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DOE OSTI · 1680005

A Lumped Stochastic Model of Coupled Neutronic Assemblies

Prinja, Anil Kant
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Abstract

The objective of the present work is to apply the Harris ansatz to coupled assemblies in a lumped setting, i.e., ignoring the neutron phase dependence, which hitherto has not been considered. A Master equation for the single-time joint distribution of neutron number in each assembly, accounting for transfer of neutrons from one assembly to another via leakage transition probabilities and intercept or view factors is derived from which equations for the mean and variance in each assembly are developed. Because of the neutronic coupling, it is necessary to additionally compute the correlation function between pairs of assemblies which gives an expanded set of moment equations to solve. The reactivity of each assembly is allowed to vary with time, although a formal mechanism that is responsible for reactivity coupling between assemblies is not considered or proposed. Following Harris, it is then hypothesized that the number distribution in each assembly is a gamma distribution with assembly-specific mean and variance computed exactly from the moment equations. Illustrative numerical results are presented for the moments of a system of four coupled assemblies under various reactivity and neutronic coupling scenarios. The gamma distribution is then used to compute the probability that the neutron population exceeds a threshold value in any assembly. The report concludes with a discussion of recommended further work on this problem.

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73 NUCLEAR PHYSICS AND RADIATION PHYSICS

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BibTeXRIS

Prinja, Anil Kant. 2020-10-19. A Lumped Stochastic Model of Coupled Neutronic Assemblies. https://doi.org/10.2172/1680005

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