Hamiltonian formulation of the gyrokinetic Vlasov-Maxwell equations

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.