A Compressible Hamiltonian Electromagnetic Gyrofluid Model

Abstract : A Lie- Poisson bracket is presented for a four-field gyrofluid model with compressible ions and magnetic field curvature, thereby showing the model to be Hamiltonian. In particular, we find that in addition to commonly adopted magnetic curvature terms present in the continuity equations, analogous terms must be retained also in the momentum equations, in order to have a Lie-Poisson structure. The corresponding Casimir invariants are presented, and shown to be associated to four Lagrangian invariants, that get advected by appropriate ''velocity'' fields during the dynamics. This differs from a cold ion limit, in which the Lie-Poisson bracket transforms into the sum of direct and semidirect products, leading to only three Lagrangian invariants.
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Communications in Nonlinear Science and Numerical Simulation, Elsevier, 2012, 17, pp.2171
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F. Waelbroeck, Emanuele Tassi. A Compressible Hamiltonian Electromagnetic Gyrofluid Model. Communications in Nonlinear Science and Numerical Simulation, Elsevier, 2012, 17, pp.2171. 〈hal-00617454〉

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