A Numerical Method for Studies of 3D Coronal Field Structures

Abstract

Three-dimensional analytic magnetohydrostatic equilibria are presently available only for some special cases (for a recent overview see e.g. Petrie and Neukirch, 1999). Therefore, one has to use numerical methods to make progress on the general problem (e.g. Sakurai, 1979; Klimchuk and Sturrock, 1992; Longbottom et al., 1998). This is especially true if one wants to model the slow pre-eruptive evolution of magnetic fields by sequences of equilibria. A very suitable class of numerical methods for such a problem are numerical continuation techniques (Allgower and Georg, 1990). These methods allow us not only to calculate equilibrium branches, but also the detection of bifurcation points and the corresponding bifurcating branches. This property can be important for gaining an understanding of the onset conditions for eruptions. In solar physics continuation methods have for example been used by Zwingmann (1987) and Platt and Neukirch (1994), but only for symmetric (two-dimensional) systems. In this paper we describe the extension of the continuation code used by Zwingmann (1987) and Platt and Neukirch (1994) to non-symmetric (three dimensional) systems and present test results for symmetric systems.