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We derive the conditions under which the fluid models obtained from the firsttwo moments of Hamiltonian drift-kinetic systems of interest to plasma physics,preserve a Hamiltonian structure. The adopted procedure consists of determiningclosure relations that allow to truncate the Poisson bracket of thedrift-kinetic system, expressed in terms of the moments, in such a way that theresulting operation is a Poisson bracket for functionals of the first two fluidmoments. The analysis is carried out for a class of full drift-kineticequations and also for drift-kinetic systems in which a splitting between anequilibrium distribution function and a perturbation is performed. In theformer case we obtain that the only closure, not involving integral ordifferential operators, that leads to a Poisson bracket, corresponds to that ofan ideal adiabatic gas made of molecules possessing one degree of freedom. Inthe latter case, Hamiltonian closures turn out to be those in which the secondmoment is a linear combination of the first two moments, which can be seen as alinearization of the Hamiltonian closure of the full drift-kinetic case. Anumber of weakly-3D Hamiltonian reduced fluid models of interest, for instancefor tokamak plasmas, can be derived in this way and, viceversa given a fluidmodel with a Hamiltonian structure of a certain type, a parent Hamiltoniandrift-kinetic model can then be identified. We make use of this correspondenceto identify the drift-kinetic models from which Hamiltonian fluid models formagnetic reconnection and compressible plasma dynamics in the presence of astatic but inhomogeneous magnetic field can be derived. The Casimir invariantsof the Poisson brackets of the derived fluid models are also discussed.

Hamiltonian closures for two-moment fluid models derived from drift-kinetic equations