A model of magnetic fields in a large-scale solar active region

The magnetic field configuration in a super-active region (i.e., a large, island-like delta -type spot) is simulated with a non-linear force-free field that varies slowly with time. Such a complex magnetic field exhibits the main observational characteristics of vector magnetic fields. These are the extreme inequality of positive and negative magnetic fluxes (the ratio of positive and negative fluxes is 1:6), the U-shaped magnetic inversion line, as well as the difference between dipoles and quadrupoles. The results of simulation may be used to interpret the following observed phenomena: (1) Large flares often occur in regions of mixed polarities or quadrupoles near a U-shaped inversion line. (2) In the quasi-bipolar regions near U-shaped inversion line, almost no large flares appear or there are merely small flares. (3) Large-scale rotational motion and flux emergence within active regions may give rise to quadrupolar magnetic topological separatrices and produce large current sheets, and hence intense magnetic reconnections and major flares are induced. The method used in the computation of non-linear force-free fields is a natural extension of Woodbury's relaxation method in polar coordinates. The common ill-posed solutions are thereby avoided. This makes the linear and non-linear force-free solutions to be mutually consistent, so there is a continuous and smooth transition between the two.