Alfvén wave propagation and mode coupling in non-uniform media

In this thesis we investigate the process of MHD Alfvén-fast wave mode coupling in non-uniform media. To do this we begin by developing a Cartesian model using the linear MHD equations. We consider two test cases to verify and benchmark the accuracy of the simulation before beginning our investigations. Using this simulation we present investigations using both 2D and 3D initialisations, which consider the efficiency with which an Alfvén wave pulse can transmit energy through a non-uniformity of Alfvén speed. We also consider the impact on the structure of the Alfvén wave pulse. We find the Alfvén wave transmits energy with good efficiency in each case, despite the wave pulse experiencing significant distortion. We then modify the simulation developed for Wright and Elsden, 2020, in order to investigate the propagation of an Alfvénic wave pulse through a dipole field. In this case we expect the non-uniform magnetic field to force the Alfvénic wave pulse to couple to the fast mode. Again we find highly efficient energy transmission despite significant distortion to the structure of the wave pulse. Overall the results of this thesis demonstrate the robust nature of Alfvén wave pulses, which propagate energy efficiently through non-uniform mediums, even with significant distortion to the spatial structure of the wave pulse. These results show how Alfvén waves are able to play a significant role in the transport of energy in non-uniform mediums, such as planetary magnetospheres, where we may expect wave mode coupling to impact energy transmission.