Derivation of Pál-Bell equations for two-point reactors, and its application to correlation measurements

Murata, Naoyuki; Yamane, Yoshihiro; Nishina, Kojiro

doi:10.1016/0306-4549(81)90098-0

Cited by 8 publications

(2 citation statements)

References 21 publications

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“…used Pal-Bell equations and accounted for a constant transit time to derive a Rossi-alpha equation for a symmetrical two-region system [30]. If transit time is ignored, their equation reduces to that of Edelmann et al [31].…”

Section: Rossi-alpha Measurementsmentioning

confidence: 99%

Analysis of the Temporal Response of Coupled Asymmetrical Zero-Power Subcritical Bare Metal Reactor Systems

Klain

2017

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The behavior of symmetrical coupled-core systems has been extensively studied, yet there is a dearth of research on asymmetrical systems due to the increased complexity of the analysis of such systems. In this research, the multipoint kinetics method is applied to asymmetrical zeropower, subcritical, bare metal reactor systems. Existing research on asymmetrical reactor systems assumes symmetry in the neutronic coupling; however, it will be shown that this cannot always be assumed. Deep subcriticality adds another layer of complexity and requires modification of the multipoint kinetics equations to account for the effect of the external neutron source. A modified set of multipoint kinetics equations is derived with this in mind. Subsequently, the Rossi-alpha equations are derived for a two-region asymmetrical reactor system. The predictive capabilities of the radiation transport code MCNP6 for neutron noise experiments are shown in a comparison to the results of a series of Rossi-alpha measurements performed by J. Mihalczo utilizing a coupled set of symmetrical bare highly-enriched uranium (HEU) cylinders. The ptrac option within MCNP6 can generate time-tagged counts in a cell (list-mode data). The list-mode data can then be processed similarly to measured data to obtain values for system parameters such as the dual prompt neutron decay constants observable in a coupled system. The results from the ptrac simulations agree well with the historical measured values. A series of case studies are conducted to study the effects of geometrical asymmetry in the coupling between two bare metal HEU cylinders. While the coupling behavior of symmetrical systems has been reported on extensively, that of asymmetrical systems remains sparse. In particular, it appears that there has been no previous research in obtaining the coupling time constants for asymmetrically-coupled systems. The difficulty in observing such systems is due in part to the iii v List of Tables viii List of Figures x

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Section: Rossi-alpha Measurementsmentioning

confidence: 99%

Analysis of the Temporal Response of Coupled Asymmetrical Zero-Power Subcritical Bare Metal Reactor Systems

Klain

2017

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“…They are obtained from the same time sequential response but with different formula in the data processing (8). Table 4 shows the eigenvalue separations obtained by Feynman-a method.…”

Section: Rod-drop Methodsmentioning

confidence: 99%

Analysis of First-Harmonic Eigenvalue Separation Experiments on KUCA Coupled-Core.

Kato

Yamamoto

Kitada

et al. 1998

J. Nucl. Sci. Technol.

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The first-harmonic eigenvalue separation, the difference between the fundamental and the first order eigenvalues of the higher harmonic neutron transport equations, which were measured at the Kyoto University Critical Assembly (KUCA) has been analyzed. A method was proposed to calculate the first order eigenvalue based on the discrete ordinate method. The 3-D effect, energy group effect, mesh size effect, and transport effect were investigated. Among these effects, the transport effect was significant and when it was taken into account, the calculated eigenvalue separation approached the measured value on the KUCA coupled-core.

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Two mathematical expressions for the pulse decay in a two-point reactor

Nishina

Murata

Fujii

1985

Annals of Nuclear Energy

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Derivation of Pál-Bell equations for two-point reactors, and its application to correlation measurements

Cited by 8 publications

References 21 publications

Analysis of the Temporal Response of Coupled Asymmetrical Zero-Power Subcritical Bare Metal Reactor Systems

Analysis of the Temporal Response of Coupled Asymmetrical Zero-Power Subcritical Bare Metal Reactor Systems

Analysis of First-Harmonic Eigenvalue Separation Experiments on KUCA Coupled-Core.

Two mathematical expressions for the pulse decay in a two-point reactor

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