Wound magnetostatics and flaring

Abstract

We discuss the winding of a force-free axisymmetric magnetic field rooted on a heavy conductor onz=0. In quadrupolar symmetry the field expands in the half-spacez>0 and the toroidal flux concentrates on a conical surface. After a mean twist of 208°, the conical layer hosts large toroidal current loops with reversal of the magnetic flux on either side. The evolution of the field structure is described by scale-free static solutionsB∼r −(p+2), withp taking values between 0 and 2. The large expansion factor of the field structure is suggestive of flaring originating on the solar photosphere.