Self-Consistent Models of Solar Magnetic Structures in Three Dimensions,

Methods for the calculation of self-consistent MHD equilibria in three dimensions are very important as a first step in analysing the magnetic structures which are, for example, responsible for solar eruptive events. Usually, analytical progress is only possible if a number of restrictive assumptions is made. Despite these restrictions, analytical solutions can be very useful for simple modelling purposes. Numerical methods on the other hand, largely work without restrictive assumptions but are limited by the available computational-resources. We present a 3D equilibrium code based on a numerical continuation method and discuss the possible future applications of the code to magnetic structures in the solar atmosphere and to the study of onset criteria for eruptions.