Magnetic reconnection in a comparison of topology and helicities in two and three dimensional resistive MHD simulations

Abstract: Through a direct comparison between numerical simulations in two and three dimensions, we investigate topological effects in reconnection. A simple estimate on increase in reconnection rate in three dimensions by a factor of $\sqrt{2}$, when compared with a two-dimensional case, is confirmed in our simulations. We also show that both the reconnection rate and the fraction of magnetic energy in the simulations depend linearly on the height of the reconnection region. The degree of structural complexity of a magnetic field and the underlying flow is measured by current helicity and cross-helicity. We compare results in simulations with different computational box heights.