On Hamiltonian And Action Principle Formulations Of Plasma Dynamics

A general discussion of Hamiltonian and action principle formulations for fluid and plasma models is given. A procedure, based on Hamilton's principle of mechanics but adapted for continua, for the construction of action principles for fluid and kinetic models is given. The transformation from action principles in terms of the Lagrangian variable description to the Eulerian variable description in terms of noncanonical Poisson brackets is described. Two examples are developed: ideal MHD and Braginskii's fluid model with gyroviscosity.