-3778
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
Physics

Citation Formats

Brizard, A.  J., Morrison, P.  J., Burby, J.  W., de Guillebon, L., and Vittot, M. Lifting of the Vlasov–Maxwell bracket by Lie-transform method. United States: N. p., 2016. Web. doi:10.1017/s0022377816001161.
Brizard, A.  J., Morrison, P.  J., Burby, J.  W., de Guillebon, L., & Vittot, M. Lifting of the Vlasov–Maxwell bracket by Lie-transform method. United States. doi:10.1017/s0022377816001161.
Brizard, A.  J., Morrison, P.  J., Burby, J.  W., de Guillebon, L., and Vittot, M. Thu . "Lifting of the Vlasov–Maxwell bracket by Lie-transform method". United States. doi:10.1017/s0022377816001161.
@article{osti_1534395,
title = {Lifting of the Vlasov–Maxwell bracket by Lie-transform method},
author = {Brizard, A.  J. and Morrison, P.  J. and Burby, J.  W. and de Guillebon, L. and Vittot, M.},
abstractNote = {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.},
doi = {10.1017/s0022377816001161},
journal = {Journal of Plasma Physics},
issn = {0022-3778},
number = 6,
volume = 82,
place = {United States},
year = {2016},
month = {12}
}

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