Singular structure of magnetic islands resulting from reconnection

Magnetic island equilibria resulting from reconnection in magnetohydrodynamic (MHD) simulations are explored in a two-dimensional slab geometry. Magnetic islands are evolved to finite amplitude with a nonzero resistivity. The resistivity and flows are then set to zero and the system is allowed to relax toward equilibrium. A $y$ -type singular current layer in the equilibrium state is identified for all but systems with the smallest values of the tearing mode stability parameter ${\mathrm{\Delta }}^{\prime }$ . It is shown that the length of the equilibrium $y$ line tracks the length of the Sweet–Parker current layer that develops during reconnection. This suggests that the formation of Sweet–Parker current layers during magnetic reconnection in the resistive MHD model is a consequence of the presence of a singularity in post-reconnection state. A threshold in ${\mathrm{\Delta }}^{\prime }$ for singular behavior is also identified.