In this paper, two equations from plasma physics are analyzed using two different mathematical procedures to yield information of interest for fusion energy. In the first case, Lie’s technique of computing symmetries of differential equations is applied to a specific case of the Grad-Shafranov equation. The case considered contains the majority of exact solutions from the literature. The full symmetry group is computed and new group-invariant solutions are obtained from these symmetries. The basic results and methods behind this technique are given along with several plots of the level sets or flux surfaces of the new solutions. In addition, a mathematical technique which was first used to prove the non-existence of solitons in quantum field theory is employed to derive an integral relation for any solution of the Sinh-Poisson equation. The original technique is modified to allow for a finite boundary and results are computed for two different boundary geometries. / text

A dual photomultiplier system and a field probe has been used to study the optoelectrical phenomena is commercially pure SF6 and mixtures posºtºve of SF6 with oxygen free N2, underAimpulse voltages in a point plane gap. The luminous extension of the predischarge, the electric field at the cathode, and where possible the velocity of discharge propagation has been measured. An extrapolation technique has been used to estimate the critical pressure, and the results have been compared with those of other recently published work. An attempt has been made to establish the different regimes of operation with regard to leader formation both prior to and after streamers cross the gap. This has been done with particular emphasis on the d/r ratio and the field variation with increment in voltage. The cloud model has been shown to be inoperative under impulse voltage conditions such as in this thesis. Comparisons have been made of critical pressure determined under d. c. conditions with any available results obtained using impulse voltages. An attempt has been made to explain the large discrepancy particularly in SF6 between the calculated and experimentally determined values of Vi , the corona initiation voltage. The internal electric field and the electrostatic radius, -of the, discharge channel has been estimated. The analysis of the experimental results has been carried out for the stem and leader stages of the discharge development using an electrostatic model, prior to the streamers crossing the, gap and reaching the cathode, By comparing the , results with those of other authors, it has been shown that : the results of the leader internal electric field are in reasonable agreement with the work of others

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