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arXiv · 1606.06652

Lifting of the Vlasov-Maxwell Bracket by Lie-transform Method

A. J. Brizard·P. J. Morrison·J. W. Burby·L. de Guillebon·M. Vittot
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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 derive explicit Hamiltonian formulations for the guiding-center and gyrokinetic Vlasov-Maxwell equations that have 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.

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A. J. Brizard, P. J. Morrison, J. W. Burby, L. de Guillebon, M. Vittot. 2016-06-21. Lifting of the Vlasov-Maxwell Bracket by Lie-transform Method. https://doi.org/10.1017/s0022377816001161

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