New relativistic solutions for classical charges in an electromagnetic field.

The well-known Lorentz-force equation is expressed covariantly in a new eigenspinor formalism. The eigenspinor in classical electrodynamics arises as an element of bilinear Lorentz transformations in the framework of the Clifford algebra Cℓ3. The paravector subspace of the algebra, a four-dimensional space defined to contain scalars and spatial vectors, shares the metric structure of Minkowski spacetime. With the flexible advantage of Clifford algebras in vector operations and the almost magical property of idempotent projectors of the algebra, the eigenspinor approach simplifies computations and aids geometrical intuition in problems involving the relativistic motion of charged particles. The eigenspinor method is also applied to circularly polarized standing waves. In addition, the spectrum of scattered radiation from a charge in a single pulse is calculated. Finally, new analytic solutions are determined for charged-particle dynamics in a directed plane wave plus a constant electric or magnetic field. The solutions suggest a new method of accelerating charged particles that invites experimental verification and application. (Abstract shortened by UMI.)Dept. of Physics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1998 .Y83. Source: Masters Abstracts International, Volume: 39-02, page: 0520. Adviser: W. E. Baylis. Thesis (M.Sc.)--University of Windsor (Canada), 1998.