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arXiv · 1411.1790

Hamiltonian formulation of the gyrokinetic Vlasov-Maxwell equations

J. W. Burby·A. J. Brizard·P. J. Morrison·H. Qin
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Abstract

The gyrokinetic Vlasov-Maxwell equations are cast as an infinite-dimensional Hamiltonian system. The gyrokinetic Poisson bracket is remarkably simple and similar to the Morrison-Marsden-Weinstein bracket for the Vlasov-Maxwell equations. By identifying many of the bracket's Casimirs, this work enables (i) the derivation of gyrokinetic equilibrium variational principles and (ii) the application of the energy-Casimir method and the method of dynamically-accessible variations to study stability properties of gyrokinetic equilibria.

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J. W. Burby, A. J. Brizard, P. J. Morrison, H. Qin. 2014-11-06. Hamiltonian formulation of the gyrokinetic Vlasov-Maxwell equations. https://doi.org/10.1016/j.physleta.2015.06.051

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