On the application of numerical continuation methods to two- and three-dimensional solar and astrophysical problems

Abstract

In this thesis, applications of a numerical continuation method to two- and three-dimensional bifurcation problems are presented. The 2D problems are motivated by solar applications. In particular, it is shown that the bifurcation properties of a previously studied model for magnetic arcades depend strongly on the pressure function used in the model. The bifurcation properties of a straight flux model for coronal loops are investigated and compared with the results of linear ideal MHD stability analysis. It is shown that for line-tied boundary conditions, the method for the calculation of the equilibrium sequence determines whether the first or the second bifurcation point coincides with the linear stability threshold. Also, in this thesis, the 3D version of the continuation code is applied for the first time. The problems treated with the 3D code are therefore chosen with the intention to demonstrate the general capabilities of the code and to see where its limitations are. Whereas the code performs as expected for relatively simple albeit nonlinear bifurcation problems, a clear need for further development is shown by more involved problems.