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

A new mathematical procedure is presented to calculate special self-consistent three-dimensional analytic solutions of the magnetohydrostatic (MHS) equations. The derivation of the procedure is based on previous work by Low (1985, 1991, 1992, 1993a, 1993b) and Bogdan & Low (1986). Compared to this previous work, the method presented here has the advantage of being more systematic concerning the mathematical treatment of the problem. This is reflected by the fact that the present approach 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 been very intensively studied in the past, the knowledge accumulated in quantum mechanics about solutions of the Schrodinger equation can now be applied to the problem of calculating self-consistent three-dimensional solutions of the MHS equations. In this paper, special attention will be paid to the case of a plasma around a spherical self-gravitating body (like a star). For this special case, by using the newly developed tools, we derive the first explicit solutions including the additional field-aligned currents. The solutions complement those given by Bogdan & Low (1986). One possible application of the new solutions is the modeling of the solar corona.