{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/19034"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/19034","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Third-order charged particle beam optics","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Sagalovsky, Leonid"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Cardman, Lawrence S."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T11:54:57Z","date_published":"2011-05-07T11:54:57Z","updated_at":"2026-07-22T22:25:12Z","subjects":["Optics"],"languages":["eng"],"rights":["Copyright 1989 Sagalovsky, Leonid"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8924935","AAI8924935"],"render_values":[{"text":"(UMI)AAI8924935","href":null,"code":true},{"text":"AAI8924935","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/19034","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Cardman, Lawrence S."]},{"key":"dc:creator","label":"Author","values":["Sagalovsky, Leonid"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T11:54:57Z","10000-01-01","1989"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Optics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1989 Sagalovsky, Leonid"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8924935","AAI8924935","http://hdl.handle.net/2142/19034"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Made available in DSpace on 2011-05-07T11:54:57Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8924935.pdf: 3984234 bytes, checksum: 4fd23ac28a47bd73e76857a19e936569 (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:34:12Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:12:58-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Third-order charged particle beam optics"]}]}],"canonical_facts":{"dc:contributor":["Cardman, Lawrence S."],"dc:creator":["Sagalovsky, Leonid"],"dc:date":["2011-05-07T11:54:57Z","10000-01-01","1989"],"dc:description":["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.","Made available in DSpace on 2011-05-07T11:54:57Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 8924935.pdf: 3984234 bytes, checksum: 4fd23ac28a47bd73e76857a19e936569 (MD5) Previous issue date: 1989","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:34:12Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:12:58-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["(UMI)AAI8924935","AAI8924935","http://hdl.handle.net/2142/19034"],"dc:language":["eng"],"dc:rights":["Copyright 1989 Sagalovsky, Leonid"],"dc:subject":["Optics"],"dc:title":["Third-order charged particle beam optics"],"dc:type":["text"],"thesis:degree_discipline":["Physics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:12Z"}