Hamiltonian structure of a collisionless reconnection model valid for high and low $?$ plasmas

The noncanonical Hamiltonian formulation of a recently derived four-field model describing collisionless reconnection is presented. The corresponding Lie-Poisson bracket is shown to be a sum of a direct and semi-direct product forms and to possess four infinite independent families of Casimir invariants. Three out of four of these families are directly associated with the existence of Lagrangian invariants of the model. Two of the invariants generalize previously discovered invariants of a two-field model for reconnection in low-? plasmas. Finally a variational principle is given for deriving general equilibrium equations and an example of an equilibrium solution is described explicitely.