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Chang, Shau-Jin Sagalovsky, Leonid 2011-05-18T17:15:59Z 2011-05-18T17:15:59Z 10000-01-01 1989 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. Submitted by Carolyn Mead (cmead2@illinois.edu) on 2011-05-18T17:15:59Z No. of bitstreams: 1 1989_sagalovsky.pdf: 7134770 bytes, checksum: e117a389994ff1a52f47b03d21e2b9a7 (MD5) Made available in DSpace on 2011-05-18T17:15:59Z (GMT). No. of bitstreams: 1 1989_sagalovsky.pdf: 7134770 bytes, checksum: e117a389994ff1a52f47b03d21e2b9a7 (MD5) Previous issue date: 1989 Restriction data tranferred 2014-07-01T11:14:44-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: Thesis Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Carolyn Mead (cmead2@illinois.edu) on 2011-05-18T17:16:00Z Item is restricted indefinitely. Thesis U of I Only 3478193 http://hdl.handle.net/2142/23945 en 1989 Leonid Sagalovsky third-order charged particle beam optics power series expansion transfer matrices Third-order charged particle beam optics Dissertation / Thesis text Physics Physics University of Illinois at Urbana-Champaign Dissertation Ph.D.