Mean field model for the formation of filament channels on the Sun

The coronal magnetic field is subject to random footpoint motions that caus e small-scale twisting and braiding of held lines. We present a mean field theory describing the effects of such small-scale twists on the large-scale coronal field. This theory assumes that the coronal field is force free, w ith electric currents flowing parallel or antiparallel to magnetic field li nes. Random footpoint motions are described in terms of diffusion of the me an magnetic field at the photosphere. The appropriate mean field equations are derived, and a numerical method for solving these equations in three di mensions is presented. Preliminary results obtained with this method are al so presented. In particular the formation of filament channels is studied. Filament channels are regions where the coronal magnetic field is strongly aligned with the underlying polarity inversion line in the photosphere. It is found that magnetic flux cancellation plays an important role in the for mation of such channels. Various models of the coronal field are presented, including some in which the axial held is assumed to originate from below the photosphere. The models reproduce many of the observed features of fila ment channels, but the observed hemisphere pattern of dextral and sinistral channels remains a mystery.