Hamiltonian reduced fluid model for plasmas with temperature and heat flux anisotropies

International audienceWe derive a Hamiltonian fluid model for strongly magnetized plasmas describing the evolution, for an arbitrary number of species, of density, velocity and electromagnetic fluctuations as well as of the temperature and heat flux fluctuations associated with motions parallel and perpendicular to the direction of a background magnetic field. The model is derived as a reduction of the infinite hierarchy of equations obtained by taking moments, with respect to Hermite-Laguerre polynomials in velocity-magnetic moment coordinates, of a Hamiltonian drift-kinetic system. A closure relation directly coupling the heat flux fluctuations in the directions parallel and perpendicular to the background magnetic field is shown to provide a fluid reduction which preserves the Hamiltonian character of the parent drift-kinetic model. An alternative set of dynamical variables is found, in terms of which the Poisson bracket of the fluid model takes a simple direct sum structure and permits an easy identification of the Casimir invariants. Such invariants, in the limit of translational symmetry with respect to the direction of the background magnetic field, turn out to be associated with Lagrangian invariants of the fluid model. It is pointed out that the coupling between parallel and perpendicular heat flux evolutions introduced by the closure, is necessary in order to guarantee the existence of a Hamiltonian structure with a Poisson bracket obtained as extension of a Lie-Poisson bracket