Experimental analyses of bismuth sample reactivity worth at Kyoto University Critical Assembly

Sample reactivity worth experiments are carried out by substituting aluminum (Al) plates for bismuth (Bi) ones at the Kyoto University Critical Assembly. At the beginning, uncertainty quantification of bismuth isotope is conducted by deterministic calculations with nuclear data library JENDL-4.0, with the use of experimental results of sample reactivity worth. Then, with the combined use of current (Bi) and previous (Pb) experimental results that demonstrate the comparative difference in the sensitivity and uncertainty of Bi and Pb isotopes, experimental results of cross-section uncertainties of Bi isotope are available for examination of neutron characteristics of Pb–Bi coolant material in the accelerator-driven system. From the experimental analyses, further uncertainty analyses by neutron transport calculations are needed for several reactions of Bi isotope, especially with the use of the covariance data of capture, elastic scattering and inelastic scattering reactions in another nuclear data library.     

Uncertainty quantification of criticality in solid-moderated and -reflected cores at Kyoto University Critical Assembly

Uncertainty quantification is conducted for the criticality of excess reactivity and control rod worth obtained at the Kyoto University Critical Assembly (KUCA). By combining SRAC2006 and MARBLE code systems, the sensitivity coefficients of the cross sections for aluminum-27 (²⁷Al) comprising mainly of core components are large in the solid-moderated and -reflected cores (A cores) at KUCA. Also, the uncertainty is dominant in the uranium-235 isotope by the covariance data of JENDL-4.0, and a quantitative value is about 150 pcm induced by the JENDL-4.0 data library in the KUCA A cores, whereas the covariance data of ²⁷Al are not prepared in JENDL-4.0. Moreover, the effect of decreasing uncertainty is obtained by applying the cross-sectional adjustment method to the uncertainty analyses. From the results, a series of uncertainty quantifications is expected to clarify the uncertainty of sub-criticality in accelerator-driven system experiments with spallation neutrons in the KUCA A cores.     

Reaction rate analyses of accelerator-driven system experiments with 100 MeV protons at Kyoto University Critical Assembly

At the Kyoto University Critical Assembly, a series of reaction rate experiments is conducted on the accelerator-driven system (ADS) with spallation neutrons generated by the combined use of 100 MeV protons and a lead–bismuth target in the subcritical state. The reaction rates are measured by the foil activation method to obtain neutron spectrum information on ADS. Numerical calculations are performed with MCNP6.1 and JENDL/HE-2007 for high-energy protons and spallation process, JENDL-4.0 for transport and JENDL/D-99 for reaction rates. That the reaction rates depend on subcriticality is revealed by the accuracy of the C/E (calculation/experiment) values. Nonetheless, the accuracy of the reaction rates at high-energy thresholds remains an important issue in the fixed-source calculations. From reaction rate analyses, the indium ratio is newly defined as another spectrum index with the combined use of ¹¹⁵In(n, γ)^116mIn and ¹¹⁵In(n, n′)^115mIn reaction rates, and considered useful in examining the neutron spectrum information on ADS with spallation neutrons.     

First nuclear transmutation of 237Np and 241Am by accelerator-driven system at Kyoto University Critical Assembly

This study demonstrates, for the first time, the principle of nuclear transmutation of minor actinide (MA) by the accelerator-driven system (ADS) through the injection of high-energy neutrons into the subcritical core at the Kyoto University Critical Assembly. The main objective of the experiments is to confirm fission reactions of neptunium-237 (²³⁷Np) and americium-241 (²⁴¹Am), and capture reactions of ²³⁷Np. Subcritical irradiation of ²³⁷Np and ²⁴¹Am foils is conducted in a hard spectrum core with the use of the back-to-back fission chamber that obtains simultaneously two signals from specially installed test (²³⁷Np or ²⁴¹Am) and reference (uranium-235) foils. The first nuclear transmutation of ²³⁷Np and ²⁴¹Am by ADS soundly implemented by combining the subcritical core and the 100 MeV proton accelerator, and the use of a lead-bismuth target, is conclusively demonstrated through the experimental results of fission and capture reaction events.     

Measurement of large negative reactivity of an accelerator-driven system in the Kyoto University Critical Assembly

Large negative reactivity of a subcritical system driven by a pulsed 14 MeV neutron source has been measured in the Kyoto University Critical Assembly. The subcriticality of the accelerator-driven system (ADS) ranged in effective multiplication factor roughly from 0.98 to 0.92, which corresponded to an operational range of an actual ADS proposed by Japan Atomic Energy Agency. As the measurement technique, pulsed neutron method, power spectral analysis for pulsed neutron source, accelerator-beam trip method were employed. From neutron count decay data obtained by the pulsed neutron experiment, not only the prompt-neutron decay constant of fundamental mode but also a higher spatial mode could be derived. The subcriticality was also determined from the fundamental decay constant. The measured cross-power spectral density consisted of a familiar correlated reactor-noise component and many uncorrelated delta-function-like peaks at the integral multiple of pulse repetition frequency. The fundamental prompt-neutron decay constant, i.e., the subcriticality determined from the latter uncorrelated peaks was consistent with that obtained by the above pulsed neutron experiment. However, the magnitude of the former correlated component was reduced with an increase in the subcriticality and eventually this component became almost white at deeply subcritical state ranging in the multiplication factor under 0.95. Consequently, the determination of the decay constant from the correlated component was impossible under such a subcritical state. As data analysis method for the beam trip experiment, both the conventional integral count method and the least-squares inverse kinetics method (LSIKM) were employed. The LSIKM analysis led to the consistent subcriticality with that obtained by the pulsed neutron experiment, while the integral count method significantly underestimated the subcriticality. This underestimation originated from a residual background count, which was maintained after the beam trip. The LSIKM was mostly not influenced by such a slight count rate.     

Assessment of Some Cross Section Libraries through Analyses of Coupled-Core Critical Experiments by Monte Carlo Calculations

An experiment was performed on the natural circulation test loop HRTL-5, which simulates the geometry and system design of the 5 MW full power natural circulation nuclear heating reactor. Different flow modes, including density wave oscillation and flow excursion et al., were observed in a wide range of inlet sub-cooling at 1.5MPa. By means of self-developed computational codes, the bifurcation chart has been obtained. Consequently the flow excursion boundary has been determined. Through the analysis on the excursion boundary, the method to avoid the flow excursion during startup has been presented. Analytical results show: (1) with the decreasing heat flux or the increasing system pressure, the static flow excursion occurs at higher inlet temperature and its range in the instability maps becomes narrower correspondingly; (2) to decrease the outlet two-phase resistance or increase the inlet single-phase resistance is beneficial to avoid the flow excursion; (3) by means of increasing the system pressure to start up the reactor with low heat flux, the flow excursion and low steam quality density wave oscillation can be successfully avoided. This investigation is meaningful to the reactor safety and the design of the nuclear heating reactors.     

Significant spatial dependence observed in inverse kinetics analysis for a loosely coupled-core system of the Kyoto University Critical Assembly

A loosely coupled-core system was constructed in the Kyoto University Critical Assembly to study the spatial effect observed in inverse kinetics analysis of control rod reactivity worth. In a rod drop experiment, the conventional inverse kinetic method resulted in a space- and time-dependent rod worth, which depended significantly on detector position and varied remarkably with the elapse of time. In another rod worth measurement, where a control rod was continuously inserted, the similar spatial dependence could be also observed. In this study, a modal expansion approach was proposed to reduce the above spatial dependence of the measured rod worth. Applying the present approach to inverse kinetics analysis, the troublesome dependence could be solved to obtain space-independent rod worth. This approach requires only the eigenfunctions of fundamental and higher modes for an unperturbed system but makes both static and transient calculations for various perturbed systems unnecessary.     

Analyses with latest major nuclear data libraries of the fission rate ratios for several TRU nuclides in the FCA-IX experiments

In the 1980s, a series of integral experiments was conducted in FCA-IX assemblies with systematically changed neutron spectra covering from the intermediate to fast ones. The experiments provide systematic data of central fission rates for TRU nuclides containing minor actinides, ²³⁷Np, ²³⁸Pu, ²³⁹Pu, ²⁴²Pu, ²⁴¹Am, ²⁴³Am, and ²⁴⁴Cm. Regarding the fission rate ratios relative to ²³⁹Pu, benchmark models had been recently developed for validation of nuclear data for the TRU's fission cross sections. In this paper, the latest major nuclear data libraries, JENDL-4.0, ENDF/B-VII.1, and JEFF-3.2, are compared on the benchmark models. For the libraries, the analyses by a Monte Carlo calculation code show obvious overestimations particularly for the fission rate ratios of ²⁴⁴Cm to ²³⁹Pu. Additionally, a large discrepancy about by 20% between the libraries is revealed for the fission rate ratio of ²³⁸Pu to ²³⁹Pu measured in the intermediate neutron spectrum. The causes of discrepancies are furthermore clarified by sensitivity analyses.     

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.     

Analysis of Critical Experiments Using Medium-Enriched-Uranium Fuel in Kyoto University Critical Assembly (KUCA)

The critical experiments using medium-enriched-uranium (MEU) fuel in the Kyoto University Critical Assembly (KUCA), a light-water-moderated and heavy-water-reflected cylindrical core, were started in May 1981, as a part of the international Reduced Enrichment for Research and Test Reactors (RERTR) program.

The following KUCA critical experiments were analyzed: (1) the criticality measurements for high-enriched-uranium (HEU) and MEU cores and (2) the reactivity effect measurements of boron burnable-poison (BP) for MEU cores. Five-group constants were generated using the EPRI-CELL code, and two-dimensional diffusion calculations were performed using a conventional finite-difference code DIF3D(2D), and a finite-element code 2D-FEM-KUR. Some of the results from the two diffusion codes were compared with each other. Advantage was taken of the finite-element method for the application of the 2D-FEM-KUR code to a detailed analysis of the BP effect measurements.

Differences between the results of calculations and experiments were less than 1.8% in C/E ratios for eigenvalues. The agreement between the results obtained using the DIF3D(2D) code and the 2D-FEM-KUR code was excellent. The calculated results of the BP effects with use of the 2D-FEM-KUR code approximately agreed with the experiments.     

Development of analysis method for sodium void reactivity of step type FBR cores by using group-wise Monte Carlo code

A new method is proposed to separate the sodium void reactivity of step type FBR cores to components including non-leakage terms and a leakage term by using a newly developed perturbation code MCPERT where fluxes and adjoint fluxes are derived from a group-wise Monte Carlo code. The step type FBR core is a core where the height of the inner core is smaller than that of the outer core and a large sodium plenum region is located above the core so as to decrease the sodium void reactivity. The conventional diffusion perturbation method cannot treat such a large void region due to the diffusion approximation, while the Monte Carlo code can treat it exactly. In this study, a group-wise Monte Carlo code GMVP with a 70-group constant set JFS-3-J3.3 is employed to evaluate the neutron fluxes and adjoint fluxes which are used as inputs to the MCPERT code to evaluate the non-leakage terms. The leakage term is derived from the difference of the total sodium void reactivity evaluated by the direct calculation of GMVP and the summation of the non-leakage terms. It is found that the proposed method can provide the result approximately consistent to the ratio of the reactivity components derived from the conventional method.     

核截面不确定性引起的keff不确定度的直接蒙特卡罗方法计算

核截面数据不确定性是现阶段造成核装置的k_eff计算不确定度的重要因素,本文采用直接蒙特卡罗方法分析核截面数据引起的k_eff不确定度。直接蒙特卡罗方法首先根据核截面协方差矩阵直接模拟产生多套随机核截面数据,然后利用现有堆芯计算程序计算核装置的k_eff,最后对k_eff计算结果进行统计,得出由核截面数据引起的k_eff计算不确定度。通过对Jezebel-²³⁹Pu基准装置和中国实验快堆首炉堆芯进行计算和分析,验证了方法的合理性与可行性。     

Optimization treatment of point-wise nuclear data in Monte Carlo criticality and burnup calculations

The Monte Carlo codes used for neutron transport calculations are always time consuming, a large proportion of which is possessed by the treatment of continuous-energy cross sections. In this paper, two companion methods are developed for the optimization treatment of point-wise nuclear data, the first of which is called Computational-Expense Oriented (CEO) method based on the unionized energy grid approach and reconstructs only the computationally expensive cross sections in neutron transport simulation, and the other of which is called energy bin (EB) method, a companion of CEO method when the reaction rate tallies for MC-coupling burnup calculation are performed. These two methods are implemented in the code RMC, a Monte Carlo (MC) code used for reactor analysis, and tested on fast reactor core and BWR assembly problems. The numerical results show that CEO method, in comparison with reconstructing all cross sections under the unionized grid, requires the sharply decreased computer memory while achieving almost the same computational efficiency, and EB method can optimize the processing of nuclide-specific energy grid search and thus effectively reduce the total search number while requiring very small computer memory.     

蒙特卡罗方法在CZT探测器测量乏燃料组件燃耗中的应用

利用碲锌镉（CZT）探测器组成的γ谱探测系统是一种测量乏燃料组件燃耗的较有效的方法。本文利用蒙特卡罗方法,借助于Geant4软件包计算在两种测量方式、多个准直高度条件下组件中¹³⁷Cs和¹³⁴Cs的全能峰探测效率,对测量结果的正确评价分析具有一定意义。另外,采用偏倚抽样方法确定源粒子发射方向,极大提高了CZT探测器全能峰探测效率。     

Measurement and analysis of reflector reactivity worth by replacing stainless steel with zirconium at the fast critical assembly (FCA)

A reflector reactivity worth was measured by replacing stainless steel with zirconium at the FCA. The experimental result of the positive reflector reactivity worth demonstrates the effectiveness of the zirconium reflector compared with the SS reflector in the fast reactor core. This paper also focuses on the validation of standard calculation methods used for fast reactors with JENDL-4.0. As a result, it is confirmed that the standard calculation methods for the reflector reactivity worth show agreement within the experimental error.     

Whole Core Calculations of Power Reactors by Use of Monte Carlo Method

Abstract

Whole core calculations have been performed for a commercial size PWR and a prototype LMFBR by using vectorized Monte Carlo codes. Geometries of cores were precisely represented in a pin by pin model. The calculated parameters were k _eff, control rod worth, power distribution and so on. Both multigroup and continuous energy models were used and the accuracy of multigroup approximation was evaluated through the comparison of both results. One million neutron histories were tracked to considerably reduce variances. It was demonstrated that the high speed vectorized codes could calculate k _eff, assembly power and some reactivity worths within practical computation time. For pin power and small reactivity worth calculations, the order of 10 million histories would be necessary. It would be difficult for the conventional scalar code to solve such large scale problems while the present codes consumed computation time less than 30 min for a PWR and 1 hour for an LMFBR. Required number of histories to achieve target design accuracy were estimated for those neutronic parameters.