Coronal Mass Ejection: Initiation, Magnetic Helicity, and Flux Ropes. II. Turbulent Diffusion-driven Evolution

We consider a three-dimensional bipolar magnetic field B, occupying a half-space, which is driven into evolution by the slow turbulent diffusion of its normal component on the boundary. The latter is imposed by fixing the tangential component of the electric field and leads to flux cancellation. We first present general analytical considerations on this problem and then construct a class of explicit solutions in which B keeps evolving quasi-statically through a sequence of force-free configurations without exhibiting any catastrophic behavior. Thus, we report the results of a series of numerical simulations in which B evolves from different force-free states, the electric field on the boundary being imposed to have a vanishing electrostatic part (the latter condition is not enforced in the analytical model, and thus it is possible a priori for the results of the two types of calculations to be different). In all the cases, we find that the evolution conserves the magnetic helicity and exhibits two qualitatively different phases. The first one, during which a twisted flux rope is created, is slow and almost quasi-static, while the second one is associated with a disruption, which is confined for a small initial helicity and global for a large initial helicity. Our calculations may be relevant for modeling the coronal mass ejections that have been observed to occur in the late dispersion phase of an active region. In particular, they may allow us to understand the role played by a twisted flux rope in these events.