Magnetic Relaxation in the Solar Corona

This is a mathematical study of the long-lived hydromagnetic structures produced in the tenuous solar corona by the turbulent, resistive relaxation of a magnetic field under the condition of extremely high electrical conductivity. The relaxation theory of Taylor (1974), originally developed for a laboratory device, is extended to treat the open atmosphere where the relaxing field must interact with its surrounding fields. A boundary-value problem is posed for a two dimensional model that idealizes the corona as the half Cartesian plane filled with a potential field (i) that is anchored to a rigid, perfectly conducting base, and, (ii) that embeds a force-free magnetic field in the form of a flux rope oriented horizontally and perpendicular to the Cartesian plane. The flux rope has a free boundary which is an unknown in the construction of a solution for this atmosphere. Pairs of magnetostatic solutions are constructed to represent the initial and final states of a flux-rope relaxation that conserves both the total magnetic helicity and total axial magnetic flux, using a numerical iterative method specially developed for this study. The collection of numerical solutions found provides an insight into the interplay among several hydromagnetic properties in the formation of long-lived coronal structures. In particular, the study shows (i) that the outward spread of reconnection between a relaxing flux-rope and its external field may be arrested at some outer magnetic flux-surface within which a constant-α force-free field emerges as the minimum-energy state, and, (ii) that this outward spread is complicated by an inward, partial collapse of the relaxing flux-rope produced by a loss of internal magnetic pressure. Subject headings: MHD — Sun: magnetic fields — Sun: corona Department of Mathematics and Statistics, Wichita State University Department of Applied Mathematics, University of Colorado Institute for Mathematics Applied to the Geosciences, National Center for Atmospheric Research High Altitude Observatory, National Center for Atmospheric Research