Feynman-α Method Research Articles

General formulae for the Feynman-α method with the bunching technique

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 Pál-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.

Reactor Noise Experiments by Using Acquisition System for Time Series Data of Pulse Train

An acquisition system for the time series data of a pulse train was developed to perform the reactor noise experiments. Using this acquisition system, some important reactor kinetic parameters can be obtained by using various data analysis methods for the reactor noise experiments, which facilitates to achieve new experimental knowledge about characteristics of them proposed so far through direct comparison among the results of various methods. In the present study, the prompt neutron decay constant αpat two near delayed critical states of a core constructed in the Kyoto University Critical Assembly were measured by four well-known data analysis methods; the Feynman-α, the Rossi-α (Type-I and Type-II) and the frequency analysis methods. The results showed that ap values measured by the Type-I Rossi-α and the frequency analysis methods agreed with those by the Feynman-α method considering both effects of the delayed neutrons and the counting loss of neutron counter, whereas it was impossible to obtain the adequate αp values by the Type-II Rossi-α method. Moreover, it was demonstrated that one cannot neglect both effects for the measurement of αp by the Feynman-a method, whereas those by the Type-I Rossi-a and the frequency analysis methods hardly suffered.

Variance-to-mean method generalized by linear difference filter technique

The conventional variance-to-mean method (Feynman-α method) seriously suffers the divergency of the variance under such a transient condition as a reactor power drift. Strictly speaking, then, the use of the Feynman-α is restricted to a steady state. To apply the method to more practical uses, it is desirable to overcome this kind of difficulty. For this purpose, we propose an usage of higher-order difference filter technique to reduce the effect of the reactor power drift, and derive several new formulae taking account of the filtering. The capability of the formulae proposed was demonstrated through experiments in the Kyoto University Critical Assembly. The experimental results indicate that the divergency of the variance can be effectively suppressed by the filtering technique, and that the higher-order filter becomes necessary with increasing variation rate in power.

Experimental investigation of the count-loss effect due to the time interval between counting-gates in the Feynman-α method

Yamane and Hayashi derived a new formula for the variance-to-mean ratio that takes the channel advance time of a multi-channel scaler into account. If the channel advance time is much smaller than the channel width (as in practice), then its effect can be numerically shown to be negligible. It might be for this reason that experimental results that validate the new formula have never been published. However, by introducing an artificial long channel advance time equal to the width of one channel, the effect becomes significant and can be demonstrated experimentally. With these experimental results, the new formula could be validated.

Formulation of data synthesis technique for Feynman-α method

We intend to develop a subcritically monitor based on the Feynman-α method, which detects a change in the prompt neutron decay constant caused by a change in the reactivity of a system containing nuclear fuel materials. For the practical use of this method, quick data processing is necessary to facilitate a real time measurement and it needs to be applicable to a wide range of count rates in the neutron detector. The Feynman-α method, based on pulse counting, has a serious problem relating to the counting statistics, namely the count loss effect due to the dead time of counter itself and the following counting circuit. To eliminate the count loss effect, especially in a high count rate region, a quick correction technique should be established to ensure accurate measurement. As a candidate for this, we have developed the data-synthesis technique which processes synthesized data generated by adding multiple time-series data acquired by independent neutron detectors. The present paper provides the derivation of a formula for this data-synthesis technique and the result of a numerical examination on its applicability.

Experimental investigations of dead-time effect on Feynman-α method

The variance-to-mean measurements were carried out in the ex- and in-core experiments to demonstrate the validity and applicability of the improved expression for data analysis, which was derived by considering the dead-time effect of neutron counter. In the ex-core experiment, the validity of the dead-time term, which was added to the conventional expression for the consideration of the dead-time effect, could be confirmed, and the dead time of the counter employed was also determined. In the in-core (Feynman-α) experiment, it is confirmed that both the inherent decay constant and the dead time could be obtained by the application of the improved expression to data analysis. The above results indicate that the improved expression is available for the data analysis of the Feynman-α experiment performed under high-count-rate conditions.

Count-loss effect due to time interval between counting-gates in Feynman-α method

The Feynman-α (variance-to-mean ratio) method is a neutron noise analysis based on the statistical characteristics of neutron counts accumulated within counting-gate time (gate width). The kinetic parameters of reactor physics are evaluated from the gate width dependence of these characteristics, so that we need to accumulate many neutron count data for various gate widths. Hence huge measuring time is required to get the kinetic parameters with good accuracy. To save measuring time, we make use of the bunching technique proposed by T. Misawa, in which we accumulate time series data of neutron counts within a fundamental gate width T by using a multi-channel scaler device having dwell time T, and synthesize any data for longer gate widths by bunching these data. When the multi-channel scaler device is used in this bunching technique, count loss time exists between adjacent channels because of channel advance time Δ. Although this channel advance time is generally small, it seems that loss of correlated neutron counts brings about a serious problem. In this report, therefore, the rigorous formula containing the channel advance time was derived for a single core system based on the multi-gate Pal-Bell equation without delayed neutrons, in order to investigate the effect due to the loss of correlated neutron counts. From numerical study for a light water moderated-core, it was concluded that the influence of the loss of correlated counts depended on only the channel advance time-to-fundamental gate width ratio Δ T , and it became prominent as Δ T value increased.

Measurement of Prompt Neutron Decay Constant and Large Subcriticality by the Feynman-α Method

The Feynman-α experiments were carried out using light-water-moderated and -reflected cores loaded with highly enriched uranium fuel at the Kyoto University Critical Assembly. An experimental technique using a multichannel scaler was developed to improve the accuracy of measurement and to shorten measuring time. Then, the βeff/l values of single and coupled cores with different neutron spectra were measured to demonstrate the capability of the present technique for measuring the prompt neutron decay constant α. Moreover, the Feynman-α method was applied to measuring large subcriticalities. Through these experiments, it is found that the present technique greatly improves the accuracy of a measurement, and the one-point reactor approximation is applicable to a tightly coupled core. It is also found that the subcriticality down to approximately -35 $ can be measured by this method if the position of the neutron detector is chosen carefully, and the present Feynman-α method can be applied to a subcriticality monitoring system.

Simple determination of low power on reflected reactors using the Feynman-α experiment

When a low power meter for a reactor is calibrated by using the Feynman-α method, the absolute power is obtained by the product of the power deduced from the one-point reactor formula and the g-factor which was introduced as the spatial correction factor on the Rossi-α measurement. In this paper, for the purpose of experimental usage, formulae of the g-factor for the different geometries are derived by one speed approximation and its characteristics are systematically surveyed. A simple formula of the g-factor for a spherical core is presented and applied. This formula can estimate the value of the g-factor with appropriate accuracy.

炉雑音解析研究専門委員会の活動,(II)

The more important activities of the Special Committee on Reactor Noise Analysis of the Atomic Energy Society of Japan are presented. They relate to experimental work undertaken mainly prior to the 2 nd Florida Symposium (1966). A review is presented of results obtained with the application of various techniques, such as, frequency analysis, correlation technique, binary noise technique, Rossi-α method, Feynman-α method and P method, these experiments being undertaken in connection with studies on reactor parameters and stability.