A NUMERICAL STUDY OF THE SUDDEN ERUPTION OF SHEARED MAGNETIC-FIELDS

We investigate the quasi-static evolution of an idealized magnetic con figuration in the solar corona that is subjected to photospheric shear ing motions. The initial, unsheared field in our calculations is a mag netic dipole located at the center of the Sun. The assumed photospheri c shearing motions are latitude-dependent and antisymmetric about the equator. The quasi-static evolution of the coronal field is calculated using the magneto-frictional method. A key difference between our stu dy and previous work is that the outer computational boundary is place d exceedingly far from the solar surface where the shearing motions ar e applied. This is achieved by writing the basic equations of the magn eto-frictional method in terms of the logarithm of radial distance. We find that initially, the coronal magnetic field expands steadily as t he footpoint displacement is increased. However, when the footpoint di splacement exceeds a certain critical amount, the qualitative behavior of the evolving field suddenly changes, so that the outward expansion of the field lines becomes a much more rapidly increasing function of the footpoint displacement. We propose that this sudden transition to a regime with very sensitive dependence on boundary conditions plays an important role in the onset of eruptive phenomena in the solar atmo sphere.