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https://hdl.handle.net/2142/23945
Description
Title
Third-order charged particle beam optics
Author(s)
Sagalovsky, Leonid
Issue Date
1989
Doctoral Committee Chair(s)
Chang, Shau-Jin
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
third-order
charged particle
beam optics
power series expansion
transfer matrices
Language
en
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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