The heating and activity of the solar corona: 3. Dynamics of a low beta plasma with three-dimensional null points

We investigate the self-consistent nonlinear evolution of an initially force-free three-dimensional magnetic field subjected to stress on two boundaries, The results illustrate how complicated magnetic field structures, such as those found in the solar corona, evolve dynamically when forced by stress from boundaries and how the energy which is temporarily stored in the magnetic field may be converted into other forms of energy such as heat, flow energy, and fast particles. The initial model state is triple periodic and contains eight magnetic null points, During the time evolution, the current density concentrates near particular locations in space that can be identified with the singular field lines connecting pairs of null points of the initial state, Current sheets are found to grow out of the singular lines formed by the intersection of surfaces across which the magnetic connectivity is discontinuous. Jets of plasma shoot out from the edges of the currents sheets, driven by the ''sling-shot'' Lorentz force created by reconnecting magnetic field lines. As a result of the reconnection, most of the magnetic connectivity between the two boundaries is lost, and the remaining magnetic field develops arcade-like structures along the boundaries, These arcade structures are long-lived, and the system enters a quasi-stationary state, where small-scale current sheets are continually appearing and disappearing, The distribution of size of these current sheets is limited only by the numerical resolution, The current sheets dissipate the energy supplied by the boundary driving and also slowly deplete the magnetic energy from the initial constant alpha magnetic field, The dissipation occurs in an increasing number of current sheets of decreasing size at higher numerical resolution, which keeps the overall reconnection rate nearly independent of the numerical resolution, This suggests that ''fast reconnection'' may occur through the collaborative effort of a large number of many small-scale current sheets, rather than in the very large magnetic Reynolds number limit of single current sheets that has been so extensively discussed in the literature. This has important applications to both the problem of understanding coronal heating and the search for efficient hare energy release mechanisms.