Three-dimensional solar magnetic field extrapolation using analytical magnetohydrostatic equilibrium solutions

The majority of coronal magnetic field extrapolation methods use photospheric observations as boundary conditions together with the assumption of a force-free or even potential corona. However, observations suggest that the photosphere and chromosphere are not force-free and that, therefore, currents perpendicular to the magnetic field should be present in the lower layers of the solar atmosphere. As a result, to properly model these non-force-free regions, extrapolation methods based on magnetohydrostatic (MHS) equilibria are needed. Compared to force-free equilibria, MHS equilibria include the pressure gradient force and the gravitational force in addition to the Lorentz force. This thesis primarily investigates the potential of linear MHS extrapolation to become a practical, efficient and convenient tool for local coronal field modelling. A detailed investigation is carried out into asymptotic solutions of a specific family of MHS equilibrium equations. This is important because these asymptotic solutions can help to increase the numerical efficiency of MHS models. In addition, theoretical and practical techniques are explored to enable the application of the analytical model presented in this thesis to observational data and to further reduce its computation time. Using specialised codes which were written during the course of the work for this thesis, we demonstrate the capabilities of this new magnetic field extrapolation method. Furthermore, we test the results based on our method by comparing them to "ground-truth" data from other extrapolation methods and from MHD simulations. Furthermore, we present the very first applications of the newly developed tool to observational data. For these applications we use data by the Helioseismic Magnetic Imager onboard the Solar Dynamics Observatory, and by the Polarimetric and Helioseismic Imager onboard Solar Orbiter. Advantages and disadvantages of the model are discussed together with opportunities to further increase its efficiency. Although the code developed is not yet ready for public release, it has the potential to be developed into a publicly available tool for 3D MHS extrapolation for use by the broader scientific community.