Feynman-α and Rossi-α analyses for a subcritical reactor system driven by a pulsed spallation neutron source in Kyoto University Critical Assembly

ABSTRACT

For a subcritical reactor system driven by a periodically pulsed spallation neutron source in Kyoto University Critical Assembly (KUCA), the Feynman-α and the Rossi-α neutron correlation analyses were carried out to determine the prompt-neutron decay constant and quantitatively to confirm a non-Poisson characteristics of the neutron source. In these correlation analyses, a non-negligible contribution of delayed neutrons and a non-Poisson character of the source were considered, and each pulse was assumed to be a delta function. When a neutron counter was placed closely to the reactor core, the prompt-neutron decay constant determined from the present Feynman-α analysis well agreed with that done from a previous analysis for the same subcritical system driven by an inherent neutron source. However, the decay constant determined from the present Rossi-α analysis was in poor agreement with that done from the above previous analysis. This disagreement originated from an inevitable excitation of a higher mode. In the Rossi-α counting probability distribution, the excitation deformed a sharp cusp arising from the delta function to a smooth convex shape. When the data around the convex top were masked for least-squares fitting of the present Rossi-α formula, the disagreement could be successfully resolved. Compared with the previous Feynman-α and Rossi-α analyses under the Poisson inherent source, the non-Poisson spallation source definitely enhanced the respective prompt-neutron correlation amplitudes. The enhancement rate increased with an increase in subcriticality. Moreover, the Degweker’s factor (m ₂-m ₁ ²)/m ₁ ² of 0.067 ± 0.011, which indicated a non-Poisson character of the present spallation source, could be determined from the present correlation analysis and the non-zero value of the factor convinced us that the present source had a different statistical distribution from the Poisson.     

Statistical error estimation of the Feynman-α method using the bootstrap method

Applicability of the bootstrap method is investigated to estimate the statistical error of the Feynman-α method, which is one of the subcritical measurement techniques on the basis of reactor noise analysis. In the Feynman-α method, the statistical error can be simply estimated from multiple measurements of reactor noise, however it requires additional measurement time to repeat the multiple times of measurements. Using a resampling technique called “bootstrap method,” standard deviation and confidence interval of measurement results obtained by the Feynman-α method can be estimated as the statistical error, using only a single measurement of reactor noise. In order to validate our proposed technique, we carried out a passive measurement of reactor noise without any external source, i.e. with only inherent neutron source by spontaneous fission and (α,n) reactions in nuclear fuels at the Kyoto University Criticality Assembly. Through the actual measurement, it is confirmed that the bootstrap method is applicable to approximately estimate the statistical error of measurement results obtained by the Feynman-α method.     

Power spectral analysis for a thermal subcritical reactor system driven by a pulsed 14 MeV neutron source

A series of power spectral analyses for a thermal subcritical reactor system driven by a pulsed 14 MeV neutron source was carried out at Kyoto University Critical Assembly (KUCA), to determine the prompt-neutron decay constant of the accelerator-driven system (ADS). The cross-power spectral density between time-sequence signal data of two neutron detectors was composed of a familiar continuous reactor noise component and many delta-function-like peaks at the integral multiple of pulse repetition frequency. The prompt-neutron decay constant inferred from the reactor noise component of the cross-power spectral density was consistent with that obtained by a pulsed neutron experiment. However, the reactor noise component of the auto-power spectral density of each detector was hidden by a white chamber noise in the higher-frequency range and this feature resulted in a considerable underestimation of the decay constant. For several runs with a low pulse-repetition frequency, furthermore, we attempted to infer the decay constant from point data of the delta-function-like peaks. The analysis for a run under a slightly subcritical state resulted in the consistent decay constant; however, those for other runs under significantly subcritical states underestimated the decay constant. Considering the contribution of a spatially higher mode to the point data, the above underestimation was solved to obtain the consistent decay constant. While the Feynman-α formula for a pulsed neutron source is too complicated to be fitted directly to variance-to-mean ratio data, the present analysis on frequency domain is much simpler and the conventional formula based on the first-order reactor transfer function is available for fitting to power spectral density data.     

Accelerator driven subcritical system as a future neutron source in Kyoto University Research Reactor Institute (KURRI) —Basic study on neutron multiplication in the accelerator driven subcritical reactor—

A basic study on the nuclear characteristics in the accelerator driven subcritical reactor (ADSR) was performed through a series of neutronics calculations in view of a future neutron source in Kyoto University Research Reactor Institute (KURRI) for the joint use program among researchers of Japanese universities. In this series of calculations, it was assumed that three kinds of monoenergetic neutrons were isotropically generated at the center of spherical and homogeneous cores with different moderator-to-fuel volume ratios in order to examine the spectrum mismatching effect between injected neutrons and fission neutrons born in the subcritical core. The results of calculations clearly showed the spectrum mismatching effect on the neutron multiplication in the ADSR.     

Study on inherent neutron sources in MSR

The molten salt reactor(MSR) has received much recent attention. The presence of beryllium and the mixing of actinides with light nuclei in the fuel salt result in a relatively strong neutron source that can affect the surveillance at subcritical and transient characteristics during operation. In this study, we predict the inherent neutron sources based on a MSR model. The calculation shows that in the fresh core, the inherent neutron sources are mainly from alpha-induced neutrons. After power operation, the inherent neutron sources become remarkably stronger due to photoneutrons. Although being an insignificant part in the total neutron population during operation, the inherent neutron sources can be used as the installed neutron source after shutdown. If the MSR has continuously operated at full power(2 MWt) for 10 days,then there would be no need for the installed source within80 days after shutdown. After operating constantly for500 days, the installed neutron source can be eliminated within 2 years after shutdown.     

Sensitivity of fuel failure detection by the delayed neutron measurement in the primary cooling circuit of HANARO

The sensitivity of the fuel failure detection system based on the delayed neutron measurement in the primary cooling circuit of a research reactor, HANARO is investigated. The neutrons around the primary cooling pipe during normal operation of HANARO are measured with BF₃ detector, and their count rate is 900 cps. They are regarded as photoneutrons due to the high energy gamma-rays from N-16 and delayed neutrons from the fission of the uranium contaminated on the fuel surface. The contribution of each neutron source is analyzed by measuring the changes of the neutron counts before and after the abrupt shutdown of reactor. In order to estimate the sensitivity of the fuel failure detection, the neutron count rate of BF₃ detector is predicted by Monte Carlo calculation. The generation, transportation and detection of the photoneutrons and the delayed neutrons are simulated for the geometry similar to the experiments. From the calculations and experiments, it is ascertained that the photoneutron contribution to the total count rate is about 20–30%, and that the delayed neutron count rate is expected to about 720 cps. The fission rate in the flow tube of the reactor core by the surface contamination is obtained from the deduced delayed neutron count rate, and it is estimated to 1.66 × 10⁵ fissions/cm³ s. From the MCNP calculation, it is confirmed that this fission rate can originate from the contaminated uranium of 120 μg, which is about 13% of the maximum allowable surface contamination on the fuel surface. The sensitivity of U-235 mass detection by the delayed neutron measurement can be concluded to about 0.2 μg-U²³⁵/cps. Thus, it is confirmed that the delayed neutron detection is sensitive enough to monitor the fuel failure, and that the neutron count rate is high enough for stable signal with short counting time.     

核电厂无源启动中子探测器选型与试验研究

为监测核电厂首循环装料、停堆以及启动过程中的堆芯状态,国内外核电厂一般在堆芯引入2个一次中子源组件,但一次中子源均为国外进口,存在进口受限的问题。为解决此问题,研究首循环取消一次中子源组件,采用燃料组件自发裂变产生的中子作为启动用中子源。燃料组件自发裂变产生的中子强度远低于一次中子源。针对以上情况,需在堆外采用更高灵敏度的探测器进行中子注量率的监测。本文在分析各种高灵敏度探测器基本原理的基础上,给出高灵敏度中子探测器的选型建议,并对其性能进行了试验验证,试验结果表明:3He正比计数管即使在γ剂量率大于0.1 Gy/h时,设置合适的甄别电压,也可以有效甄别γ噪声,试验验证的最大γ剂量率为1.0 Gy/h。      

有源符合中子法探测高浓缩铀的技术研究

开展了有源符合中子法探测^235U富集度为90．34％的小圆柱状金属铀块裂变材料的方法与技术研究。使用有源井型中子符合计数装置测量金属铀块中^235U受Am-Li中子源诱发后产生的裂变中子,运用最小二乘法的计算方法将测得的中子总计数率、真符合计数率分别与金属铀块质量做线性拟合,其线性相关性系数达0．999;在此基础上,进一步测量了在相同质量金属铀的条件下不同源、样距及不同样品形状的中子计数变化趋势。     

Study of the neutron multiplication effect in an active neutron method

The neutron multiplication effect appears when an item contains large amounts of nuclear material. The neutron multiplication effect in this paper means the effect of subsequent fission reactions which are caused by fission neutrons produced by interrogation neutrons from a neutron generator. The previous active neutron method could not distinguish between first-fission and subsequent-fission neutrons and might overestimate the amount of nuclear material. However, the neutron multiplication effect in the active neutron method has not been adequately investigated. We discuss the evaluation method of the multiplication effect in the fast neutron direct interrogation method, one of the active neutron methods, using simulations with the Monte Carlo code MVP and experiments involving uranium waste drums. The first-generation neutrons from an external neutron source generate fission neutrons called second-generation neutrons, the second-generation neutrons generate third-generation neutrons, and so on. This study supposes that the neutron multiplication effect is mainly caused by the third-generation neutrons under the condition that the fourth-generation neutrons are much fewer. This paper proposes a correction method for the neutron multiplication effect in the measured data.     

某压水堆首次装料次临界监督结果分析

某压水堆使用已活化的二次中子源（ASNS）完成首次装料。在首次装料期间,堆内临时中子探测器（TND）发生响应试验结果远高于仿真结果问题和计数率大幅度下降问题。为了查明上述问题的原因,监督工作组对二次中子源特性和由ASNS建立的辐射场进行了分析,对核燃料次临界增殖中子对TND计数率的影响进行了分析和验证,对使用ASNS进行反应堆首次装料的次临界监督数据进行了分析。结果表明：TND周围的辐射场为γ射线和中子形成的混合辐射场;在中子源组件与TND之间安装核燃料组件后,核燃料次临界增殖中子对TND计数率的影响是使其升高;ASNS衰变产生了大量γ射线,TND输出的γ脉冲在主放大器内发生峰堆积导致脉冲幅度畸变,TND响应试验结果远高于仿真结果的原因是脉冲幅度甄别器无法有效甄别畸变后的γ脉冲和中子脉冲;TND计数率大幅度下降的原因为核燃料中的铀屏蔽掉了由ASNS射向TND的大部分γ射线。源量程通道和TND的运行状态满足首次装料程序对次临界监督设备的要求。     

Neutronics analysis of a stacked structure for a subcritical system with LEU solution driven by a D-T neutron source for 99Mo production

The utilization of neutrons markedly affects the medical isotope yield of a subcritical system driven by an external D-T neutron source.The general methods to improve the utilization of neutrons include moderating,multiplying,and reflecting neutrons,which ignores the use of neutrons that backscatter to the source direction.In this study,a stacked structure was formed by assembling the multiplier and the low-enriched uranium solution to enable the full use of neutrons that backscatter to the source direction and further improve the utilization of neutrons.A model based on SuperMC was used to evaluate the neu-tronics and safety behavior of the subcritical system,such as the neutron effective multiplication factor,neutron energy spectrum,medical isotope yield,and heat deposi-tion.Based on the calculation results,when the intensity of the neutron source was 5×1013 n/s,the optimized design with a stacked structure could increase the yield of 99Mo to 182 Ci/day,which is approximately 16％higher than that obtained with a single-layer structure.The inlet H2O coolant velocity of 1.0 m/s and initial temperature of 20℃were also found to be sufficient to prevent boiling of the fuel solution.     

Improvement of Neutron Source Introduction Method for Absolute Measurements of Low Reactor Power

The neutron source introduction method was applied to absolute measurements of low reactor power at the Static Experiment Critical Facility STACY. To obtain the effective neutron source intensity more accurately, which is a key parameter for the source introduction method, the neutron source is newly defined as fission neutrons from the first fission reaction caused by neutrons emitted from the external neutron source. To obtain the newly defined effective neutron source intensity, the probability that a neutron from the external neutron source causes a fission reaction is calculated using the Monte Carlo code MCNP. This calculation took into consideration the three-dimensional complicated core structures. Furthermore, the fission reaction distribution, fundamental mode forward and adjoint flux distribution in a critical state were calculated using the three-dimensional transport code THREEDANT. Following the principle of the neutron source introduction method, an external neutron source was inserted near the STACY core tank and the reactor power was measured. The reactor powers by the neutron source introduction method were in good agreement with the ones from the analyses of the FP activity generated by high power operation.     

铀水栅零功率反应堆的功率刻度

反应堆功率的测量,在堆功率高时一般用热工方法,功率低时,可用各种堆物理方法,如中子源引进法、中子统计法和全堆总裂变率法。 中子源引进法误差较大,中子统计法需知探测器在堆内的效率和堆的β_(aff)值,此二者都较难测量。全堆总裂变率法是由测量堆的总裂变率来求得堆功率,它可避免前面两种方法的缺点,但需依赖裂变率相对分布的     

Pulsed neutron source measurements in the subcritical ADS experiment YALINA-Booster

A subcritical zero-power source-driven coupled core, the YALINA-Booster, has been constructed for experimental investigations of neutron kinetics of source-driven systems. In this study, the reactivity of two subcritical configurations has been determined by the area ratio method. The prompt neutron decay constants have been evaluated through slope fitting of the prompt neutron decay as well as through the pulsed Rossi-α method. It is shown that the slope fitting method and the pulsed Rossi-α method give stable results whereas the area ratio method results show spatial dependence. The reasons for the spatial spread are addressed.     

Preliminary measurements of the prompt neutron decay constant in MASURCA

Pulse counting techniques have been used to measure the prompt decay constant = (β - ) / Λ in the MASURCA reactor of CEA at critical state. The data has been analyzed in time domain using Rossi- and Feynman- techniques, and in frequency domain using the cross power spectral density.

The Rossi- technique has been studied using one and two detectors. Due to the strong inherent spontaneous fission source, the one-detector variant gives a very strong white-noise signal, which is absent in the two-detector method. Because each neutron detected recorded not only a pulse, but also an echo after 120 ns, corrections had to be made to the theory applied.

The Feynman- technique is even more sensitive to the echo in the signals, and quite large corrections had to be made. Nevertheless the results obtained are in reasonable agreement with those of the correlation methods. For both measurement techniques, experiments of long duration are needed to get accurate results. The results obtained agree within 10% with calculations.

The prompt decay constant has also been measured with a continuous current technique. From the cross power spectral density thus obtained, the -value is in agreement with that of the pulse counting techniques.     

Determination of neutron generation time in miniature neutron source reactor by measurement of neutronics transfer function

The prompt neutron generation time Λ and the total effective fraction of delayed neutrons (including the effect of photoneutrons) β have been experimentally determined for the miniature neutron source reactor (MNSR) of Syria. The neutron generation time was found by taking measurements of the reactor open-loop transfer function using newly devised reactivity-step- ejection method by the reactor pneumatic rabbit system. Small reactivity perturbations i.e. step changes of reactivity starting from steady state, were introduced into the reactor during operation at low power level i.e. zero-power. Relative neutron flux and reactivity versus time were obtained. Using transfer function analysis as well as least square fitting techniques and measuring the delayed neutrons fraction, the neutron generation time was determined to be 74.6±1.57 μs. Using the prompt jump approximation of neutron flux, the total effective fraction of delayed neutrons was measured and found to be 0.00783±0.00017. Measured values of Λ and β were found to be very consistent with calculated ones reported in the Safety Analysis Report.     

24.4KeV中子诱发^235U裂变的产额测量

一、前言 对~(235)U热中子裂变已经作了充分的研究,裂变产物的产额作了广泛的测量,并对实验数据进行了多次编评。但是对于其它单能中子诱发~(235)U裂变研究还远远不够,尤其是keV能区的中子更是如此。J.G.Cuninghame等测量了130-1700keV中子诱发~(235)U裂变中一些核素的产额。但是低于130keV中子诱发的裂变研究,文献中未见过报道。为了研究产额随中子能     

A New Static and Dynamic One-Point Equation and Analytic and Numerical Calculations for a Subcritical System

In this study we derived a new one-point equation based on the balance of fission neutrons. The equation has the same form as the conventional equation using k _eff which represents the neutron balance in the whole core. The variables of the new equation are the number of fission neutrons and delayed neutron precursors, and the coefficients are the multiplication rates of prompt fission neutrons, delayed neutrons and source neutrons. In the conventional equation, the variables are weighted by the adjoint flux; in other words, they are adjusted to the critical state. The variables in the new equation correspond to actual values even in a deep subcritical state; hence, the physical meaning of each term is clear.

The dynamic behavior of a slab core with an external source was analyzed through calculations based on the new equation. Deterministic and probabilistic calculations of the equation were performed for a typical accelerator-driven system in the static state.     

Effects of neutron spectrum and external neutron source on neutron multiplication parameters in accelerator-driven system

The neutron multiplication parameters: neutron multiplication M, subcritical multiplication factor k_s, external source efficiency φ^*, play an important role for numerical assessment and reactor power evaluation of an accelerator-driven system (ADS). Those parameters can be evaluated by using the measured reaction rate distribution in the subcritical system. In this study, the experimental verification of this methodology is performed in various ADS cores; with high-energy (100 MeV) proton–tungsten source in hard and soft neutron spectra cores and 14 MeV D–T neutron source in soft spectrum core. The comparison between measured and calculated multiplication parameters reveals a maximum relative difference in the range of 6.6–13.7% that is attributed to the calculation nuclear libraries uncertainty and accuracy for energies higher than 20 MeV and also dependent on the reaction rate distribution position and count rates. The effects of different core neutron spectra and external neutron sources on the neutron multiplication parameters are discussed.     

球形浓缩铀装置的中子价值和裂变率分布测量

为得到Rossi-α测量临界装置的瞬发中子衰减常数的空间修正因子，利用²⁵²Cf中子源测量带贫化铀反射层的球形浓缩铀临界装置(CFBR-Ⅱ)的中子价值空间分布，同时用浓缩铀裂变电离室测量该装置的裂变率空间分布，得到该装置的空间修正因子为1.096。