  Moment closures of the Vlasov-Amp{\`e}re system, whereby higher moments are
represented as functions of lower moments with the constraint that the
resulting fluid system remains Hamiltonian, are investigated by using water-bag
theory. The link between the water-bag formalism and fluid models that involve
density, fluid velocity, pressure and higher moments is established by
introducing suitable thermodynamic variables. The cases of one, two and three
water-bags are treated and their Hamiltonian structures are provided. In each
case, we give the associated fluid closures and we discuss their Casimir
invariants. We show how the method can be extended to an arbitrary number of
fields, i.e., an arbitrary number of water-bags and associated moments. The
thermodynamic interpretation of the resulting models is discussed. Finally, a
general procedure to derive Hamiltonian N-field fluid models is proposed.
