Distinguishing the coronal magnetic field and its evolution can unlock key information on solar energetic eruptions such as the Coronal Mass Ejections (CMEs). CMEs are formed as magnetic flux ropes, i.e. magnetic field lines twisted about each other. They are the main drivers of space weather effects on Earth. Understanding the structure of the internal magnetic field of the CME would help determine the severity of the resulting geomagnetic storm. Predicting the onset and the orientation of the flux rope axis is a major focus of current space weather research.
For this purpose, a numerical study on the kinematic emergence of a twisted flux rope into a coronal magnetic field is performed using the Magneto-frictional method (MFM). The MFM is an exciting prospect as it is sufficiently accurate and computationally inexpensive. The initiation of the eruption is through ideal Magnetohydrodynamic (MHD) kink instability. In this case, the kink instability occurs when the windings of the field lines about the flux rope axis exceeds a critical value.
This thesis presents the set-up of the Fan & Gibson flux rope with different configurations. This was in hopes of studying the slow energization of the coronal field arcade with the emergence of a current carrying flux rope. The results of the simulations presented here show that the several key factors such as the height at which the flux rope is stopped and its twist play a major role in the dynamics of the flux rope in making it kink unstable. One of the main motivations was to use the results to discuss the performance of the MFM in comparison to MHD and how capable it is in capturing ideal MHD phenomenon.
The simulations are also used to investigate the formation of sigmoidal current layer often seen before the onset of eruption. In the results presented here, the sigmoidal ’S’ shaped current layer is formed as the flux rope becomes kink unstable. This sigmoidal current layer is analysed for different configurations of the flux rope. These results have suggested that accurate dynamic modelling of the coronal magnetic field is essential for successful space weather prediction purposes.
