Nonlinear force-free reconstruction of the coronal magnetic field with advanced numerical methods

The structure and evolution of the coronal magnetic field that permeates the solar atmosphere play key roles in a variety of dynamical processes observed to occur on the Sun. Within this thesis, we use an optimization method to extrapolate the magnetic field above solar active regions based on vector magnetic field measurements made in the solar photosphere. Our method is based on the force-free assumption, i. e., the adoption that the coronal currents are co-aligned with the magnetic field. Untill today, the field extrapolation is the only means to model the coronal magnetic field on a regular basis. Existing extrapolation codes use cartesian geometry for modelling the magnetic field and do not take the curvature of the Sun’s surface into account. Therefore, they can only be applied to relatively small areas, e. g., to single active regions. In this thesis, we develop numerical methods to carry out the magnetic field extrapolation into solar corona from photospheric boundary in spherical geometry. This way we can accommodate the connectivity between several neighbouring solar active regions. Measured photospheric data are often inconsistent with the above force-free assumption. Therefore, we develop transformations to these data before nonlinear forcefree extrapolation codes can be applied. We also present a new scheme which allows to incorporate measurement error and treat regions with missing observational data.