Self-similar magnetic arcades

Abstract

We study self-similar analytical solutions for force-free magnetic field in azimuthal symmetry and arcade topology. We assume the existence of a poloidal magnetic field, anchored on a heavy spherical conductor. The field is changed by shearing the foot points of the arcade due to differential rotation. This rotation gives rise to a toroidal component in the magnetic structure which reacts by expanding the poloidal flux outwards. This could be a slow process at the early stages; however, it becomes very fast at the final stages when the poloidal flux expands to infinity. We address the question of the pressure environment confining the arcade, a pressure profile proportional to r−4 is particularly interesting as it allows finite twist before the field expands to infinity. Finally, some time evolution estimates are made to demonstrate the limitations of this study.