Progress in the understanding of several phenomena occurring in plasmas greatly benefited from the use of continuum models based on a fluid description of plasmas.
In the absence of dissipative effects, all such models are supposed to possess a Hamiltonian structure. The existence of such structure for a given model is, however, not guaranteed, in general,
unless it is implied in its derivation or shown a posteriori.
In this talk I will consider a class of so-called reduced fluid models for plasmas, which are applicable in the situation where the magnetic field can be written as the sum of
and constant component (guide field) with a fluctuating contribution depending on space and time. The amplitude of the fluctuating contribution is also assumed to be much
smaller than that of the guide field. Such very commonly adopted assumption has led, together with further assumptions, to the derivation, over the last decades, of a number of reduced fluid models, a considerable part of which were shown to possess a Hamiltonian structure.
In this context, I will first recall earlier results on the derivation of a class of reduced fluid models, which guarantees the existence of a Hamiltonian structure. Such derivation is based on a closure
of the hierarchy of fluid equations evolving moments of the perturbation of the distribution function satisfying a Hamiltonian drift-kinetic equation. In the remaining part of the talk I will consider recent extensions of this procedure, addressed to applications to collisionless space plasmas.