A method of forced extrapolation of the global magnetic field in the solar corona

We present a method of forced-field (i.e., non-force-free field: NFFF) extrapolation of the global magnetic field in the corona, on the basis of single-layer vector magnetogram, by extending an extrapolation technique of local magnetic field first developed by Hu et al. (2008). The forced coronal magnetic field is described by a system with the minimum dissipation rate (MDR) which is appropriate for the corona as a forced and open system. The obtained solution of the magnetic field can be decomposed into three components including one potential field and two linear force-free fields (LFFF). Starting from the given single-layer vector magnetogram, the bottom boundary condition for each component is determined with an iterative method to achieve a minimum difference of the transverse component between the extrapolated field and the original magnetogram. The final extrapolated forced field is given by the sum of the three component fields with the obtained bottom boundaries. The method is tested with an analytic magnetohydrostatic (MHS) solution. It is shown that the extrapolated forced field is highly consistent with the MHS solution at least from the solar disk to the heliocentric distance of 1.5 solar radii (R_⊙). For instance, the complements of normalized and mean vector errors (E′_n, E′_m) are as high as ∼97% and 95%, respectively. Further comparisons between magnetic strength, force and field line distributions indicate that the MHS solution has been successfully reconstructed.