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
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/ETD-UT-2009-12-712 |
| Date | 21 September 2010 |
| Creators | White, Ryan Lee, 1982- |
| Source Sets | University of Texas |
| Language | English |
| Detected Language | English |
| Type | thesis |
| Format | application/pdf |
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