Eruptions and Equilibria in the Solar Corona

The dynamic behaviour of the Solar Corona is dominated by its magnetic field. Complex magnetic structures can form in the corona which have the potential to catastrophically erupt, releasing vast amounts of energy in the form of coronal mass ejections – eruptions which can ultimately result in increased space weather activity. This thesis discusses a variety of numerical methods used to model the coronal magnetic field, including new approaches and techniques that could theoretically be used to improve space weather predictions. The thesis consists of three relatively unconnected chapters. We first describe a new magnetic field model which calculates a magnetofrictional equilibrium with an imposed solar wind profile. These ‘outflow fields’ appear to approximate the real coronal magnetic field more closely than the established potential field model, take a similar time to compute, and avoid the need to impose an artificial source surface. Including the solar wind tends to increase the open magnetic flux compared to a potential field, reducing the well known discrepancy with in situ observations. These equilibrium fields can be used as initial conditions for the bulk of our research, which is the application of both magnetofrictional and MHD models to investigate which quantity or quantities can best predict the loss of equilibrium of magnetic flux ropes – one of the primary mechanisms behind coronal mass ejections. Using a very large parameter study in 2.5D, we find that in our models eruptions can be predicted reliably using certain ratios between measurable diagnostic quantities. We finish the thesis by describing in detail the development of a brand-new magnetofrictional model, based on an icosahedral grid. Although we have not yet used this code to its full potential, preliminary tests indicate that this new model could be useful in future simulations involving the prediction of magnetic flux rope eruptions