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 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.
Cite
@article{arxiv.1606.06652,
title = {Lifting of the Vlasov-Maxwell Bracket by Lie-transform Method},
author = {A. J. Brizard and P. J. Morrison and J. W. Burby and L. de Guillebon and M. Vittot},
journal= {arXiv preprint arXiv:1606.06652},
year = {2016}
}
Comments
39 pages