A rigorous weight function for neutron kinetics equations of the quasi-static method for subcritical systems |
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| Affiliation: | 1. Centre for Air Transport Management, Cranfield University, MK43 0TR Bedfordshire, United Kingdom;2. Faculty of Business and Economics, Universitat Oberta de Catalunya, Av.Tibidabo, 39-43, 08035 Barcelona, Spain;3. Department of Marketing, Kristiania University College, Post Box 1190, Sentrum, 0107 Oslo, Norway;4. Faculty of Logistics, Molde University College – Specialized University in Logistics, Post Box 2110, 6402 Molde, Norway;1. Seoul Women''s University, Republic of Korea;2. Miami University, OH, USA;3. Korea National Baekdudaegan Aboretum, Republic of Korea;4. Korea University, Republic of Korea;5. Sangji University, Republic of Korea;6. Seoul National University, Republic of Korea;7. National Institute of Environmental Research, Republic of Korea;1. Division of Gynecologic Oncology, Department of Obstetrics, Gynecology & Reproductive Sciences, University of California, San Francisco, 1600 Divisadero Street, San Francisco, CA 94143-1702, USA;2. Department of Radiation Oncology, Stanford University, 400 Pasteur Drive, Stanford, CA 94305, USA;3. Division of Gynecologic Oncology, Department of Obstetrics and Gynecology, University of Washington Medical Center, 1959 NE Pacific Street, Seattle, WA 98195-6460, USA;4. Division of Gynecologic Oncology, California Pacific & Palo Alto Medical Foundation/Research Institute, Sutter Cancer Research Consortium, 3838 California Street #410, San Francisco, CA 94115, USA |
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| Abstract: | The purpose of the present work is to develop an efficient solution method to solve the time dependent multi-group diffusion equations for subcritical systems with external sources using the quasi-static method.Usually, the k-eigenfunction for an adjoint criticality equation is used as a weight function to derive a one-point neutron kinetics equation for the amplitude function in the quasi-static method. It is shown that the use of this k-eigenfunction introduces a first order error due to the change of the flux, when the systems are not close to the critical state. It is shown also that the use of the ω-eigenfunction for the adjoint time dependent equation as the weight function can eliminate such first order error resulting from ignoring the term of first order change of the shape function to solve subcriticality problems, and it gives more accurate results than the use of conventional k-eigenfunctions of the critical adjoint equation. |
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