Geomagnetic pulsations are ultra-low frequency (ULF) oscillations of the geomagnetic field that have been observed in the magnetosphere and on the Earth since the 1800’s. In the 1960’s in situ observations of the solar wind suggested that the source of pulsation activity must lie beyond the magnetosphere. In this work the influence of several solar wind plasma and interplanetary magnetic field (IMF) parameters on Pc3 pulsations are studied. Pc3 pulsations are a class of geomagnetic pulsations with frequency ranging between 22 and 100 mHz. A large dataset of solar wind and pulsation measurements is employed to develop two empirical models capable of predicting the Pc3 index (an indication of Pc3 intensity) at one hour and five minute time resolution, respectively. The models are based on artificial neural networks, due to their ability to model highly non-linear interactions between dependent and independent variables. A robust, iterative process is followed to find and rank the set of solar wind input parameters that optimally predict Pc3 activity. According to the parameter selection process the input parameters to the low resolution model (1 hour data) are, in order of importance, solar wind speed, a pair of time-based parameters, dynamic solar wind pressure, and the IMF orientation with respect to the Sun-Earth line (i.e. the cone angle). Input parameters to the high resolution model (5 minute data) are solar wind speed, cone angle, solar wind density and a pair of time-based parameters. Both models accurately predict Pc3 intensity from unseen solar wind data. It is observed that Pc3 activity ceases when the density in the solar wind is very low, even while other conditions are favourable for the generation and propagation of ULF waves. The influence that solar wind density has on Pc3 activity is studied by analysing six years of solar wind and Pc3 measurements at one minute resolution. It is suggested that the pause in Pc3 activity occurs due to two reasons: Firstly, the ULF waves that are generated in the region upstream of the bow shock does not grow efficiently if the solar wind density is very low; and secondly, waves that are generated cannot be convected into the magnetosphere because of the low Mach number of the solar wind plasma due to the decreased density.

Ultra Low Frequency (ULF) waves are a ubiquitous feature of Earth's outer atmosphere, known as the magnetosphere, having been observed on the ground for almost two centuries, and in space over the last 50 years. These waves represent small oscillations in Earth's magnetic field, most often as a response to the external influence of the solar wind. They are important for the transfer of energy throughout the magnetosphere and for coupling different regions together. In this thesis, various features of these oscillations are considered. A detailed background on the history and previous study of ULF waves relevant to our work is given in the introductory chapter. In the following chapters, we predominantly use numerical methods to model ULF waves, which are carefully developed and thoroughly tested. We consider the application of these methods to reports on ground and spaced based observations, which allows a more in depth study of the data. In one case, the simulation results provide evidence for an alternative explanation of the data to the original report, which displays the power of theoretical modelling. An analytical model is also constructed, which is tested on simulation data, to identify the incidence and reflection of a class of ULF wave in the flank magnetosphere. This technique is developed with the aim of future applications to satellite data. Further to this, we develop models both in Cartesian and dipole geometries to investigate some of the theoretical aspects of the coupling between various waves modes. New light is shed on the coupling of compressional (fast) and transverse (Alfvén) magnetohydrodynamic (MHD) wave modes in a 3D dipole geometry. Overall, this thesis aims to develop useful numerical models, which can be used to aid in the interpretation of ULF wave observations, as well as probing new aspects of the existing wave theory.