Implementing a numerical model for investigating topologically driven magnetic reconnection

Sammanfattning: Magnetic reconnection is an omnipresent phenomenon in plasma physics, and its understanding is therefore of major importance. Most of the models of magnetic reconnection existing nowadays are two-dimensional in space, or require at least a dependence of the magnetic field on two coordinates instead of all three. Relatively recently, three-dimensional reconnection models have begun to appear. In a recent model of three-dimensional reconnection, the process is triggered as soon as the topology of the magnetic field reaches a complexity threshold. It is suggested that at this point even an exponentionally small non-ideality in the magnetic field evolution can trigger magnetic reconnection, at way lower currents than expected in two-dimensional models. This master thesis work presents main ideas of this model and a pseudospectral numerical approach to test its predictions. A pseudospectral approach was chosen due to its high numerical precision. To simplify the verification of this model, non-periodic boundary conditions are necessary along one spatial direction. As pseudospectral approaches are mostly used with full-periodic boundary conditions, analytical work is necessary in order to find relevant boundary conditions and a way to implement them using a pseudospectral approach. In addition to the model and the underlying physics, this report presents how the use of a pseudospectral approach can be maintained with proper boundary conditions and shows first encouraging outputs of the numerical code. The numerical code, as it is today, can bring the plasma topology to a maximum number of exponentiations of about 5 (this number characterizes the topological complexity of the magnetic field). Still unresolved numerical issues prevent the code to bring the number of exponentiations to a value high enough to test the validity of the model itself, where reconnection is expected to happen starting a number of exponentiations of about 10 to 20. Nevertheless, the thesis suggests a number of possible ways to improve the numerical performance of the chosen model that can be pursued in the future.