THE TWO POINT FEYNMAN-α THEORY: A PRACTICAL POINT OF VIEW ON EX-CORE DETECTORS

Chen Dubi, Eshed Magali

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The Feynman-α method is perhaps the most basic realization of the so-called”reactor noise” theory, where static and kinetic parameters of the core are estimated by sampling statistical properties of the neutron count distribution in a sub critical configuration. In the Feynman-α method, the variance to mean ratio (as a function of the detection gate) is sampled, and then through a simple fitting procedure, the α eigenvalue is estimated. The theory behind the Feynman-α method relies on a single-group analysis. From a practical point of view, the single group model requires that the detector be located within or next to the reactor core. Implementation of the Feynman-α method is simple due to three facts: first, although the dynamics are determined by (at least) 5 parameters, the fit is done only for a two-parameter function. Second, these parameters are well separated: one is a constant multiplier and the second is an exponential coefficient. Third, the exponential coefficient has a clear and simple physical interpretation, which can be easily used to estimate the reactivity of the core. In the past decade, the classic Feynman-α theory has been extended to a multi-group setting, using the probability generating function formalism. However, in the resulting formulas, it seems, the above mentioned properties are often lost: implementation would require a fit on a multi-exponential function, whose decay modes are defined by the eigenvalues of a certain”reaction rate” matrix, which may not be explicitly computed, and would depend on parameters that can not be calibrated in a simple manner. The outline of the present study is to analyze a simple two region model: Core and moderator/reflector, were the reactor is located outside the core, within the moderator/reflector. In particular, through direct analysis of the reaction rate matrix, we address the practical implementation of the two point Feynman-α theory: when should we expect a good”separation” of the different decay modes, and when would the reactivity be tractable from the variance to mean ratio.

Original languageEnglish
Title of host publicationProceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021
PublisherAmerican Nuclear Society
Pages1587-1601
Number of pages15
ISBN (Electronic)9781713886310
DOIs
StatePublished - 1 Jan 2021
Event2021 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021 - Virtual, Online
Duration: 3 Oct 20217 Oct 2021

Publication series

NameProceedings of the International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021

Conference

Conference2021 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M and C 2021
CityVirtual, Online
Period3/10/217/10/21

Keywords

  • Feynman-α method
  • Noise Experiments
  • Two group stochastic transport theory

ASJC Scopus subject areas

  • Nuclear Energy and Engineering
  • Applied Mathematics

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