ON SELF-CONSISTENT 3-DIMENSIONAL ANALYTIC SOLUTIONS OF THE MAGNETOHYDROSTATIC EQUATIONS

A new mathematical procedure is presented to calculate special self-co nsistent three-dimensional analytic solutions of the magnetohydrostati c (MHS) equations. The derivation of the procedure is based on previou s work by Low (1985, 1991, 1992, 1993a, 1993b) and Bogdan & Low (1986) . Compared to this previous work, the method presented here has the ad vantage of being more systematic concerning the mathematical treatment of the problem. This is reflected by the fact that the present approa ch allows the inclusion of additional field-aligned currents in a very natural way and that the fundamental equation which has to be solved is a Schrodinger type equation. Since the Schrodinger equation has bee n very intensively studied in the past, the knowledge accumulated in q uantum mechanics about solutions of the Schrodinger equation can now b e applied to the problem of calculating self-consistent three-dimensio nal solutions of the MHS equations. In this paper, special attention w ill be paid to the case of a plasma around a spherical self-gravitatin g body (like a star). For this special case, by using the newly develo ped tools, we derive the first explicit solutions including the additi onal field-aligned currents. The solutions complement those given by B ogdan & Low (1986). One possible application of the new solutions is t he modeling of the solar corona.