Ultra low frequency oscillations of the geomagnetic field

The mathematical modelling of hydromagnetic Ultra Low Frequency pulsations of geomagnetic field lines leads to a system of equations which need to be solved under appropriate boundary and magnetospheric conditions. The resulting eigenfunctions and eigenvalues of the equations then describe the various types of pulsation and their behaviour. It is therefore useful to have accurate and quick methods of solving the equations and finding eigenfunctions and eigenvalues. In this thesis, two types of pulsation in particular will be investigated, namely, standing toroidal oscillations of geomagnetic field lines, and the coupled compressional and guided poloidal oscillations which have been associated with the onset of a substorm during a magnetic storm. Firstly an approximation technique for calculating the eigenfunctions and eigenvalues of the toroidal oscillations will be presented, which is easier to use than numerical integration, and more accurate than current approximation techniques, and then the eigenfunctions and eigenvalues of the decoupled compressional oscillation will be presented and discussed. In Chapter 2 the solar wind and its interaction with the earth's magnetic field is described briefly, and then the theory and observations of geomagnetic pulsations (particularly those to be discussed later) are reviewed qualitatively. The theory of transverse and compressional oscillations is then presented in more detail in Chapter 3, leading up to systems of equations describing toroidal, and coupled compressional and poloidal, oscillations. An accurate approximation technique for solving the toroidal equations is then presented in Chapter 4, while the decoupling and solution of the poloidal and compressional equations is described in Chapter 5. Conclusions and suggestions for further research are then presented in Chapter 6