An algorithm for calculating three gauge-invariant helicities (self-, mutual- and Berger relative helicity) for a magnetic field specified in a rectangular box is described. The algorithm is tested on a well-known force-free model (Low and Lou, 1990) presented in vector-potential form.
Possibilities in principle for satisfactory removal of the 180-azimuthal ambiguity in the transverse field of vector magnetograms and the extrapolation of magnetic fields independently of their position on the solar disk are shown. Revealed here is a
n exact correspondence between the estimated field and the nonpotential loop structure on the limb. The Metropoliss algorithm modified to work in spherical geometry is used to resolve the azimuthal ambiguity. Based on a version of the optimization method from Rudenko and Myshyakov (2009), we use corrected magnetograms as boundary conditions for magnetic field extrapolation in the nonlinear force-free approximation.
