Coronal current-sheet formation - The effect of asymmetric and symmetric shears

A 2.5D numerical code is used to investigate the results of an asymmetric shear imposed on a potential quadrupolar magnetic field under two sets of atmospheric boundary conditions - a low-beta plasma with line tying at the base, similar to the line-tied analytic model, and a hydrostatic-equilibrium atmosphere with solar gravity, typical of the observed photosphere-chromosphere interface. The low-beta simulation confirms the crucial role of the line-tying assumption in producting current sheets. The effects of a symmetric shear on the same hydrostatic-equilibrium atmosphere is examined, using more grid points to improve the resolution of the current structures which form along the flux surfaces. It is found that true current sheets do not form in the corona when a more realistic model is considered. The amount of Ohmic dissipation in the thick currents is estimated to be two to four orders of magnitude below that required to heat the corona. It is concluded that magnetic topologies of the type examined here do not contribute significantly to coronal heating.