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The count-loss effect often produces serious problems for the neutron correlation methods that employ a single neutron counting system, since this effect deteriorates the information extracted from subcritical reactor systems. On the other hand, it has been considered that the neutron correlation methods that employ two sets of neutron counting systems, e.g., the covariance-to-mean and the cross-correlation methods, are inherently robust against the count-loss effect in determining the prompt neutron decay constant. The present study investigated this virtue of the latter methods on the basis of a rigorous theoretical approach for treating the count-loss process. The investigation clarified that they indeed show the robustness against the count-loss effect except for extremely high counting rate cases. In the present study, new and alternative formulae of these methods with an explicit correction of the count-loss effect were hence proposed for such extreme cases.

In the previous study, the theoretical formulae of two time-domain reactor noise techniques, i.e., the auto-covariance and the variance-to-mean function techniques, were derived (Kitamura et al., 2018). These two techniques analyse the temporal fluctuation in continuous neutron detector current signals arising from ionization chambers such as the fission chamber. They are hence inherently insensitive to the count-loss effect that sometimes brings serious difficulties to the conventional time-domain techniques that analyse the number of detector pulse signals. With regard to these two techniques, the experimental conditions under which they successfully measure the subcriticality through determination of the prompt neutron decay constant were clarified. However, for mathematical simplicity and the sake of insight, the previous study was performed on the basis of a theoretical model neglecting delayed neutrons. The formulae of these two techniques are hence re-derived by taking delayed neutrons into consideration. Using the formulae thus derived, the delayed neutron effect in these two techniques is discussed.

The conventional time-domain reactor noise techniques analyse the number of neutron detector pulse signals, so that they sometimes encounter serious difficulties owing to the count-loss effect due to the dead time of detector systems. To avoid all the difficulties coming from the count-loss effect, a novel time-domain technique was recently proposed (Pal and Pazsit, 2015). This technique analyses the auto-covariance function of continuous current signals arising from ionization chambers such as the fission chamber, so that it is inherently insensitive to the count-loss effect. In the present study, a different time-domain technique that analyses the integral values of current signals is proposed. With regard to these two techniques, the experimental conditions under which they successfully measure the subcriticality through determination of the prompt neutron decay constant are clarified.

The rotation method is a novel method for detecting nuclear materials using a neutron source such as californium. In this method, while a neutron source is rotated rapidly nearby a measurement object, neutron measurement is carried out by synchronizing the rotation motion. If the object contains a nuclear material, as the rotation speed increases, the larger deformation of time distribution of neutron counts is observed, which in turn resulted to the detection of the nuclear material. In addition to its features of low cost and portability, this method is capable of detecting uranium that emits very few spontaneous fission neutrons. This study presents the fundamental principle of this method and its effectiveness for detecting nuclear materials through the experimental verifications.

Recently, a modified Feynman-alpha technique for the subcritical system driven by periodically triggered neutron bursts was developed. One of the main features of this technique is utilization of a simple formula that is advantageous in evaluating the subcriticality. However, owing to the absence of the theory of this technique, this feature has not been fully investigated yet. In the present study, a theory of this technique is provided. Furthermore, the experimental conditions under which the simple formula works are discussed to apply this technique to the subcriticality monitor for the accelerator-driven system.

The Feynman-alpha method has been frequently employed to measure the subcriticality of a neutron multiplying system through determination of the prompt neutron decay constant. This method, however, often encounters a difficulty with unstable multiplying systems where the neutron population is temporally varying and drifting owing to perturbations due to removal or replacement of fuels and absorbers. In the unstable multiplying systems, the delayed-neutron contribution is remarkably enhanced and makes it difficult to extract the prompt neutron decay constant from the prompt-neutron contribution. The linear difference filter methods that are variants of the Bennett variance one were hence developed to mitigate this kind of difficulty by reducing the delayed-neutron contribution. In the present study, further new variants are proposed. It is shown that the present methods with correlation indices consisting of more than three successive gates can reduce the delayed-neutron contribution more effectively than the conventional ones.

The Simmons-King and the Sjostrand (or the area-ratio) methods have been widely applied in measurement of the subcriticality of reactor systems driven by the pulsed neutron source and operated in the stationary state. In the present study, a theory-based investigation is conducted to examine the time-response of these two methods after perturbations in various parameters. As a result, the prompt neutron decay constant determined by the Simmons-King method shows a good trackability to the subcriticality. In the Sjostrand method, calibration-free determination of the subcriticality is achieved, although it needs a long delay due to an asymptotic behaviour. Furthermore, it is found that the latter method can quickly detect the perturbation in neutron yield of the pulsed neutron source. Therefore, it is expected that a strong on-line monitoring tool for the subcritical reactor system driven by the pulsed neutron source can be developed by combining these two methods.

The temporal evolution of the distribution of the number of neutrons in a time-varying multiplying system, producing only prompt neutrons, was treated recently with the master equation technique by some of the present authors. Such a treatment gives account of both the so-called zero power reactor noise and the power reactor noise simultaneously. In particular, the first two moments of the neutron number, as well as the concept of criticality for time-varying systems, were investigated and discussed. The present paper extends these investigations to the case when delayed neutrons are also taken into account. Due to the complexity of the description, only the expectation of the neutron number is calculated. The concept of criticality of a time-varying system is also generalized to systems with delayed neutrons. The temporal behaviour of the expectation of the number of neutrons and its asymptotic properties are displayed and discussed.

The zero-power reactor noise theory in a steady neutron multiplying medium was extended recently to a medium randomly varying in time to bridge the fields of the zero-power and the power reactor noise. For a time-varying medium in which the transition probability randomly fluctuates, only the use of the probability generating function technique based on the forward master equation approach is practical. However, with the forward master equation approach, the treatment of the joint moments of the neutron number and the medium state leads to a closure problem. Recently, the capability of the moment calculation technique for such cases was extended such that the closure problem could be solved exactly. The present paper describes and demonstrates this closure-free moment calculation technique in a time-varying binary multiplying medium, in which the medium state has two possible realizations. In addition to the first two moments of the neutron number N alone (irrespective of the medium state η), the joint moments of Nn and ηm, i.e., 〈Nnηm〉, were also obtained in a compact form for n = 1, 2 and arbitrary values of m, without a closure assumption. It was found that, for even m values, the asymptotic values of Nn and ηm are uncorrelated, whereas, for odd m values, they are negatively correlated, namely, their covariance is less than zero. The first two moments of the neutron number theoretically obtained were verified by the Monte Carlo technique. A perfect agreement was found between the Monte Carlo and the theoretical solutions. The closure-free moment calculation technique demonstrated in the present paper is expected to be applicable to various other problems related to the birth-and-death process with fluctuations of the transition probability, in which a closure problem occurs.

An effective method of calculating the pulsed Feynman-alpha formula for finite width pulses is introduced and applied in this paper. The method is suitable for calculating both the deterministic and the stochastic Feynman-alpha formulae, while also being capable of treating various pulse shapes through very similar steps and partly identical formulae. In the paper both the deterministic and the stochastic cases are treated for square and Gaussian pulses. The solutions show a very good agreement with the results of currently performed experiments by some of the authors at the Kyoto University Critical Assembly (KUCA). The formulae obtained are also used for a quantitative evaluation of the prompt neutron decay constant from a large number of experiments made at the KUCA for a wide range of parameters such as subcritical reactivity, pulse repetition frequency and pulse width. The suitability of the formulae to determine the prompt neutron decay constant a by curve fitting to the measured data was investigated. It was found that, despite the larger deviation from the traditional Feynman Y(T)-curves from the traditional ones with a constant source (i.e., larger ripples superimposed on a smooth curve), the stochastic pulsing method is superior to the deterministic one in that it yields the correct a value for all subcriticalities. The deterministic method also works fine for most cases, but its application is not so straightforward.

In previous works, the authors have developed an effective solution technique for calculating the pulsed Feynman- and Rossi-alpha formulae. Through derivation of these formulae, it was shown that the technique can easily handle various pulse shapes of the pulsed neutron source. Furthermore, it was also shown that both the deterministic (i.e.{} synchronizing with the pulsing of neutron source) and stochastic (non-synchronizing) Feynman-alpha formulae can be obtained with this solution technique. However, for mathematical simplicity and the sake of insight, the formal derivation was performed in a model without delayed neutrons. In this paper, to demonstrate the robustness of the technique, the pulsed Feynman- and Rossi-alpha formulae were re-derived by taking one group of delayed neutrons into account. The results show that the advantages of this technique are retained even by inclusion of the delayed neutrons. Compact explicit formulae are derived for the Feynman- and Rossi-alpha methods for various pulse shapes and pulsing methods.

In this paper, various approximations of the exponential function are tested from the viewpoint of computational efficiency, i.e. accuracy and computation time. Since considerable part of computation time is devoted to the evaluation of the exponential function in transport calculations using the characteristics method, reduction of its computation time is important. Evaluations of the approximations are carried out on a Linux operating system using two different processors, i.e. Xeon 2.8GHz with 2MB L3 cache and Pentium-III 800 MHz with 512 KB L2 cache. In order to grasp the impact of approximation error of the exponential function on transport calculation results, some sensitivity calculations are executed using the characteristics method. The evaluation results indicate that the table lookup method with linear interpolation or second-order interpolation is computationally efficient for practical calculations.

In this paper, performances of spatial homogenization methods for fuel or non-fuel cells are compared in slab geometry in order to facilitate pin-by-pin core calculations. Since the spatial homogenization methods were mainly developed for fuel assemblies, systematic study of their performance for the cell-level homogenization has not been carried out. Importance of cell-level homogenization is recently increasing since the pin-by-pin mesh core calculation in actual three-dimensional geometry, which is less approximate approach than current advanced nodal method, is getting feasible. Four homogenization methods were investigated in this paper; the flux-volume weighting, the generalized equivalence theory, the superhomogenization (SPH) method and the nonlinear iteration method. The last one, the nonlinear iteration method, was tested as the homogenization method for the first time. The calculations were carried out in simplified colorset assembly configurations of PWR, which are simulated by slab geometries, and homogenization performances were evaluated through comparison with the reference cell-heterogeneous calculations. The calculation results revealed that the generalized equivalence theory showed best performance. Though the nonlinear iteration method can significantly reduce homogenization error, its performance was not as good as that of the generalized equivalence theory. Through comparison of the results obtained by the generalized equivalence theory and the superhomogenization method, important byproduct was obtained; deficiency of the current superhomogenization method, which could be improved by incorporating the “cell-level discontinuity factor between assemblies”, was clarified.

A series of experiments was carried out by using the Kyoto University Critical Assembly and a pulsed neutron generator attached. The experiments were intended to investigate a variance-to-mean technique for measuring the prompt neutron decay constant α of the subcritical reactor system that was driven by the periodic and pulsed neutron source. As the results, it was confirmed that the α value measured by the present technique agreed with a reference value evaluated by the pulsed neutron technique. Furthermore, it was demonstrated that the present technique was available to measure the α value even when the product of α and the repetition period of pulsed neutrons was smaller than unity. Since measurement of α by the pulsed neutron technique is generally difficult under such conditions, it was concluded that the present technique was convenient for measuring the α value.

Derivation of a variance-to-mean formula was performed to obtain the prompt neutron decay constant α of the subcritical reactor system that is driven by the periodic and pulsed neutron source. The formula was derived for an experimental technique where the Y value is measured by choosing an injection of pulsed neutrons as the origin of the counting gate. By using the derived formula, it was indicated that the α value can be easily determined. From this fact, it was concluded that the present formula was useful to measure the α value for future experiments with the accelerator driven system.

Recently, the bunching technique has been widely utilized in the Feynman-α experiment using a multi-channel scaler (MCS) to measure the prompt neutron decay constant α p . Although the bunching technique enables us to perform efficient experiments, it was pointed out that an inherent count-loss process arises due to the channel advance time Δ between adjacent MCS channels. Through derivation of a Feynman-α variance-to-mean formula containing Δ by means of the multi-gate Pal-Bell equation, Yamane and Hayashi ([Yamane, Y. & Hayashi, Y. 1995]. Annals of Nuclear Energy, 22(8), 533) indicated that this count-loss process does not play any important roles when the channel advance time is much smaller than the dwell time T. However, the Δ / T ratio often becomes large in thermal systems at deep-subcritical states or fast ones, because the dwell time should be chosen to be much smaller than reciprocals of α p values for such systems. On the other hand, since the ratio of the dead time d of neutron detectors to the dwell time becomes also large when the Δ / T ratio is not small, the count-loss process due to the dead time cannot be neglected. Therefore, Feynman-α variance-to-mean and covariance-to-mean formulae containing both Δ and d were derived by means of the compound detection probabilities. Based on the covariance-to-mean formula, a new experimental technique was developed and examined at the Kyoto University Critical Assembly. The result of the examination indicated that one can measure exact α p values when Δ / T ratios are known, even though Δ / T and d / T ratios are not small.