An Application of the Lie Group Theory of Continuous Point Transformations to the Vlasov-Maxwell Equations (Plasma Physics)
Haill, Thomas Arthur
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https://hdl.handle.net/2142/70901
Description
Title
An Application of the Lie Group Theory of Continuous Point Transformations to the Vlasov-Maxwell Equations (Plasma Physics)
Author(s)
Haill, Thomas Arthur
Issue Date
1985
Department of Study
Nuclear Engineering
Discipline
Nuclear Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Nuclear
Abstract
The concept of invariance of partial differential equations under Lie groups of continuous point transformations is employed to study the Vlasov-Maxwell equations of plasma physics. These equations are first expressed in arbitrary orthogonal, curvilinear coordinates. Their invariance properties are studied in Cartesian, cylindrical and spherical geometries. One-to-one mappings between the admitted groups of point transformations in the different geometries are demonstrated.
The invariance properties of the electrostatic Vlasov-Maxwell equations in one-dimensional Cartesian, cylindrical and spherical geometries are also studied. Group invariants are used to reduce these equations to similarity form with one less independent variable. An attempt is made to solve the reduced Vlasov-Maxwell equations for a particular self-similar solution.
Finally, relationships are demonstrated between the groups of point transformations admitted by the Vlasov-Maxwell equations and the groups of point transformations admitted by the moment equations derivable from the Vlasov-Maxwell equations.
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