The form of ideal current layers in line-tied magnetic fields

It has been argued that a magnetic field which is initially continuous and is line-tied to rigid boundaries in a continuous manner cannot develop tangential discontinuities or current sheets. This would appear to have many consequences in those theories of reconnection and coronal heating which are based on the existence of such current sheets. It is shown here that while the nonexistence of current sheet may hold in a strict sense, it is possible for simple magnetic geometries to spontaneously develop current layers of nonzero thickness which are indistinguishable, in a practical sense, from genuine current sheets. The thickness of these layers can easily be more than six orders of magnitude smaller than the apparent length scale of the initial equilibrium. We suggest that numerical magnetohydrodynamics simulations have encountered such features, but lacked sufficient resolution to distinguish them from current sheets. Turbulent motion of photospheric footpoints will generate this type of current layer in about one eddy turnover.