Asymptotic Analysis of Time-Dependent Neutron Transport Coupled with Isotopic Depletion and Radioactive Decay

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We describe an asymptotic analysis of the coupled nonlinear system of equations describing time-dependent three-dimensional monoenergetic neutron transport and isotopic depletion and radioactive decay. The classic asymptotic diffusion scaling of Larsen and Keller [1], along with a consistent small scaling of the terms describing the radioactive decay of isotopes, is applied to this coupled nonlinear system of equations in a medium of specified initial isotopic composition. The analysis demonstrates that to leading order the neutron transport equation limits to the standard time-dependent neutron diffusion equation with macroscopic cross sections whose number densities are determined by the standard system of ordinary ... continued below

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Brantley, P S September 27, 2006.

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We describe an asymptotic analysis of the coupled nonlinear system of equations describing time-dependent three-dimensional monoenergetic neutron transport and isotopic depletion and radioactive decay. The classic asymptotic diffusion scaling of Larsen and Keller [1], along with a consistent small scaling of the terms describing the radioactive decay of isotopes, is applied to this coupled nonlinear system of equations in a medium of specified initial isotopic composition. The analysis demonstrates that to leading order the neutron transport equation limits to the standard time-dependent neutron diffusion equation with macroscopic cross sections whose number densities are determined by the standard system of ordinary differential equations, the so-called Bateman equations, describing the temporal evolution of the nuclide number densities.

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PDF-file: 10 pages; size: 75.9 Kbytes

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  • Presented at: M&C+SNA 2007, Monterey, CA, United States, Apr 15 - Apr 19, 2007

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  • Report No.: UCRL-CONF-224942
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 920859
  • Archival Resource Key: ark:/67531/metadc901899

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  • September 27, 2006

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  • Sept. 27, 2016, 1:39 a.m.

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  • Nov. 22, 2016, 8:01 p.m.

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Brantley, P S. Asymptotic Analysis of Time-Dependent Neutron Transport Coupled with Isotopic Depletion and Radioactive Decay, article, September 27, 2006; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc901899/: accessed July 22, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.