  We present a Hamiltonian derivation of a class of reduced plasma
two-dimensional fluid models, an example being the Charney-Hasegawa-Mima
equation. These models are obtained from the same parent Hamiltonian model,
which consists of the ion momentum equation coupled to the continuity equation,
by imposing dynamical constraints. It is shown that the Poisson bracket
associated with these reduced models is the Dirac bracket obtained from the
Poisson bracket of the parent model.
