{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/70883"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/70883","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A General Formulation of Neutron Noise for Fast Reactor Systems","abstract":"A general space- and energy-dependent formalism is developed in order to analyze zero-power neutron noise experiments in fast reactor systems. A generalized dispersion equation is combined with theoretical expressions for the experimentally measured power spectral density and variance-to-mean ratio which makes it possible to express these quantities in terms of a double moment of the Laplace and Fourier transformed Green's function of a slowing-down operator rather than those of the full Boltzmann operator.","abstract_html":"A general space- and energy-dependent formalism is developed in order to analyze zero-power neutron noise experiments in fast reactor systems. A generalized dispersion equation is combined with theoretical expressions for the experimentally measured power spectral density and variance-to-mean ratio which makes it possible to express these quantities in terms of a double moment of the Laplace and Fourier transformed Green's function of a slowing-down operator rather than those of the full Boltzmann operator.","abstract_has_math":false,"creators":["Kantrowitz, Mark Lee"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Nuclear Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T04:17:31Z","date_published":"2014-12-16T04:17:31Z","updated_at":"2026-07-22T22:26:03Z","subjects":["Engineering, Nuclear"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8302902"],"render_values":[{"text":"(UMI)AAI8302902","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/70883","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Kantrowitz, Mark Lee"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T04:17:31Z","10000-01-01","1982"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Nuclear Engineering"]},{"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":["Engineering, Nuclear"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/70883","(UMI)AAI8302902"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A general space- and energy-dependent formalism is developed in order to analyze zero-power neutron noise experiments in fast reactor systems. A generalized dispersion equation is combined with theoretical expressions for the experimentally measured power spectral density and variance-to-mean ratio which makes it possible to express these quantities in terms of a double moment of the Laplace and Fourier transformed Green's function of a slowing-down operator rather than those of the full Boltzmann operator.","Several spatial approximations are analyzed in the context of the general formalism. In each case, the power spectral density and variance-to-mean ratio are written in terms of an appropriate fast reactor dispersion law for the medium which can be calculated from the solution to a simple slowing-down equation. The resultant expressions for the power spectral density are analyzed for various combinations of neutron migration descriptions, slowing-down kernels, fission spectrum and cross section models, and detector geometries. The combinations are chosen so to determine the effects of the diffusion theory approximation, detector geometry, reactor geometry, and energy-dependent neutron migration descriptions on the power spectral density, and to evaluate the significance of various space and energy effects in the determination of subcritical reactivity from power spectral density measurements. The results of these analyses demonstrate that energy-dependent descriptions of neutron migration are extremely important in the determination of reliable and accurate subcritical reactivities from power spectral density measurements in fast reactor systems. In addition, they provide a firm foundation for the understanding and proper interpretation of zero-power neutron noise measurements in all types of reactor systems.","Made available in DSpace on 2014-12-16T04:17:31Z (GMT). No. of bitstreams: 1 8302902.pdf: 7631273 bytes, checksum: 5ea7ff1e6a96314559973bebed88e49a (MD5) Previous issue date: 1982","Embargo set by: Seth Robbins for item 71049 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","286 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1982."]},{"key":"dc:title","label":"Title","values":["A General Formulation of Neutron Noise for Fast Reactor Systems"]}]}],"canonical_facts":{"dc:creator":["Kantrowitz, Mark Lee"],"dc:date":["2014-12-16T04:17:31Z","10000-01-01","1982"],"dc:description":["A general space- and energy-dependent formalism is developed in order to analyze zero-power neutron noise experiments in fast reactor systems. A generalized dispersion equation is combined with theoretical expressions for the experimentally measured power spectral density and variance-to-mean ratio which makes it possible to express these quantities in terms of a double moment of the Laplace and Fourier transformed Green's function of a slowing-down operator rather than those of the full Boltzmann operator.","Several spatial approximations are analyzed in the context of the general formalism. In each case, the power spectral density and variance-to-mean ratio are written in terms of an appropriate fast reactor dispersion law for the medium which can be calculated from the solution to a simple slowing-down equation. The resultant expressions for the power spectral density are analyzed for various combinations of neutron migration descriptions, slowing-down kernels, fission spectrum and cross section models, and detector geometries. The combinations are chosen so to determine the effects of the diffusion theory approximation, detector geometry, reactor geometry, and energy-dependent neutron migration descriptions on the power spectral density, and to evaluate the significance of various space and energy effects in the determination of subcritical reactivity from power spectral density measurements. The results of these analyses demonstrate that energy-dependent descriptions of neutron migration are extremely important in the determination of reliable and accurate subcritical reactivities from power spectral density measurements in fast reactor systems. In addition, they provide a firm foundation for the understanding and proper interpretation of zero-power neutron noise measurements in all types of reactor systems.","Made available in DSpace on 2014-12-16T04:17:31Z (GMT). No. of bitstreams: 1 8302902.pdf: 7631273 bytes, checksum: 5ea7ff1e6a96314559973bebed88e49a (MD5) Previous issue date: 1982","Embargo set by: Seth Robbins for item 71049 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","286 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1982."],"dc:identifier":["http://hdl.handle.net/2142/70883","(UMI)AAI8302902"],"dc:subject":["Engineering, Nuclear"],"dc:title":["A General Formulation of Neutron Noise for Fast Reactor Systems"],"dc:type":["text"],"thesis:degree_discipline":["Nuclear Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:03Z"}