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

International audienceThe nonlinear dynamics of a two-dimensional model for collisionless magnetic reconnection is investigated both numerically and analytically. For very low values of the plasma $\beta$, parallel magnetic perturbations tend to be proportional to the vorticity perturbations, but as $\beta$ 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 Hamiltonian extension of the reconnection model is also presented together with a general method for extending a large class of two-dimensional fluid plasma models to three dimensions, while preserving the Hamiltonian structure. Finally, it is shown how such models can also be extended, while preserving the Hamiltonian structure, to include externally applied fields