Deriving reduced models for plasma physics via Dirac’s theory of constrained Hamiltonian systems

We present a Hamiltonian derivation of a class of reduced models in plasma physics obtained by imposing dynamical constraints on a parent Hamiltonian model. We will consider MHD equations and Maxwell-Vlasov equations as parent models. 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.