Alfven Resonance Absorption in a Non-Uniform Magnetofluid

One of the requirements for controlled nuclear fusion is the attainment of a high enough temperature so that nuclei can ovecome their mutual coulomb repulsion and fuse, releasing a great deal of energy in the process. To reach the required temperatures energy must be fed into the plasma. One method is high frequency heating of the plasma using electomagnetic waves, where the incoming wave is used to excite some of the many naturally occurring modes present in the plasma, which then decay giving up their energy to the plasma. This project deals with Alfven resonance absorption in a plasma for sup-plementry heating of a magnetically confined plasma by extending the paper 'Alfven Resonance Absorption in a Magnetofluid' by Diver and Laing. The paper is unusual in that it treats not only the Alfven resonance but also the magnetosonic resonances which are then taken to be separated in the plasma by a small distance delta so that the absorption coefficient is dependent on both of these singularities. In this original paper some incorrect modelling assumptions about the magnetosonic singularities were made and dealt only with case of small theta, where theta is the angle between the x component of the incident wave vector and the magnetic field. This thesis extends the work to finite theta and rederives the subsequent work in the paper. This work required the calculation of Bessel functions in which both the argument and the order, which were non integer varied as a continuous function of theta, this part of the project, the numerical simulation of the reflection formula, was a significant part of the whole project