Derivation and quantitative analysis of the differential self-interrogation Feynman-alpha method

Anderson, Johan; Пал, Л.; Pázsit, Imre; Chernikova, Dina; Pozzi, Sara A.

doi:10.1140/epjp/i2012-12021-3

Cited by 5 publications

(12 citation statements)

References 9 publications

(13 reference statements)

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“…The comparison of the neutron, gamma and total (neutron and gamma) variance to mean ratios is made by using quantitative values of the transition probabilities and reaction intensities obtained in a way similar to that described in [9,[13][14][15][16][17]. In addition, some quantities were obtained via processing a ptrac file.…”

Section: Numerical Illustration Of the New Versions Of The Feynman-almentioning

confidence: 99%

The neutron–gamma Feynman variance to mean approach: Gamma detection and total neutron–gamma detection (theory and practice)

Chernikova

Axell

Avdic

et al. 2015

Nuclear Instruments and Methods in Physics Research Section A:

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Two versions of the neutron-gamma variance to mean (Feynman-alpha method or Feynman-Y function) formula for either gamma detection only or total neutron-gamma detection, respectively, are derived and compared in this paper. The new formulas have particular importance for detectors of either gamma photons or detectors sensitive to both neutron and gamma radiation. If applied to a plastic or liquid scintillation detector, the total neutron-gamma detection Feynman-Y expression corresponds to a situation where no discrimination is made between neutrons and gamma particles. The gamma variance to mean formulas are useful when a detector of only gamma radiation is used or when working with a combined neutron-gamma detector at high count rates. The theoretical derivation is based on the Chapman-Kolmogorov equation with the inclusion of general reactions and corresponding intensities for neutrons and gammas, but with the inclusion of prompt reactions only. A one energy group approximation is considered. The comparison of the two different theories is made by using reaction intensities obtained in MCNPX simulations with a simplified geometry for two scintillation detectors and a 252 Cf-source. In addition, the variance to mean ratios, neutron, gamma and total neutron-gamma, are evaluated experimentally for a weak 252 Cf neutron-gamma source, a 137 Cs random gamma source and a 22 Na correlated gamma source. Due to the focus being on the possibility of using neutron-gamma variance to mean theories for both reactor and safeguards applications, we limited the present study to the general analytical expressions for Feynman-alpha formulas.

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Section: Numerical Illustration Of the New Versions Of The Feynman-almentioning

confidence: 99%

The neutron–gamma Feynman variance to mean approach: Gamma detection and total neutron–gamma detection (theory and practice)

Chernikova

Axell

Avdic

et al. 2015

Nuclear Instruments and Methods in Physics Research Section A:

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“…The equation system and its solution is rather analogous to the case of the Feynman-alpha equations in two-group theory and with one neutron energy group but including delayed neutrons as given in Ref. [13] and in Ref. [16], respectively.…”

Section: A Two-point Variance To Mean Formulamentioning

confidence: 99%

“…In this con-tribution, a stochastic theory for a branching process in a one group neutron population applied to two domains is studied, based on the previous results of Refs [7,8,13]. In particular, we consider a counterpart of the Differential Self-interrogation Variance to Mean (DSVM) formula, that is derived by using the master equation or Kolmogorov forward approach [13]. The model includes a spontaneous fission source of fast neutrons, absorption in both domains, thermal fission, and detection of fast neutrons.…”

Section: Introductionmentioning

confidence: 99%

Two-point theory for the differential self-interrogation Feynman-alpha method

et al. 2012

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A Feynman-alpha formula has been derived in a two region domain pertaining the stochastic differential self-interrogation (DDSI) method and the differential die-away method (DDAA). Monte Carlo simulations have been used to assess the applicability of the variance to mean through determination of the physical reaction intensities of the physical processes in the two domains. More specifically, the branching processes of the neutrons in the two regions are described by the Chapman -Kolmogorov equation, including all reaction intensities for the various processes, that is used to derive a variance to mean relation for the process. The applicability of the Feynman-alpha or variance to mean formulae are assessed in DDSI and DDAA of spent fuel configurations.

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“…In line with the above, the suggestion of new Safeguards technique for MOX/spent fuel assay [26], the Differential Die-away Self-Interrogation (DDSI) technique, displayed the interest towards the energy-dependent aspects of neutron counting. In connection with this, the two-group Feynman-alpha theory was elaborated in [27] where delayed neutrons were neglected, and in [28] with inclusion of delayed neutron precursors. However, fast fission and thermal detections were neglected in both papers.…”

Section: Introductionmentioning

confidence: 99%

“…However in some cases, for example, when the fission chambers are used as detectors, the energy importance makes way for the regiondependent aspect. This issue has not well been studied previously, although some expressions for the one-group tworegion Feynman-alpha formulas can be found in [31]. However, even these investigations are limited to the case of delayed neutron precursors having been neglected and detections accounted for only in one region.…”

Section: Introductionmentioning

confidence: 99%

A general analytical solution for the variance-to-mean Feynman-alpha formulas for a two-group two-point, a two-group one-point and a one-group two-point cases

Chernikova¹,

Ziguan²,

Pázsit³

et al. 2014

Eur. Phys. J. Plus

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This paper presents a full derivation of the varianceto-mean or Feynman-alpha formula in a two energy groupand two spatial region-treatment. The derivation is based on the Chapman -Kolmogorov equation with the inclusion of all possible neutron reactions and passage intensities between the two regions. In addition, the two-group one-region and the two-region one-group Feynman-alpha formulas, treated earlier in the literature for special cases, are extended for further types and positions of detectors. We focus on the possibility of using these theories for accelerator-driven systems and applications in the safeguards domain, such as the differential self-interrogation method and the differential dieaway method. This is due to the fact that the predictions from the models which are currently used do not fully describe all the effects in the heavily reflected fast or thermal systems. Therefore, in conclusion a comparative study of the two-group two-region, the two-group one-region, the onegroup two-region and the one-group one-region Feynmanalpha models is discussed.

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Derivation and quantitative analysis of the differential self-interrogation Feynman-alpha method

Cited by 5 publications

References 9 publications

The neutron–gamma Feynman variance to mean approach: Gamma detection and total neutron–gamma detection (theory and practice)

The neutron–gamma Feynman variance to mean approach: Gamma detection and total neutron–gamma detection (theory and practice)

Two-point theory for the differential self-interrogation Feynman-alpha method

A general analytical solution for the variance-to-mean Feynman-alpha formulas for a two-group two-point, a two-group one-point and a one-group two-point cases

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