Uncertainty analyses of decay heat summation calculations using JENDL,JEFF, and ENDF files

The uncertainty analyses of decay heat calculation were carried out using major evaluated nuclear data files, JENDL, JEFF, and ENDF. The uncertainties were obtained from the sensitivity of individual fission product nuclide to the decay heat summation calculation. The summation calculation was performed for a burst fission. The sensitivities derived from the analyses were for decay energy, fission yield, and decay constant among the nuclear data included in the summation calculation. The uncertainties of the calculations at 0.1 s after a fission burst are ～10% for JENDL and ～8% for JEFF and ENDF and those at 10⁴ s are less than 2% for all cases. The main differences came from the different adoption of the energy uncertainty. The sensitivity analysis can be used to improve the decay data for decay heat calculation.     

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。     

考虑有效共振积分不确定度的抽样方法研究

在核反应堆物理计算中,核数据库中的截面是影响计算结果的重要因素,研究其不确定度对结果的影响具有重要意义。本文基于3个核评价数据库,利用NJOY程序制作了70种主要锕系核素和部分裂变产物的69群协方差数据库。开发了不确定性分析程序SUACL,该程序利用上述协方差数据库和国际原子能机构制作的69群WIMSD数据库,基于随机抽样的方法产生微扰后的多个核数据库样本;然后利用DRAGON程序对NEA/OECD基准中的PWR栅元进行了计算,计算结果表明,~(235)U和~(238)U两种核素裂变-裂变、辐射俘获-辐射俘获和弹性散射-弹性散射参数对对栅元k∞的相对不确定度与其他程序的吻合良好,验证了程序和理论方法的正确性。同时利用随机抽样方法对5个制作参数的不确定度进行了研究,发现包壳厚度的不确定性对无限增殖因数有较大影响,主要原因是其本身的相对不确定度较大。     

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.     

压水堆燃耗数据库的制作与验证

基于评价数据库ENDF/B-Ⅷ.0和EAF-2010研制了一套适用于CINDER90程序的压水堆用燃耗数据库,该数据库包含中子反应截面、衰变数据和裂变产额数据3部分。中子反应截面的加工分为两步,首先采用Inverted Stack算法和CRECTJ6程序将EAF 2010库的截面分支比融入ENDF/B Ⅷ0库全套中子评价数据,然后用NJOY2016程序处理成63群截面。衰变数据和裂变产额数据分别由MF8/MT457和MF8/MT454数据加工得到,裂变产额数据共包含36个裂变核的60组产额数据。以SFCOMPO 20中Takahama 3压水堆燃料组件为基准题,对研制的燃耗数据库进行了验证。结果表明,本文制作的燃耗数据库的方法是正确的,对于某些核素,如242Amm,制作的数据库比自带库的计算结果更接近实验值。     

Computer codes for shielding calculations — 1969

An extensive library of computer codes useful for radiation transport or shielding calculations is available from the Radiation Shielding Information Center at Oak Ridge National Laboratory. In addition to the point kernel, Monte Carlo, and discrete ordinates codes used for neutron and gamma-ray transport calculations, the collection includes cross-section libraries and codes for processing cross sections, calculating fission product inventories, proton penetration of spacecraft, electron-photon transport, and analyzing neutron activation detector data to determine spectra. A list of the most current codes is given and essential information for each is included.     

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.     

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。     

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.     

强中子场裂变产物中子核反应网络方程研究

本文建立了考虑中子参加反应的裂变产物中子反应及衰变的网络方程,选用求解一阶线性刚性微分方程组的Gear方法,开发了可计算任意裂变产物核数量在不同中子场强度和中子谱下随时间变化的核反应网络方程计算系统FIRENEQ,并配套了裂变产物产额和衰变数据库FPYDDL及裂变产物核中子反应截面数据库FPNCDL。检验结果表明,计算结果正确,程序可靠。利用该程序系统,研究了裂变产物核数量在不同中子场、不同诱发中子能量下随时间的变化。     

235U裂变电离室法及金箔活化法测量热中子注量率的不确定度分析

文章简述²³⁵U裂变电离室法及金箔活化法测量热中子注量率的基本原理,并对测量过程中的各项不确定度因素进行了分析评定,包括中子衰减、裂变计数率、全谱平均反应截面、金箔活性等。计算出的两种注量率测量相对合成标准不确定度满足2%～5％的要求。对减小中子注量率测量不确定度的方法进行了讨论。     

Effect of fission products yield library on the calculation of the nuclide composition of the fuel in sodium-cooled fast reactors

The calculation of the composition of irradiated fuel for different degrees of burnup is a basic problem in the analysis of nuclear-radiological safety of objects holding spent fuel assemblies. The yield of fission products is one of the important initial indicators in burnup calculations. Methods for compiling libraries of fission products yield on the basis of the ENDF/B up-to-date evaluated nuclear data files are described. The nuclide composition of uranium oxide and uranium-plutonium-zirconium metal fuel in sodium-cooled fast reactors is analyzed by means of high-precision calculations performed with different fission product yields libraries using different computer codes MONTEBURNS–MCNP5–ORIGEN2 and the results are presented.     

基于贝叶斯机器学习对中子诱发235U裂变的产额-能量关系的研究

核裂变碎片产额是核能发展和核技术应用领域的重要基础数据,但在实验和理论上获得精确且完整的能量依赖的裂变产额到目前为止都非常困难。本文提出采用贝叶斯机器学习方法对所有收集到的中子诱发235U裂变产额实验数据进行了数据融合学习和评价。基于该评价方法对关键裂变碎片的产额 能量关系进行推断,并得到了二维的碎片累积产额分布随入射中子能量的变化关系。所得的二维产额分布能合理地反映裂变模式随能量增加的演化,但目前结果的不确定度较大,有待进一步改进。     

The Study of (<Emphasis Type="Italic">n</Emphasis>,<Emphasis Type="Italic">d</Emphasis>) Reaction Cross Sections for New Evaluated Semi-Empirical Formula Using Optical Model

Nuclear fusion can be one of the most attractive sources of energy from the viewpoint of safety and minimal environmental impact. The neutron scattering cross sections data have a critical importance on fusion reactor (and in the fusion–fission hybrid) reactors. So, the study of the systematic of (n,d) etc., reaction cross sections is of great importance in the definition of the excitation function character for reaction taking place on various nuclei at energies up to 20 MeV. In this study, non-elastic cross-sections have been calculated by using optical model for (n,d) reactions at 14–15 MeV energy. The excitation function character and reaction Q-values depending on the asymmetry term effect for the (n,d) reaction have been investigated. New coefficients have been obtained and the semi-empirical formulas including optical model non-elastic effects by fitting two parameters for the (n,d) reaction cross-sections have been suggested. The obtained cross-section formulas with new coefficients have been compared with the available experimental data and discussed.     

ENDF/B-VII.1 Neutron Cross Section Data Testing with Critical Assembly Benchmarks and Reactor Experiments

The ENDF/B-VII.1 library is the latest revision to the United States? Evaluated Nuclear Data File (ENDF). The ENDF library is currently in its seventh generation, with ENDF/B-VII.0 being released in 2006. This revision expands upon that library, including the addition of new evaluated files (was 393 neutron files previously, now 423 including replacement of elemental vanadium and zinc evaluations with isotopic evaluations) and extension or updating of many existing neutron data files. Complete details are provided in the companion paper [M. B. Chadwick et al., “ENDF/B-VII.1 Nuclear Data for Science and Technology: Cross Sections, Covariances, Fission Product Yields and Decay Data,” Nuclear Data Sheets, 112, 2887 (2011)]. This paper focuses on how accurately application libraries may be expected to perform in criticality calculations with these data. Continuous energy cross section libraries, suitable for use with the MCNP Monte Carlo transport code, have been generated and applied to a suite of nearly one thousand critical benchmark assemblies defined in the International Criticality Safety Benchmark Evaluation Project?s International Handbook of Evaluated Criticality Safety Benchmark Experiments. This suite covers uranium and plutonium fuel systems in a variety of forms such as metallic, oxide or solution, and under a variety of spectral conditions, including unmoderated (i.e., bare), metal reflected and water or other light element reflected. Assembly eigenvalues that were accurately predicted with ENDF/B-VII.0 cross sections such as unmoderated and uranium reflected ²³⁵U and ²³⁹Pu assemblies, HEU solution systems and LEU oxide lattice systems that mimic commercial PWR configurations continue to be accurately calculated with ENDF/B-VII.1 cross sections, and deficiencies in predicted eigenvalues for assemblies containing selected materials, including titanium, manganese, cadmium and tungsten are greatly reduced. Improvements are also confirmed for selected actinide reaction rates such as ²³⁶U, ^238,242Pu and ^241,243Am capture in fast systems. Other deficiencies, such as the overprediction of Pu solution system critical eigenvalues and a decreasing trend in calculated eigenvalue for ²³³U fueled systems as a function of Above-Thermal Fission Fraction remain. The comprehensive nature of this critical benchmark suite and the generally accurate calculated eigenvalues obtained with ENDF/B-VII.1 neutron cross sections support the conclusion that this is the most accurate general purpose ENDF/B cross section library yet released to the technical community.     

基于经典微扰理论的特征值灵敏度和不确定度分析

核数据不确定度作为组件/栅元计算不确定度的重要来源,备受重视和研究。本文采用经典微扰理论,推导输运计算中keff对于核数据的灵敏度系数和不确定度的计算方法。基于ENDF/B-Ⅶ.1制作多群协方差数据库,并根据所采用的组件输运求解程序的截面模型对分反应道协方差矩阵进行归并。开发灵敏度和不确定度分析程序COLEUS,对传统压水堆燃料栅元进行计算分析。数值结果表明,栅元计算的keff对235 U每次裂变中子产额的扰动最为敏感,238 U俘获截面对keff不确定度的贡献最大。目前的核数据的不确定度会给keff带来0.4%~0.5%的不确定度。     

Alpha Induced Reaction Cross Section Calculations of Tantalum Nucleus

The fusion energy is attractive as an energy source because the fusion will not produce CO₂ or SO₂ and so fusion will not contribute to environmental problems, such as particulate pollution and excessive CO₂ in the atmosphere. The fusion reaction does not produce radioactive nuclides and it is not self-sustaining, as is a fission reaction when a critical mass of fissionable material is assembled. Since the fusion reaction is easily and quickly quenched the primary sources of heat to drive such an accident are heat from radioactive decay and heat from chemical reactions. Both the magnitude and time dependence of the generation of heat from radioactive decay can be controlled by proper selection and design of materials. Tantalum is one of the candidate materials for the first wall of fusion reactors and for component parts of irradiation chambers. Accurate experimental cross-section data of alpha induced reactions on Tantalum are also of great importance for thermonuclear reaction rate determinations since the models used in the study of stellar nucleosynthesis are strongly dependent on these rates (Santos et al. in J Phys G 26:301, 2000). In this study, neutron-production cross sections for target nuclei ¹⁸¹Ta have been investigated up to 100 MeV alpha energy. The excitation functions for (α, xn) reactions (x = 1, 2, 3) have been calculated by pre-equilibrium reaction mechanism. And also neutron emission spectra for ¹⁸¹Ta (α, xn) reactions at 26.8 and 45.2 MeV have been calculated. The mean free path multiplier parameters has been investigated. The pre-equilibrium results have been calculated by using the hybrid model, the geometry dependent hybrid (GDH) model. Calculation results have been also compared with the available measurements in literature.