The Hamiltonian structure and Euler-Poincar\'{e} formulation of the Vlasov-Maxwell and gyrokinetic systems
Abstract
We present a new variational principle for the gyrokinetic system, similar to the Maxwell-Vlasov action presented in Ref. 1. The variational principle is in the Eulerian frame and based on constrained variations of the phase space fluid velocity and particle distribution function. Using a Legendre transform, we explicitly derive the field theoretic Hamiltonian structure of the system. This is carried out with a modified Dirac theory of constraints, which is used to construct meaningful brackets from those obtained directly from Euler-Poincar\'{e} theory. Possible applications of these formulations include continuum geometric integration techniques, large-eddy simulation models and Casimir type stability methods. [1] H. Cendra et. al., Journal of Mathematical Physics 39, 3138 (1998)
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Cite
@article{arxiv.1301.6066,
title = {The Hamiltonian structure and Euler-Poincar\'{e} formulation of the Vlasov-Maxwell and gyrokinetic systems},
author = {J. Squire and H. Qin and W. M. Tang and C. Chandre},
journal= {arXiv preprint arXiv:1301.6066},
year = {2013}
}
Comments
36 pages, 1 figure