Hamiltonian formulation of the gyrokinetic Vlasov-Maxwell equations
J. W. Burby, A. J. Brizard, P. J. Morrison, and H. Qin
TL;DR
This paper formulates the gyrokinetic Vlasov-Maxwell equations as a Hamiltonian system, simplifying the Poisson bracket and enabling new stability analysis methods for gyrokinetic equilibria.
Contribution
It introduces a simple Hamiltonian formulation and Poisson bracket for the gyrokinetic Vlasov-Maxwell equations, facilitating stability studies.
Findings
Simplified gyrokinetic Poisson bracket similar to Vlasov-Maxwell case
Identification of Casimirs for the gyrokinetic system
Enabling variational and energy-Casimir stability methods
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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