Hamiltonian four-field model for magnetic reconnection: nonlinear dynamics and extension to three dimensions with externally applied fields

The nonlinear dynamics of a two-dimensional (2D) model for collisionless magnetic reconnection is investigated both numerically and analytically. For very low values of the plasma ?, parallel magnetic perturbations tend to be proportional to the vorticity perturbations, but as ? 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 2D model. Ageneral method for extending a large class of 2D 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.