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https://hdl.handle.net/2142/19034
Description
Title
Third-order charged particle beam optics
Author(s)
Sagalovsky, Leonid
Issue Date
1989
Doctoral Committee Chair(s)
Cardman, Lawrence S.
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Optics
Language
eng
Abstract
The motion of a charged particle through a magnetic field configuration can be described in terms of deviation from a certain ideal trajectory. One uses power series expansion of the phase-space coordinates to obtain the transfer matrices for a particular optical system.
In this thesis we present a complete third-order theory of computing transfer matrices and apply it to magnetic elements in an accelerator beam-line. A particular attention is devoted to studying particles' orbits in an extended fringing field of a dipole magnet. Analytical solutions are obtained up to the third order in the formalism of the matrix theory. They contain form factors describing the fall-off pattern of the field. These form factors are dimensionless line integrals of the field strength and its derivative. There is one such integral in the first-order solution, two in the second, and nine in the third.
An alternate way of describing charged particle optics is also presented. It is based on a Hamiltonian treatment and uses certain symplectic operators, which are defined in terms of Poisson brackets, to parametrize the transfer map of a system. We apply this approach to the fringing field problem and obtain a third-order solution. We furthermore show how to convert this solution into conventional transfer matrices by examining the connection between the non-canonical matrix theory and the Hamiltonian description.
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