Asymptotic Analysis of Time-Dependent Neutron Transport Coupled with Isotopic Depletion and Radioactive Decay
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.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 920859
- Report Number(s):
- UCRL-CONF-224942; TRN: US200805%%210
- Resource Relation:
- Conference: Presented at: M&C+SNA 2007, Monterey, CA, United States, Apr 15 - Apr 19, 2007
- Country of Publication:
- United States
- Language:
- English
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