The Hamiltonian formulation of a plasma four-field fluid model that describes collisionless reconnection is presented. The formulation is noncanonical with a corresponding Lie-Poisson bracket. The bracket is used to obtain new independent families of invariants, so-called Casimir invariants, three of which are directly related to Lagrangian invariants of the system. The Casimirs are used to obtain a variational principle for equilibrium equations that generalize the Grad-Shafranov equation to include flow. Dipole and homogeneous equilibria are constructed. The linear dynamics of the latter is treated in detail in a Hamiltonian context: canonically conjugate variables are obtained; the dispersion relation is analyzed and exact thresholds for spectral stability are obtained; the canonical transformation to normal form is described; an unambiguous definition of negative energy modes is given; and thresholds sufficient for energy-Casimir stability are obtained. The Hamiltonian formulation also is used to obtain an expression for the collisionless conductivity and it is further used to describe the linear growth and nonlinear saturation of the collisionless tearing mode.

The nonlinear dynamics of a two-dimensional model for collisionless magnetic reconnection is investigated both numerically and analytically. For very low values of the plasma β, parallel magnetic perturbations tend to be proportional to the vorticity perturbations, but as β increases detachment of these quantities takes place. The subsequent difference between the structure of the vorticity and the parallel magnetic perturbations can be explained naturally in terms of the "normal" field variables that emerge from the noncanonical Hamiltonian theory of the model. A three-dimensional extension of the reconnection model is also presented, its Hamiltonian structure is derived, and the corresponding conservation properties are compared with those of the two-dimensional model. A general method for extending a large class of twodimensional fluid plasma models to three dimensions, while preserving the Hamiltonian structure, is then presented. Finally, it is shown how such models can also be extended, while preserving the Hamiltonian structure, to include externally applied fields, that can be used, for instance, for modelling resonant magnetic perturbations.

A Lie-Poisson bracket is presented for a four-field gyrofluid model with compressible ions and magnetic field curvature, thereby showing the model to be Hamiltonian. In particular, in addition to commonly adopted magnetic curvature terms present in the continuity equations, analogous terms must be retained also in the momentum equations, in order to have a Lie-Poisson structure.The corresponding Casimir invariants are presented, and shown to be associated to four Lagrangian invariants, that get advected by appropriate "velocity" fields during the dynamics. This differs from a cold ion limit, in which the Lie-Poisson bracket transforms into the sum of direct and semidirect products, leading to only three Lagrangian invariants.