THE 3-D BOUNDARY-ELEMENT FORMULATION OF LINEAR FORCE-FREE MAGNETIC-FIELDS WITH FINITE-ENERGY CONTENT IN SEMIINFINITE SPACE

In this paper, a formulation describing a force-free magnetic field with constant alpha, either alpha not equal O or alpha = O, with finite energy content in semi-infinite space, z > O, above the Sun is proposed and solved uniquely by a numerical method: the boundary element method (BEM). The method is effective and convenient in extrapolating the magnetic field above the solar surface, Gamma, directly from the measured magnetogram. Meanwhile, no additional data treatment is needed. Based on the existence of such a field, the uniqueness of the solution in the present formulation is proved and some useful properties are obtained. The validity is also demonstrated by its application to the magnetic field computation in the chromosphere from observed magnetogram data. The practical feasibility is thus discussed and further confirmed.