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Numerical studies of the Fokker-Planck equation

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AlastairMcGowanPhDThesis.pdf (21.80Mb)
Date
1992
Author
McGowan, Alastair David
Supervisor
Sanderson, J. J.
Funder
Science and Engineering Research Council (SERC)
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Abstract
Jorna and Wood recently developed a program that numerically solved the Fokker-Planck equation in spherical geometry. In this thesis, we describe how the original program has been redeveloped to produce a program that is an order of magnitude quicker and that has superior energy and density conservation. The revised version of the program has been used to extend the work of Jorna and Wood on thermal conduction in laser produced plasmas. It has been shown that the effect of curvature on heat flow can be described from a purely geometrical argument and that for aspect ratios similar to those found in targets, the heat flow is reduced by approximately 10%. Also, it has been shown, in contradiction with Jorna and Wood, that the inclusion of the anisotropic portion of the Rosenbluth potentials does not have a significant effect on the heat flow. Even for highly anisotropic plasmas, the inclusion of the anisotropic portion only increases the heat flow by 10%. In addition, the revised version of the program has been used to study the energy relaxation of model distributions It has been shown that the relaxation time of most non - thermal distributions depends on the detailed structure of the distribution and that the normal Spitzer collision time can under-estimate or over-estimate the time required for energy relaxation.
Type
Thesis, PhD Doctor of Philosophy
Collections
  • Mathematics & Statistics Theses
URI
http://hdl.handle.net/10023/13995

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