On self-consistent three-dimensional analytic solutions of the magnetohydrostatic equations.

Details On self-consistent three-dimensional analytic solutions of the magnetohydrostatic equations. On self-consistent three-dimensional analytic solutions of the magnetohydrostatic equations.

Sep 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26a...301..628n&link_type=abstract

Astronomy and Astrophysics, v.301, p.628

Astronomy and Astrophysics

Astrophysics

27

Magnetohydrodynamics, Plasmas, Sun: Magnetic Fields, Sun: Corona, Stars: Magnetic Fields

Scientific paper

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 Schroedinger type equation. Since the Schroedinger equation has been very intensively studied in the past, the knowledge accumulated in quantum mechanics about solutions of the Schroedinger 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. These solutions complement those given by Bogdan & Low (1986). One possible application of the new solutions is the modeling of the solar corona.

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