Neutron energy dependence of delayed neutron yields and its assessments

Incident neutron energy dependence of delayed neutron yields of uranium and plutonium isotopes is investigated. A summation calculation of decay and fission yield data is employed, and the energy dependence of the latter part is considered in a phenomenological way. Our calculation systematically reproduces the energy dependence of delayed neutron yields by introducing an energy dependence of the most probable charge and the odd–even e?ect. The calculated fission yields are assessed by comparison with JENDL/FPY-2011, delayed neutron activities, and decay heats. Although the fission yields in this work are optimized to delayed neutron yields, the calculated decay heats are in good agreement with the experimental data. Comparison of the fission yields calculated in this work and JENDL/FPY-2011 gave an important insight for the evaluation of the next Japanese evaluated nuclear data library (JENDL) .     

基于抽样方法的燃耗计算核素积存量不确定度分析

基于抽样基本原理研究了应用于燃耗计算的不确定度分析方法,并开发了燃耗计算不确定度分析程序。基于评价核数据库ENDF/B-Ⅷ.0的裂变产额标准差和衰变常量标准差计算得到了衰变常量协方差矩阵和带相关性的裂变产额协方差矩阵,并结合SCALE6.2程序包的56群反应截面协方差数据库,对Takahama-3压水堆组件基准题中SF95-4样品进行不确定度分析。计算了反应截面、衰变常量和裂变产额不确定度引起的核素积存量的不确定度。计算结果表明,反应截面的不确定度是锕系核素积存量不确定度的主要来源,裂变产额和衰变常量的不确定度对部分裂变产物的积存量会引入较大的不确定度。但考虑裂变产额相关性后,裂变产额引起的不确定度显著降低。     

Uncertainty quantification of neutron multiplication factors of light water reactor fuels during depletion

Nuclear data-induced uncertainties of infinite neutron multiplication factors (k_∞) during fuel depletion are quantified in a single cell and a 3×3 multi-cell including burnable absorbers. Uncertainties of reaction cross sections, fission yields, decay half-lives and decay branching ratios provided in the JENDL libraries are taken into account. Hundred percent uncertainties are assumed to nuclear data to which uncertainty information are not provided in JENDL. Uncertainties propagation calculations are carried out with the adjoint-based procedure, and required sensitivity profiles of k_∞ with respect to these nuclear data are efficiently calculated by the depletion perturbation theory. Covariance matrices for fission yields and decay data in a simplified burnup chain are successfully generated by the stochastic-based procedure. k_∞ uncertainties of about 0.6% during fuel depletion are obtained, and it is shown that actinoids reaction cross sections are dominant contributors. Nuclide-wise decomposition of the uncertainties and observation of component-wise sensitivity profiles provide physical interpretations. By virtue of the adjoint-based procedure, several parametric surveys are also conducted. Contributions of uncertainties in fission products (FPs) nuclides are quantified, and important nuclides and energy ranges are identified for further evaluation of nuclear data of FP nuclides. Effect of cooling period on k_∞ uncertainties is also discussed.     

Burnup Calculation Sensitivity and Uncertainty Analysis Method of Fission Yield and Decay Half-life

The calculation model of sensitivity coefficient for decay half-life and fission product yield in burnup calculation was derived based on generalized perturbation theory, which considered the interaction between nuclear concentration and neutron flux. A code was developed to calculate sensitivity and uncertainty of effective neutron multiplication factors and nuclide concentration caused by nuclear data. Covariance matrix of fission yield for a simplified burnup library was generated based on standard deviation data of independent fission yield in evaluated nuclear data library to improve the accuracy of uncertainty quantification. Uncertainties induced by decay half-life and fission yield on infinite neutron multiplication factors and nuclide concentration for TMI-1 pin-cell in the UAM burnup benchmark were quantified based on ENDF/B-Ⅶ.1. The numerical results show that the uncertainty of infinite neutron multiplication factors induced by decay half-lives and fission yields is low, while the uncertainty of concentration of some fission product nuclide is high.     

针对裂变产额和半衰期的燃耗计算灵敏度和不确定度分析方法

基于广义微扰理论推导了裂变产额和半衰期的燃耗灵敏度系数理论模型,该模型考虑了原子核密度和中子通量的相互影响,并开发了燃耗计算中有效增殖因数和原子核密度等响应参数对核数据的灵敏度和不确定度分析程序。基于评价核数据中裂变产物独立产额的标准差数据,产生了针对压缩燃耗数据库的裂变产额协方差矩阵,以提高不确定度的计算精度。基于ENDF/B-Ⅶ.1数据库量化了UAM基准题TMI-1栅元无限增殖因数及重要裂变产物和重核的原子核密度由裂变产额和半衰期引入的不确定度。数值结果表明,对于栅元无限增殖因数,裂变产额和半衰期引入的不确定度很小;对于部分裂变产物的原子核密度,裂变产额和半衰期会引入较大的不确定度。     

Validation of Pb nuclear data by Monte Carlo analyses of sample reactivity experiments at Kyoto University Critical Assembly

Sample reactivity experiments on the uncertainty analyses of Pb nuclear data are carried out by substituting Al plates for Pb ones at the Kyoto University Critical Assembly, as part of basic research on Pb–Bi for the coolant. Numerical simulations of sample reactivity experiments are performed with the Monte Carlo calculation code MCNP6.1 together with four nuclear data libraries JENDL-3.3, JENDL-4.0, ENDF/B-VII.0 and JEFF-3.1, to examine the accuracy of cross-section uncertainties of Pb isotopes by comparing measured and calculated sample reactivities. A library update from JENDL-3.3 to JENDL-4.0 is demonstrated by the fact that the difference between Pb isotopes of the two JENDL libraries is dominant in the comparative study, through the experimental analyses of sample reactivity by the MCNP approach. In addition, JENDL-4.0 reveals a slight difference from ENDF/B-VII.0 in all Pb isotopes and ²⁷Al, and from JEFF-3.1 in ²³⁸U and ²⁷Al. Based on these results, further experiments are needed to investigate the uncertainties of Bi isotopes with the use of the Pb–Bi and Bi plates.     

不同235U快裂变缓发中子群参数比较和验证

分析了ENDF/B7、JEFF3.1、JENDL3.3、CENDL2.2及Keepin数据中的²³⁵U快裂变缓发中子群参数的差异,通过CFBR-Ⅱ堆超瞬发临界实验检验了这几套缓发中子数据的准确性。检验结果表明,用于计算反应堆反应性,Keepin缓发中子群参数仍比数据库数据准确;数据库数据中,JEFF3.1的8群结构数据好于其他数据库6群结构数据。     

Validation of decay heat calculation results of ORIGEN2.2 and CASMO5 for light water reactor fuel

Comparing with the fission product nuclide (FP) decay heat summation calculation result in MeV/sec/fission based on the JENDL FP decay and yield data files 2011 for the burst fission, FP decay heat calculated by ORIGEN2.2 coupled with JENDL-4.0 base library ORLIBJ40 was verified at the cooling time from 1 sec to 10⁸ sec for ²³⁵U (thermal), ²³⁸U (fast), ²³⁹Pu (thermal) and ²⁴¹Pu (thermal). For these fission nuclides, FP decay heat calculated by CASMO5 at the same cooling time after a short irradiation (10⁴ sec) was also compared with that of ORIGEN2.2. In the analysis of decay heat measurements at the cooling time from 2.3 years to 27 years consisting of four data sets on the fuel assemblies discharged from the US PWRs and BWRs, and the Swedish PWRs and BWRs, the average values of the ratios of the calculated to measured results (C/E's) were from 0.972 to 1.031 for ORIGEN2.2, and from 0.977 to 1.016 for CASMO5. The standard deviations of C/E's for the four data sets were from 0.02 to 0.03 for the both codes except for those of the US BWR fuel assemblies which were from 0.11 to 0.12. The obtained C/E's were similar to those in the precedent study.     

Simplified Sensitivity Method for Uncertainty Evaluation in Decay-Heat Calculations due to Experimental Errors of Fission Yields

A simplified method to evaluate uncertainty of calculated decay heat is presented. Numerical analyses to provide the sensitivity coefficients were made only for uniform changes of the parameters used for the estimations of fractional yields. The deviations of the decay heat from the reference were approximately proportional to the magnitudes of the parameter changes. Then, a general formula for the sensitivity coefficients was theoretically derived from the first order approximation and the correlation due to the charge conservation law between complementary fragments was taken into account. The sensitivity for the charge distribution width σ A was less than 1/10 of that for the most probable charge ZP. The evaluation of experimental errors for ZP and σ A values were performed using radio-chemical data by Wahl and mass separator data by Clerc, and then the decay heat uncertainties were estimated by using the resultant ZP and σ A experimental errors. Evaluated uncertainties of the decay heat for thermal neutron induced fission of ²³⁶U after burst irradiation were 2.98% at the cooling time of 2.7 s, 1.70% at 8.2 s, 1.72% at 68.7 s, 0.64% at 700 s and 0.74% at 12,000 s, respectively.     

Performance of the CENDL-3.2 and other major neutron data libraries for criticality calculations

Nuclear data are the cornerstones of reactor physics and shielding calculations.Recently,China released CENDL-3.2 in 2020,and the US released ENDF/B-Ⅷ.0 in 2018.Therefore,it is necessary to comprehensively evaluate the criticality computing performance of these newly released evaluated nuclear libraries.In this study,we used the NJOY2016 code to generate ACE format libraries based on the latest neutron data libraries（including CENDL-3.2,JEFF3.3,ENDF/B-Ⅷ.0,and JENDL4.0）.The MCNP code was used to ...     

Determination of AKR-2 leakage beam and verification at iron and water arrangements

In this paper computational procedures and the experimental determination of the AKR-2 (Technical University Dresden) beam parameters are described. The calculations were performed using the MCNPX code (Pelowitz, 2002) and the nuclear data libraries ENDF/B VI.2., ENDF/B VII.0., JEFF 3.1., JENDL 3.3 and BROND 3. The nuclear data were processed using the NJOY code (MacFarlane and Muir, 1994). The measurements were performed with a two-parameter stilbene spectrometer (Bures et al., 2002).     

裂变产额的Zp模型评价方法及燃耗不确定度分析

裂变产额在核科学技术和核工程中有着重要的应用,发展可靠、高效的产额评价方法和相应燃耗计算不确定度分析方法,对于建立高质量的产额数据库具有重要的意义。本文根据裂变产物核衰变模式和衰变分支比,建立独立产额与累积产额的转换矩阵,用于Zp模型的扩展,使之适用于独立产额和累积产额的统一描述,并以此建立了用于产额统一评价的拟合程序ZpFit。把ZpFit程序应用于中子诱发235U裂变产物产额评价,获得了自洽的独立产额、累积产额和相应的协方差数据,并建立ENDF格式的中子诱发235U裂变的产额数据库。在此基础上,计算了UAM燃耗基准题的TMI 1栅元的kinf、重要核素原子核密度的不确定度,比对了本工作评价的产额数据和ENDF/B Ⅷ0评价库中产额数据传递给响应量的相对不确定度,结果基本一致,差异不大。     

Thermal scatter treatment of iron in transport of photons and neutrons

The present paper deals with measured as well as calculated energy spectra of neutron and photon beams from the AKR-2 experimental reactor after having passed through Fe layers and Fe/H₂O combined layers. The experiment results are compared with calculations presented in various nuclear data libraries, such as, ENDF/B VI.2., ENDF/B VII., BROND 3, JENDL 3.3 and JEFF 3.1. Two models were used to calculate the neutron transport. The first takes into account the atomic structure of the material, whereas the other neglects the effect of inter-atomic bonds assuming the atomic nucleus behaviour to follow the free gas model.     

Measurement of 232Th(n,f) and 232Th(n,γ) reaction rates in thorium powder cylinder bombarded with D-T neutrons†

In order to provide reference for the evaluation of thorium parameters for the conceptual design of fusion–fission hybrid energy reactor, a dedicated integral experiment was carried out in a thorium powder cylinder bombarded with D-T neutrons. Thorium capture and fission rates in the 0° direction to the incident D⁺ beam were obtained using the activation method followed by the off-line gamma-ray technique, experimental uncertainties were ～3.1% for thorium capture rate, and were 5.5%, 8.1%, and 6.3% for thorium fission rates based on fission products ^85mKr, ¹⁴³Ce, and ⁸⁷Kr, respectively. The thorium fission rate based on ^85mKr agreed well with the simulation employing ENDF/B-VII.0 library data. The influence of the oxygen contained in the thorium oxide powder and the scattering neutrons from the experimental hall was also evaluated. MCNP simulations employing ENDF/B-Ⅶ.0, JENDL-4.0 library data agreed with experiment within uncertainties except that employing ENDF/B-Ⅶ.1 (6.0%) and CENDL-3.1 (7.9%) for thorium fission rate, while for thorium capture rate, simulation employing JENDL-4.0 agreed with experiment best. The influence of reaction channels of thorium transport medium employing different library data on the thorium reaction rates could be neglected according to the simulation. The thorium capture to fission ratio demonstrated that the fuel breeding efficiency is quite low and energy production plays a leading role under the neutron spectra in this experiment.     

Analysis of integral experiment on erbia-loaded thermal spectrum cores using Kyoto University Critical Assembly by MCNP code with various cross section libraries

Under the project on high burnup nuclear fuel development using erbium as a burnable poison, a series of experiments were performed at the Kyoto University Critical Assembly. The experimental results have formed the basis for this study which aims to analyze the suitability of various evaluated nuclear data libraries for using them in neutronic calculations under the project. The MCNP code was used for the analysis. Calculation model geometry was fully detailed, and ENDF, JENDL, JEFF, and TENDL libraries were used during calculation. For the cross sections of erbium nuclides, the analysis revealed that calculated results upon all the libraries corresponded with experimental data within the errors. However, in some libraries, significant differences were found in case of carbon and uranium nuclides under certain conditions.     

Decay heat

Many aspects of the nuclear fuel cycle require accurate and detailed knowledge of the energy release rate from the decay of radioactive nuclides produced in an operating reactor. In addition to the safety assessment of nuclear power plant, decay heat estimates are needed for the evaluation of shielding requirements on fuel discharge and transport routes and for the safe management of radioactive waste products extracted from spent fuel during reprocessing. The decay heat estimates may be derived by either summation calculations or Standard equations.This paper reviews the development of these evaluation methods and traces their evolution since the first studies of the 1940s. In contrast to many of the previous reviews of this subject, both actinide and fission product evaluation methods are reviewed in parallel. Data requirements for summation calculations are examined and a summary given of available codes and their data libraries. The capabilities of present-day summation methods are illustrated through comparisons with available experimental results. Uncertainties in summation results are examined in terms of those in the basic nuclear data, irradiation details and method of calculation. The evolution of decay heat Standards is described and a brief examination made of their reliability and ability to provide suitably conservative decay heat estimates. Finally, to illustrate the use of present summation methods, comparisons are given of both the actinide and fission product decay heat levels from typical fuel samples in a variety of reactor systems.     

不同核评价数据库中Pb和Bi的截面对铅基快堆k_(eff)的影响

铅基快堆是GIF官方发布的第四代核能系统堆型之一,不同的核评价数据库中铅截面的较大差别会影响铅基快堆物理设计计算的准确性。本文利用国际上最新发布的核评价数据库JENDL-4.0、JEFF-3.2、ENDF/B-Ⅶ.0和BROND-3.1,制作了关键核素Pb、Bi的连续点截面,利用国际基准题评价手册中的PMF035和国际原子能机构发布的铅基快堆RBEC-M基准题以及cosRMC程序,对Pb和Bi的截面对系统有效增殖因数的影响进行了详细研究。对于PMF035带Pb反射层的临界基准题,上述所有核数据库的新版本较旧版本的计算偏差均有所减小,其中BROND的改善最为明显。对于RBEC-M基准题,使用ENDF/B-Ⅶ.0核数据库的计算结果与基准报告中结果符合较好;使用上述其他新版本数据库中截面数据替换计算结果表明,采用不同库中的Pb、Bi截面数据会使计算结果出现不同的偏差,其中,JENDL-4.0中Pb截面对计算结果的影响较Bi截面的影响大。     

Estimation of Beta- and Gamma-Ray Spectra for JENDL FP Decay Data File

Beta- and gamma-ray spectra of fission product nuclides were estimated by a theoretical model for the nuclides having no or incompletely measured spectral data. The estimation was performed with Gross Theory of Beta Decay. The estimated spectra were so stored in JENDL FP Decay Data File 2000 as to keep the consistency between the average decay energy value derived from the spectrum and that used for decay heat analysis. The JENDL spectra of FP nuclides and the aggregate beta- and gamma-ray spectra of fission product nuclides calculated using the JENDL spectra showed good agreement with measured data.     

熔岩玻璃体核素衰变热功率的计算

温度是影响熔岩玻璃体溶解速度的关键因素,为此,本文计算了核试验后10~300 000d内熔岩玻璃体中核素衰变热功率,评估了核素衰变热功率对熔岩玻璃体的温度和溶解速度的影响程度。采用了国际原子能机构给出的100kt TNT当量地下核试验产生的、半衰期大于1a的放射性核素含量,利用其中裂变产物核素137 Cs的含量推算累积裂变产额大于0.1%、半衰期为1d~1a的短寿命裂变产物核素的含量。分析了各核素的放射性衰变特点,采用ENDF/BⅦ库中核素衰变辐射的平均α能量、平均电子能量和平均电磁辐射能量计算各核素在熔岩玻璃体内因衰变而沉积的能量。计算结果表明:核素衰变热功率呈分段幂函数衰减;在10~2 000d、2 000~60 000d和60 000d之后的时段内,衰变热功率分别主要源于短寿命裂变产物核素、长寿命裂变产物核素和锕系元素。核素衰变热功率对熔岩玻璃体的温度和溶解速度的影响不大,1 000d后影响非常小。