Applicability of several Feynman-α formulae to a subcritical thermal reactor

ABSTRACT

For an university training and research reactor of Kindai University, the Feynman-α analyses based on several formulae are carried out to examine the applicability of these formulae to the subcritical thermal reactor system. The original formula, in which the effect of delayed neutrons is neglected, results in a prompt-neutron decay constant sensitive to an upper limit of the gate time range of the analysis and consequently has difficulty in determining the decay constant. This difficulty originates from the neglect of delayed neutrons. An improved formula, where a term proportional to the gate time is added to the original formula, gives a desirable decay constant insensitive to the upper limit and the insensitive decay constant well agrees with that obtained from the Rossi-α analysis. The application of a difference filtering technique also leads to a successful result similar to the above improved formula. An alternative index Z to the traditional index Y of the original formula has been sometimes employed as an indication of the non-Poisson nature of the counting statistics. The Z is defined as dividing the Y by the mean number of neutron counts accumulated in the gate time. The formula for the Z never results in a reasonable decay constant even though the effect of delayed neutrons is considered. This study suggests that the improved formula considering delayed neutrons for the Y and the formula for the difference filtering technique should be employed to determine the prompt-neutron decay constant of thermal reactors.

KEYWORDS:

• UTR
• thermal reactor
• feynman-α
• formula
• applicability
• prompt neutron
• decay constant
• delayed neutron

Disclosure statement

No potential conflict of interest was reported by the authors.

Nomenclature

$A_i$ residues of zero-power reactor transfer function

F total fission rate in a whole core [1/s]

G(s) zero-power reactor transfer function

$s_i$ poles of zero-power reactor transfer function [1/s] $({\alpha }_i=-s_i)$

T gate time (width) [s]

$T_{Max}$ upper limit of gate-time range set for Feynman-α analysis [s]

Greek

$\alpha$ prompt-neutron decay constant [1/s] $\left(\alpha ={\alpha }_7=-s_7\right)$

${\beta }_i$ effective fraction of ith delayed-neutron group

$\epsilon$ detection efficiency of a neutron counter

${\lambda }_i$ decay constant of precursor of ith delayed-neutron group [1/s]

${\lambda }_f$ probability per unit time that a neutron induces a fission event [1/s]

$\mathrm{\Lambda }$ generation time [s]

$\bar{\nu }$ first factorial moment of number of neutrons generated in fission event

$\overline{\nu \left(\nu -1\right)}$ second factorial moment of number of neutrons generated in fission event

$\rho$ reactivity