Coronal magnetic fields produced by photospheric shear

The magnetofrictional method for computing force-free fields is used to examine the evolution of the magnetic field of a line dipole, when there is relative shearing motion between the two polarities. It is found that the energy of the sheared field can be arbitrarily large compared with the potential field. It is also found that it is possible to fit the magnetic energy, as a function of shear amplitude, by a simple functional form. The fit parameters depend only on the distribution of normal field in the photosphere and the form of the shearing displacement. They show that the energy is relatively more enhanced if the shear occurs: (1) where the normal field is strongest; and/or (2) in the inner region of the dipole, near the axis; and/or (3) over a large fraction of the dipole area.