Monte Carlo uncertainty quantification of the effective delayed neutron fraction

The applicability of Monte Carlo techniques, namely the Monte Carlo sensitivity method and the random-sampling method, for uncertainty quantification of the effective delayed neutron fraction β_eff is investigated using the continuous-energy Monte Carlo transport code, MCNP, from the perspective of statistical convergence issues. This study focuses on the nuclear data as one of the major sources of β_eff uncertainty. For validation of the calculated β_eff, a critical configuration of the VENUS-F zero-power reactor was used. It is demonstrated that Chiba's modified k-ratio method is superior to Bretscher's prompt k-ratio method in terms of reducing the statistical uncertainty in calculating not only β_eff but also its sensitivities and the uncertainty due to nuclear data. From this result and a comparison of uncertainties obtained by the Monte Carlo sensitivity method and the random-sampling method, it is shown that the Monte Carlo sensitivity method using Chiba's modified k-ratio method is the most practical for uncertainty quantification of β_eff. Finally, total β_eff uncertainty due to nuclear data for the VENUS-F critical configuration is determined to be approximately 2.7% with JENDL-4.0u, which is dominated by the delayed neutron yield of ²³⁵U.     

Application of Finite Element Method to Two-Dimensional Multi-Group Neutron Transport Equation in Cylindrical Geometry

The finite element method is applied to the spatial variables of multi-group neutron transport equation in the two-dimensional cylindrical (r, z) geometry. The equation is discretized using regular rectangular subregions in the (r, z) plane. The discontinuous method with bilinear or biquadratic Lagrange's interpolating polynomials as basis functions is incorporated into a computer code FEMRZ. Here, the angular fluxes are allowed to be discontinuous across the subregion boundaries.

Some numerical calculations have been performed and the results indicated that, in the case of biquadratic approximation, the solutions are sufficiently accurate and numerically stable even for coarse meshes. The results are also compared with those obtained by a diamond difference S _n code TWOTRAN-II. The merits of the discontinuous method are demonstrated through the numerical studies.     

A Proposal on Data Treatment In the Feynman-α Experiment

A new algorithm of Monte Carlo criticality calculations for implementing Wielandt's method, which is one of acceleration techniques for deterministic source iteration methods, is developed, and the algorithm can be successfully implemented into MCNP code. In this algorithm, part of fission neutrons emitted during random walk processes are tracked within the current cycle, and thus a fission source distribution used in the next cycle spread more widely. Applying this method intensifies a neutron interaction effect even in a loosely-coupled array where conventional Monte Carlo criticality calculation methods have difficulties, and a converged fission source distribution can be obtained with fewer cycles. Computing time spent for one cycle, however, increases because of tracking fission neutrons within the current cycle, which eventually results in an increase of total computing time up to convergence. In addition, statistical fluctuations of a fission source distribution in a cycle are worsened by applying Wielandt's method to Monte Carlo criticality calculations. However, since a fission source convergence is attained with fewer source iterations, a reliable determination of convergence can easily be made even in a system with a slow convergence. This acceleration method is expected to contribute to prevention of incorrect Monte Carlo criticality calculations.     

锰浴法测量中子源发射率中各修正因子的蒙特卡罗计算

在采用锰浴法对放射性同位素中子源的发射率进行测量时,MnSO₄溶液中⁵⁵Mn仅俘获部分源中子,故需考虑对未被⁵⁵Mn俘获部分的修正。用蒙特卡罗粒子输运程序MCNP对中子源强标准装置的锰浴系统进行模拟计算,对实验测量结果进行修正,并通过由国际计量局（BIPM）组织的中子源强度国际比对,验证了计算所建立模型的可靠性。利用MCNP程序的微扰计算功能,通过考虑MnSO₄溶液的密度、源及其承托物材料的密度、源的位置、锰浴半径以及反应截面的改变对计算结果的影响,对模拟计算结果的不确定度进行了详细评定,提供了一种蒙特卡罗模拟计算结果不确定度的评定方法。     

一种基于~(103)Rh(n,n′)~(103)Rh~m反应的快中子注量监测方法

给出了一种基于~(103)Rh(n,n′)~(103)Rh~m反应监测快中子注量的方法。根据干扰核素半衰期不同的特点,选取合适的冷却和测量时间,降低了~(103)Rh(n,n′)~(103)Rh~m活化率测量中干扰核素的影响。根据152Eu标定实验结果,利用遗传算法优化探测器尺寸,建立探测器蒙特卡罗算法模型。利用模型校正~(99)Mo-~(99)Tcm放射源实验效率,解决了探测器效率标定和射线自吸收问题。开展了快中子注量监测,实验结果与铁、硫、镍等快中子监测箔一致性较好,测量不确定度约为13.1%。     

Application of CR-39 Track Detector to Neutron Spectrum Measurement

A new technique for estimating the neutron energy spectrum with CR-39 track detectors has been proposed for application to a singly pulsed neutron field where prevailing counters cannot operate properly. The CR-39 sample exposed to neutrons was intermittently etched, then the major and minor radii of respective etch pits were measured for each etching stage and the growth curve was obtained. The analysis method of growth curves was also designed, with which both the energy and the angle of recoil protons could be evaluated and converted into the energy of neutrons incident normally.

The neutron irradiation experiments were carried out with the 46 MeV electron linear accelerator at the Research Reactor Institute, Kyoto University. It was confirmed from comparing with the reference spectrum measured by the neutron time-of-flight method that the present growth-curve method is useful for the estimation of the neutron energy distribution between about 0.3 and 2 MeV. Moreover, we have experimentally examined the unfolding method suggested by Matiullah and Durrani in order to extend the application of CR-39 detector to higher energies.     

最优化方法应用于裂变核反应理论计算的研究

中子诱发裂变核反应的反应机制十分复杂,需由光学模型、复合核模型等共同描述,因此需同时对大量参数进行调节才能正确描述裂变核反应数据。本文在FUNF裂变核反应模型基础上,利用先进的最优化方法MINUIT,结合MPI的并行计算方法,研究了MINUIT对裂变核反应调参的工作原理,并以中子诱发238U的裂变核反应为例,验证了裂变核反应数据优化方法的可靠性。     

Count-loss effect in subcriticality measurement by pulsed neutron source method, (I) investigation on count-loss effect in determination of neutron decay constant

The count-loss effect in determination of neutron decay constant by pulsed neutron source method was investigated. It was found that overestimation of neutron decay constant due to count-loss effect is seen while underestimation appears superiorly as the intensity of pulsed neutron source is getting higher. It was further demonstrated that the well-known count-loss correction procedures are not effective for overestimation although they suppress underestimation. Therefore, the pulsed neutron source method should be modified so as to have robustness against the count-loss effect.     

90°伴随粒子法D-D中子产额测量修正因子计算

开展了90°伴随粒子法D-D中子产额测量中的修正因子理论计算方法研究,基于MATLAB软件平台,开发了用于修正因子计算的计算机程序.计算给出了厚靶条件下,入射氘能量在20-700 keV范围,90°伴随粒子法D-D中子产额测量各向异性修正因子Rthick、中子和质子产额比(Yd,n/Yd,p)thick及总修正因子RY,并与早先的研究结果进行了对比,分析了计算结果的不确定度,总修正因子计算数据的不确定度约为2％.     

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.     

脉冲中子源法测量铅基零功率反应堆Venus-Ⅱ次临界度

本文利用脉冲中子源法测量了铅基零功率反应堆Venus-Ⅱ在4种燃料棒装载情况下的次临界度,简要介绍了脉冲中子源法测量次临界度的原理、测量系统及实验结果等,通过面积比法分析了各探测器的计数率时间谱,确定了系统次临界度。测量结果表明,当系统有效增殖因数在0.94附近时,不同位置处的探测器测量结果之间呈明显差异。基于MCNP理论模拟计算,分别用空间修正因子和普适的微扰法对面积比测量结果进行必要修正,消除了空间效应对实验结果的影响。在系统有效增殖因数约0.94时,经修正的面积比法能精确给出系统的次临界度。本实验研究为ADS嬗变系统的次临界度精确测量提供了一种有效方法。     

Use of Alcan's Al-B4C metal matrix composites as neutron absorber material in TN International's transportation and storage casks

Abstract

Major issues in the area of transportation and/or storage of radioactive materials are reliability and safety of engineering components. Among the functions to be undertaken, transportation and storage systems shall allow the criticality control of the transported matter, the control of its temperature, as well as the capacity to withstand the mechanical stresses due to normal, incidental and accidental conditions of use. In most cases, criticality control requires the use of an internal arrangement made of a neutron absorber material, which must also have high thermal conductivity properties to ensure the temperature control. When, as in many AREVA-TN International applications, the design takes credit of the neutron absorber material as a structural component, it must show high mechanical performance. Alcan's Al-B₄C metal matrix composites (Al-B₄C MMCs) meet all the above mentioned requirements, due to their special capability of capturing neutrons, their light weight, and their superior thermal conductivity and mechanical properties. The significant advantage of Alcan's technology is its flexibility with regards to a wide range of boron carbide contents and matrix alloys (from AA1XXX to AA6XXX). This enables the adjustment of the properties to the exact needs of the design. TN International presently uses extruded and/or rolled Al-B₄C MMC parts in several of its internal arrangements. The present paper gives an overview of the manufacture processes of Alcan's Al-B₄C MMCs, from the mixing of B₄C into liquid aluminium to the extrusion and rolling operations. It describes the methods and results for the qualification tests in terms of the neutron absorption, thermal, physical and mechanical properties of the material. Finally, details are given on the use of Alcan's MMCs as a neutron absorber with enough credit for structural material in TN International's TN24 designs.     

Monte Carlo Analysis of Streaming Effect through Annular Gaps around Piping Legs in Sodium Pool to Secondary Sodium Activation of the Demonstration Fast Breeder Reactor

A top-entry loop-type reactor is one of the favorable options for Demonstration Fast Breeder Reactor (DFBR) which is now under development in Japan as a part of conceptual design study. Annular gaps around top-entry piping raise neutron streaming in upward direction in the sodium pool of reactor vessel. It enhances neutron flux level around decay heat exchangers (DHX's) in the pool and at the penetrations in primary biological shield for piping connecting to the vessels of intermediate heat exchangers (IHX's), and consequently enhance secondary sodium activations in these heat exchangers, which is one of the main issues for shielding design. In this study, three-dimensional Monte Carlo analysis method was applied to make precise evaluation of the neutron streaming effect with combination of some techniques for reduction of statistical error within reasonable CPU time. It is established that the contribution of neutron streaming to the secondary sodium activation in DHX's hardly reaches a level of 30% and that design analysis with two-dimensional discrete ordinates method gives conservative evaluation of the secondary sodium activations in DHX's and IHX's.     

X射线衍射技术用于酒精检测的实验研究

酒精是液体安检中非常重要的检测对象,准确的溶液浓度分析,有利于安检系统对于液体物质危险等级的评定以及后续的检查。衍射峰也可能成为一项重要的物理参数,为液体分类提供有价值的识别信息。采用X射线衍射（XRD）实验方法,对不同浓度的酒精溶液进行了X射线衍射实验。为提高衍射谱测量的准确性,对实际测量中的系统误差进行了分析,并提出了几何标定方法。经过几何标定和能谱校正,得到了衍射峰位与酒精浓度的关系。     

Measurements of Resonance Neutron Self Shielding Factors for Gold and Silver Using Slowing-Down Time Spectrometer

Abstract

The resonance neutron self-shielding factors for cylindrical samples of various thicknesses of gold and silver have been measured in the narrow energy groups with a lead slowing-down time spectrometer as a neutron source.

Calculation by Wigner's rational approximation gives 10–20% smaller self shielding factors than the experimental ones except for the limiting cases of sample thickness.

The collision probability theory, on the other hand, was found to give rather good agreement with the experiments in all the measured cases.     

Irradiation Behaviors of Nuclear Grade Graphite in Commercial Reactor, (III) Mechanical Properties

Bending and compressive strengths, and Young's modulus were measured for Pechiney nuclear grade graphite irradiated in the temperature range 220～400°C in the environment of CO₂ in a commercial reactor, up to the neutron fluence 6.2 × 10¹⁹ and 2.2 × 10²⁰n/cm² (E>0.85 MeV), respectively.

All of them increased owing to neutron irradiation, and the changes in both strengths were almost similar in the whole range of irradiation temperature, however the changes in Young's modulus depended on irradiation temperature.

It was clarified in the present experiment that both strengths were related with Young's modulus and the relation could be expressed by the formula σ=kE ⁿ, where σ and E are strength and Young's modulus, respectively, and n is constant which has different value for bending or compressive strength and also for their measured direction.     

Variant of Green's Function Nodal Method for Neutron Diffusion

A variant of the Green's function nodal method derived from the boundary integral form of the multigroup neutron diffusion equation in rectangular geometry is presented. As usual in the nodal methods, the multi-dimensional diffusion equation is integrated in the transverse direction. The resulting 1D diffusion equation is solved following the Boundary Element technique in one dimension. In this way a weighted residual method is obtained, with a Green's function for weighting, but with different boundary conditions than normally applied in the Green's function nodal methods. Mathematical formulation of the method is given and the iteration procedure is described. A computer program BINDIF has been designed, based on the new method. Its capabilities include the solution of the multigroup neutron diffusion equation of ID, 2D and 3D rectangular lattices. The BINDIF program has been checked against other methods used for global reactor calculations on benchmark problems, representative of realistic power reactor cores. The results indicate that the method is attractive to design highly efficient algorithms for a large mainframe, a personal computer or a parallel processor.     

Averaging the neutron diffusion equation

This paper presents a general theoretical analysis of the neutron motion problem in a nuclear reactor, where large variations on neutron cross-sections normally preclude the use of the classical neutron diffusion equation. A volume-averaged neutron diffusion equation (VANDE) is derived which includes correction terms to diffusion and nuclear reaction effects. A method is presented to determine closure-relationships for the VANDE (e.g., effective diffusivity). In order to describe the distribution of neutrons in a highly heterogeneous configuration, it was necessary to extend the classical neutron diffusion equation. Thus, the averaged diffusion equation includes two correction factors: the first correction is related with the absorption process of the neutron and the second correction is a contribution to the neutron diffusion, both parameters are related to neutron effects on the interface of a heterogeneous configuration. As an example of the VANDE, the plane source in an infinite medium was considered to study the effects of the correction factors on the neutron flux, and the results were compared with classic solution.     

Development of Spectral History and Pin Power Correction Methods for Pin-by-Pin Core Analysis Method Using Three-Dimensional Direct Response Matrix

Spectral history and pin power correction methods have been developed for the pin-by-pin core analysis method using the three-dimensional direct response matrix (3D-DRM). The direct response matrix is formalized using four subresponse matrices in order to respond to a core eigenvalue k and thus it can be recomposed at each outer iteration in the core analysis. For core analysis, it is necessary to take into account the historical effect, which is related to spectral heterogeneity. The spectral history method is used to evaluate the nodal burn-up spectrum obtained by using the outgoing neutron current instead of the nodal flux because the 3D-DRM method does not use the nodal flux. The pin power correction method corrects the fuel rod neutron production rates obtained in the pin-by-pin calculation. These two methods were tested in a heterogeneous system. The test results show that the neutron multiplication factor error and nodal neutron production rate errors can be reduced by half during burn-up. The root-mean-square differences between the relative fuel rod neutron production rate distributions and the maximum error of relative fuel rod production rate can also be reduced by half. This means that the developed methods can reflect the effects of intra- and interassembly heterogeneities during burn-up and can be used for core analysis.     

Resonance Calculation for Large and Complicated Geometry Using Tone's Method by Incorporating the Method of Characteristics

A new efficient approach for evaluating the background cross section, which is based on Tone's method, is presented. Though the collision probability method is used in the conventional Tone's method, the method of characteristics (MOC) is used in the present method. Since the computation time of MOC is shorter than that of the collision probability method in a large and complicated geometry, the present method will be useful not only for lattice physics calculation, but also for analyses of advanced reactors with complicated geometry. Verification calculations are carried out in two configurations, i.e., a PWR fuel assembly geometry and a multiassembly geometry adjacent to the baffle-reflector region. The validity of the present method has been confirmed through the results of verification calculations.