Solution of the Feynman Equation for Time Evolving Fission Chains

Technical Report · Tue Sep 10 04:00:00 EDT 2019

DOI:https://doi.org/10.2172/1561452· OSTI ID:1561452

Snyderman, Neal J. ^[1]; Chandrasekaran, Hema ^[1]

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1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

The partial differential equation proposed by Feynman describing the time evolution of a fission chain in metal is solved by a method also proposed by Feynman. The partial differential equation is reduced to a transcendental algebraic equation. The solution involves roots of a 7th order polynomial. Both the roots and the transcendental equation are then solved numerically. Two populations are computed from the probability generating function, the internal number of neutrons in time, and the accumulated number of leaked neutrons in time. This same equation also describes a limit of a thermal reactor, where induced fission is totally driven by neutrons that have thermalized and are diffusing in a moderator.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: AC52-07NA27344
• OSTI ID: 1561452
• Report Number(s): LLNL-TR--789326; 987410
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS