Spontaneous current sheets in an ideal hydromagnetic fluid

Parker's theory of spontaneous current sheets, or magnetic tangential discontinuities, in electrically perfectly conducting fluids is demonstrated for globally untwisted magnetic fields in the Chandrasekhar-Kendall representation. All the three-dimensional, globally untwisted fields sharing the same flux distribution, fixed at the rigid boundary of the domain, span an infinity of different field topologies, each preserved in a field under the frozen-in condition. The general result is obtained and illustrated that only one of these topologies allows a field to relax into an everywhere continuous force-free state, namely, the potential field uniquely determined by the boundary flux distribution. All other topologies require the field to find a force-free state containing inevitable tangential magnetic discontinuities. This result extends a class of two-dimensional demonstrations of the Parker theory to three dimensions. A field of a fixed topology and boundary flux distribution can be in a continuous state in one equilibrium but may have to contain inevitable tangential discontinuities on transition to another equilibrium. This property, demonstrated here with untwisted fields, is probably the hydromagnetic origin of flares occurring in the course of slow evolution in the solar corona.