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 investigatedboth numerically and analytically. For very low values of the plasma ?, parallel magnetic perturbations tend tobe proportional to the vorticity perturbations, but as ? increases, detachment of these quantities takes place. Thesubsequent difference between the structure of the vorticity and the parallel magnetic perturbations can be explainednaturally 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, andthe corresponding conservation properties are compared with those of the 2D model. Ageneral method for extendinga large class of 2D fluid plasma models to three dimensions, while preserving the Hamiltonian structure, is thenpresented. 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.