Development and validation of the code COUPLE3.0 for the coupled analysis of neutron transport and burnup in ADS

The analysis of the fuel depletion behavior is critical for maintaining the safety of accelerator-driven subcritical systems(ADSs). The code COUPLE2.0 coupling 3-D neutron transport and point burnup calculation was developed by Tsinghua University. A Monte Carlo method is used for the neutron transport analysis, and the burnup calculation is based on a deterministic method. The code can be used for the analysis of targets coupled with a reactor in ADSs. In response to additional ADS analysis requirements at the Institute of Modern Physics at the Chinese Academy of Sciences, the COUPLE3.0 version was developed to include the new functions of(1) a module for the calculation of proton irradiation for the analysis of cumulative behavior using the residual radionuclide operating history,(2) a fixed-flux radiation module for hazard assessment and analysis of the burnable poison, and(3) a module for multi-kernel parallel calculation, which improves the radionuclide replacement for the burnup analysis to balance the precision level and computational efficiency of the program. This paper introduces thevalidation of the COUPLE3.0 code using a fast reactor benchmark and ADS benchmark calculations. Moreover,the proton irradiation module was verified by a comparison with the analytic method of calculating the210 Po accumulation results. The results demonstrate that COUPLE3.0 is suitable for the analysis of neutron transport and the burnup of nuclides for ADSs.     

Preparation and verification of mixed high-energy neutron crosssection library for ADS

An accelerator-driven subcritical system(ADS)is driven by an external spallation neutron source, which is generated from a heavy metal spallation target to maintain stable operation of the subcritical core, where the energy of the spallation neutrons can reach several hundred megaelectron volts. However, the upper neutron energy limit of nuclear cross-section databases, which are widely used in critical reactor physics calculations, is generally 20 MeV.This is not suitable for simulating the transport of highenergy spallation neutrons in the ADS. We combine the Japanese JENDL-4.0/HE high-energy evaluation database and the ADS-HE and ADS 2.0 libraries from the International Atomic Energy Agency and process all the data files for nuclides with energies greater than 20 MeV. We use the continuous pointwise cross-section program NJOY2016 to generate the ACE-formatted cross-section data library IMPC-ADS at multiple temperature points. Using the IMPC-ADS library, we calculate 10 critical benchmarks of the International Criticality Safety Benchmark Evaluation Project manual, the 14-MeV fixed-source problem of the Godiva sphere, and the neutron flux of the ADS subcritical core by MCNPX. To verify the correctness of the IMPCADS, the results were compared with those calculated using the ENDF/B-VII.0 library. The results showed thatthe IMPC-ADS is reliable in effective multiplication factor and neutron flux calculations, and it can be applied to physical analysis of the ADS subcritical reactor core.     

IAEA加速器驱动系统(ADS)中子学基准问题的计算

为了验证加速器驱动洁净核能系统研究拟采用的程序系统,对IAEA加速器驱动系统(ADS)中子学第一阶段基准问题进行了校算。其中,散裂中子源的计算采用LAHET程序;中子输运计算采用MCNP程序,核素的燃耗计算采用0RIGEN2。计算结果与IAEA的ADS研究协调项目组(ADSCRP)成员俄罗斯和瑞典的结果吻合较好。     

CASCADE/INPE code system

The CASCADE/INPE code system, developed jointly by the Joint Institute of Nuclear Search and IATé, is intended for calculating the transport of charged particles and neutrons in the energy range from several GeV down to thermal energy in media with a complicated geometry and composition. It includes as individual blocks the CASCADE and MCNP-4B programs and an interface-program. The CASCADE block is used to model the interaction of charged particles with target nuclei and particle transport in the medium at energies greater than a fixed cutoff energy (20 MeV for neutrons). Transport of neutrons with energy below 20 MeV is modeled using the MCNP-4B block. The interface program is intended for processing computational results using the CASCADE block and preparation of initial data for the MCNP-4B block. An example of the calculation of the characteristics of a subcritical reactor with an external neutron source is presented, 1 figure, 6 references. Translated from Atomnaya énergiya, Vol. 87, No. 4, pp. 283–286, October, 1999.     

Neutronics and burnup analysis of an accelerator-based tru-nitride fuel transmutation system with the ATRAS code

The neutronics and burnup analyses of an accelerator-based transmutation system with tungsten target and TRU-nitride fuel were performed with a newly developed code system named ATRAS (Accelerator-based Transmutation Reactor Analysis System). The ATRAS code is an integrated code system which can perform the hadronic cascade process above 20 MeV and neutron transport and core burnup process below 20 MeV with the spallation neutron source.

The specifications of the transmutation system are investigated. The core consists of the central spallation target region and the surrounding TRU-mononitride fuel region. The core is driven by protons at an energy of 1.0 GeV. This system was also proposed as a benchmark problem in the “OECD NEA/NSC Benchmark on Physics aspects of Different Transmutation Concepts”.

According to the calculation results by the ATRAS code, higher power density and transmutation rate were achieved with nitride fuel, and the neutron spectrum was slightly harder than that of the metallic fuel system. The burnup calculation for thermal power 800 MW was also performed with the ATRAS code. It is shown that about 300 kg of TRU are transmuted annually.     

基于OpenMC的瞬发中子衰减常数计算模块开发与验证

瞬发中子基波衰减常数α可定量描述反应堆内中子随时间的变化,是计算绝对反应性所需的中子动力学参数之一,对次临界（特别是较深次临界）绝对反应性的精确测量具有重要意义。本文在开源程序OpenMC基础上,基于k α迭代方法,以中子径迹长度上的平均时间吸收权重修正作为k α迭代参数因子,在输运过程中对瞬发、缓发中子分别考虑,开发了具有瞬发α本征值问题计算功能的OpenMC PA模块。以Godiva衍生基准题和MUSE 4次临界实验装置为计算对象,对程序计算瞬发α本征值问题能力进行验证。结果表明,该计算模块有优于MCNP4C的计算速度与计算范围,计算值与参考值的相对误差小于05%。OpenMC PA能满足次临界系统瞬发α本征值和中子动力学参数计算需求。     

基于高阶CRAM的燃耗程序开发与验证

本文基于高阶切比雪夫有理近似方法（CRAM）研制了点燃耗程序ICRAM,并内耦合于蒙特卡罗输运程序OpenMC,形成了一套燃耗计算分析程序OPICE。与传统部分分式分解（PFD）形式的CRAM相比,高阶不完全局部分解（IPF）形式的CRAM具有数值稳定性好、计算精度高和步长包容性更好等特点,满足高保真燃耗计算发展的需求。为提高耦合计算精度,OPICE采用了预估-校正和子步法两种耦合策略,支持纯衰变、定通量和定功率3种计算模式。通过OECD/NEA压水堆栅元燃耗基准题和快堆燃耗基准题的验证,程序计算结果与实验值及各参考值吻合良好,初步验证了OPICE的正确性与有效性。     

Development and Validation of Burnup Code Based on High-order Chebyshev Rational Approximation Method

Based on high-order Chebyshev rational approximation method (CRAM), a point-burnup code named ICRAM was developed and internally coupled to Monte Carlo code OpenMC, forming a burnup calculation and analysis program OPICE. Compared with the traditional partial fraction decomposition (PFD) form of CRAM, the high-order incomplete partial fractions (IPF) form of CRAM has the characteristics of good numerical stability, high calculation accuracy and better step tolerance, etc., which meets the needs of high-fidelity burnup calculation development. In order to improve the accuracy of coupling calculations, two coupling strategies including prediction-correction method and sub-step method were implemented in OPICE. Three different calculation modes were supported by OPICE to execute the decay, constant flux and constant power calculations. By calculating the OECD/NEA burnup benchmark and fast reactor burnup benchmark, the calculation results of OPICE are in good agreement with the experimental data and each reference value. The correctness and validity of OPICE are verified preliminarily.     

基于最佳一致逼近多项式的燃耗计算方法研究

本文研究了一种基于最佳一致逼近多项式（MMPA）的燃耗计算方法求解燃耗方程。相比于切比雪夫有理近似方法（CRAM）和围道积分有理近似方法（QRAM）,MMPA方法只需一次矩阵求逆计算即可求解燃耗方程,且所有计算都是实数运算,具有数值稳定性好、求解效率高等优点。进一步研制了基于MMPA方法的点燃耗程序AMAC,并耦合蒙特卡罗输运程序OpenMC,采用衰变例题、固定辐照例题、OECD/NEA压水堆栅元燃耗基准题和沸水堆组件燃耗基准题进行验证,程序计算结果与实验值及各参考值吻合良好,初步验证了MMPA方法在理论和数值上的正确性和有效性。     

基于OpenMC的多群截面库制作及有效性验证

OpenMC是麻省理工大学计算反应堆物理组开发的开源蒙特卡罗程序,能够方便地制作适用于特定堆芯中子能谱分布的多群反应截面及高阶勒让德散射截面以用于离散坐标输运程序ANISN的计算。本文基于ENDF/B-Ⅶ.1和CENDL-3.1评价数据库,利用OpenMC计算制作了ANSIN格式的多群截面并通过基准题的计算验证计算结果的准确性。通过截面转换程序的编写,将OpenMC给出的堆芯各阶勒让德散射分量,堆芯中子能谱分布,散射、吸收反应率以及裂变中子产生速率等信息转换为ANISN程序可读取的截面库格式。采用制作的截面库利用ANINS计算有效中子增殖因子及堆芯中子通量分布。结果表明,ANISN确定论的计算结果与OpenMC给出的蒙特卡罗计算结果相吻合,验证了这种方法可有效地为ANISN提供截面数据,将来可推广应用于二维、三维确定论中子输运计算。     

Preliminary Experiments on Accelerator-Driven Subcritical Reactor with Pulsed Neutron Generator in Kyoto University Critical Assembly

A series of preliminary experiments on an accelerator-driven subcritical reactor (ADSR) with 14 MeV neutrons were conducted at Kyoto University Critical Assembly (KUCA) with the prospect of establishing a new neutron source for research. A critical assembly of a solid-moderated and -reflected core was combined with a Cockcroft-Walton-type accelerator. A neutron shield and a beam duct were installed in the reflector region for directing as large a number as possible of the high-energy 14MeV neutrons generated by deuteron-tritium (D-T) reactions to the fuel region, since the tritium target is located outside the core. And then, neutrons (14MeV) were injected into a subcritical system through a polyethylene reflector. The objectives of this paper are to investigate the neutron design accuracy of the ADSR with 14MeV neutrons and to examine experimentally the neutronic properties of the ADSR with 14MeV neutrons at KUCA. The reaction rate distribution and the neutron spectrum were measured by the foil activation method for investigating the neutronic properties of the ADSR with 14 MeV neutrons. The eigenvalue and fixed-source calculations were executed using a continuous-energy Monte Carlo calculation code MCNP-4C3 with ENDF/B-VI.2 for the subcriticality and the reaction rate distribution, respectively; the unfolding calculation was done using the SAND-II code coupled with JENDL Activation Cross Section File 96 for the neutron spectrum. The values of the calculated subcriticality and the reaction rate distribution were in good agreement with those of the experiments. The results of the experiments and the calculations demonstrated that the installation of the neutron shield and the beam duct was experimentally valid and that the MCNP-4C3 calculations were accurately carried out for analyzing the neutronic properties of the ADSR with 14MeV neutrons at KUCA.     

ADS次临界系统中子时空动力学计算与瞬态分析

加速器驱动次临界反应堆(ADS)中子时空动力学计算需要考虑外中子源和空间分布的影响,比临界系统中子动力学计算要复杂得多。本文将改进准静态(IQS)近似与蒙特卡罗(MC)方法相结合,对于带外源的ADS次临界系统中子时空动力学过程,形状函数、动力学参数由MCNPX程序计算得到,幅度函数与集总参数热工反馈模型进行耦合计算,并开发了IQS/MC计算程序可视化操作界面。针对CIADS靶堆耦合系统参考方案物理模型,对引入束流瞬变及无保护失流工况过程进行瞬态模拟计算分析,给出了堆芯相对功率、燃料温度及冷却剂出口温度随时间的变化曲线。同时,将中子注量率进行分群计算,得到了堆芯分能群的相对中子注量率网格分布随时间的变化,模拟结果与理论分析一致。     

Physical studies of minor actinide transmutation in the accelerator-driven subcritical system

The accelerator-driven subcritical system(ADS)with a hard neutron energy spectrum was used to study transmutation of minor actinides(MAs). The aim of the study was to improve the efficiency of MA transmutation while ensuring that variations in the effective multiplication factor(k_(eff)) remained within safe margins during reactor operation. All calculations were completed using code COUPLE3.0. The subcritical reactor was operated at a thermal power level of 800 MW, and a mixture of mononitrides of MAs and plutonium(Pu) was used as fuel.Zirconium nitride(ZrN) was used as an inert matrix in the fuel elements. The initial mass composition in terms of weight percentages in the heavy metal component(IHM)was 30.6% Pu/IHM and 69.4% MA/IHM. To verify the feasibility of this MA loading scheme, variations in k_(eff), the amplification factor of the core, maximum power density and the content of MAs and Pu were calculated over six refueling cycles. Each cycle was of 600 days duration, and therefore, there were 3600 effective full power days.Results demonstrated that the effective transmutation support ratio of MAs was approximately 28, and the ADS was able to efficiently transmute MAs. The changes in other physical parameters were also within their normal ranges.It is concluded that the proposed MA transmutation scheme for an ADS core is reasonable.     

Speed-up of cross-section collapsing with weight-window for subcritical burnup calculation

In the author’s group, a fusion–fission (FF) hybrid energy system has been analyzed using our own burnup calculation system consisting of Monte Carlo transport code MCNP-4C and point burnup code ORIGEN2.1. Since the neutron energy spectrum changes along with progress of burnup in a subcritical system, it is necessary to update one-group cross-section library in each burnup step. The one-group cross-sections are normally updated by collapsing the evaluated nuclear data such as JENDL and ENDF using a neutron flux calculated by an appropriate transport code such as MCNP. The collapsed cross-sections are handed over to ORIGEN, and the reaction rates for burnup of elements are thereafter estimated accurately.As well known, MCNP generates track-length (TL) data in the neutron transport calculation, which are base data to estimate the neutron flux. We thus use the track-length data directly instead of the calculated neutron flux, in order to evaluate the reaction rate as accurately as possible. However, the number of TLs becomes extremely large and thus it takes a longer computation time. We therefore reduce the number of TLs used in the cross-section collapsing process as far as the accuracy is conserved. However, in some energy region the number of TLs is inversely too small to conserve the original cross-section accuracy of the evaluated nuclear data files, because the number of TL data per unit energy is smaller than that of the nuclear data.In the present study, the weight-window (WW) technique of MCNP was applied to our burnup calculation system in order to control the number of TLs in such an energy region artificially and to complete the collapsing process accurately in the whole energy region. As a result, the variance of the calculated neutron flux thus deteriorates slightly, but the number of TLs could be successfully adjusted to conserve the accuracy of the nuclear data file in the whole energy region. And the accurate reaction rate estimation for burnup with MCNP was finally realized and simultaneously the computation time could be saved reasonably.     

基于切比雪夫有理近似方法的点燃耗程序开发

基于切比雪夫有理近似方法（CRAM）开发了点燃耗求解程序。程序采用2套燃耗数据库,精细燃耗数据库和简化燃耗数据库,并将点燃耗程序与输运系统耦合。计算了定注量率辐照问题和衰变问题,以及JAEA轻水堆基准题,计算结果与国际知名程序对比。结果表明,程序在定注量率辐照问题和衰变问题的计算上,核子密度精度与ORIGEN2相当,单栅元和组件计算结果与HELIOS1.11以及参考解吻合良好。      

Study on kinetics of subcritical system: Contribution of delayed neutrons to the transient after a reactivity insertion

It is generally difficult to employ three dimensional spaces and time dependent kinetics by using a Monte Carlo method for nuclear reactor kinetics, because the random work analysis of a neutron becomes extremely difficult when conditions for neutron transport change with time.

However, in most cases of kinetic analysis, in particular relevant to ADS systems, we meet with many cases, where the lifetime of prompt neutron is much shorter than that of the neutron transport condition. In calculating the kinetic evolution of a subcritical (SC) system, in this paper we propose a new calculation technique where a steady state equation for the neutron flux and a time-dependent one for the delayed neutron precursor density will be treated.

In this paper, the accuracy of this theory is investigated by using a simple point reactor equation for several cases typical for ADS system. We obtained strict solution Φ* as a reference solution, Φ1 as a solution by the present method, and Φ2 as a solution where both neutrons and delayed neutron precursors are treated by using static equations. The obtained results show a good agreement between Φ1 and Φ*, though the Φ2 agrees with Φ* poorly in all our cases. Finally, we can employ a conventional Monte Carlo code for neutron transport and analysis many kinetics problems of ADS systems with the help of delayed neutron precursor analysis.     

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.     

加速器驱动的10 MW次临界反应堆物理方案研究

加速器驱动的次临界系统（ADS）是未来最有可能实现工业化嬗变核废料的装置。通过设计1个10 MW的ADS物理方案,研究ADS的嬗变能力。采用MCNPX和ORIGEN的耦合程序,利用基于ENDF6.8处理所得的6个温度（300、600、900、1 200、1 500、1 800 K）下连续能量核数据库,计算得到ADS随燃耗时间变化的有效增殖因数k_eff、功率峰因子和质子束流强度。同时通过计算给出了该设计方案下ADS燃料多普勒系数、冷却剂空泡系数和有效缓发中子份额,利用这些物理量研究了该ADS方案的安全特性,并通过燃耗计算研究了ADS的嬗变能力。结果表明,在1 000 d燃耗时长内,k_eff和质子流强随时间的波动较小,燃料燃耗深度较浅,系统可提升功率运行,在假想事故下系统能保持次临界状态。系统嬗变支持比约为8。     

COSINE软件包组件计算程序LATC的燃耗计算模块开发与验证

燃耗计算是反应堆组件参数计算程序的核心功能之一,其计算精度直接影响堆芯物理计算精度。本文系统研究了组件参数计算程序中燃耗计算方法,建立了燃耗计算理论模型,给出了能有效解决燃耗方程刚性的数值方法,根据此方法编制了LATC程序的燃耗计算模块并进行了数值验证。计算结果表明,该燃耗计算模块精度较高,在大燃耗步、深燃耗下仍可得到合理可信的结果。     

从广义自持链式反应观点看加速器驱动系统

用广义自持链式反应的观点探讨了加速器驱动系统 (ADS)的基本内涵。认为次临界反应堆、质子加速器和靶所组合的整体仍可看成一个 (临界的 )自持链式反应堆。这个反应堆不同于通常临界反应堆的特点是每次裂变后的二次中子不仅包含裂变释放的中子而且还包含部分裂变释能 (通过质子加速器及靶 )所转换的中子。正是有了这些附加中子 ,使得加速器驱动系统每次裂变的有效二次中子数增加了。一个ADS系统能够稳定运行的条件是ADS的次临界堆和加速器能够相互匹配使得ADS系统的有效二次中子数达到这样的水平 ,以致在ADS系统内能够形成自持的中子链式反应。因此尽管ADS的反应堆部分是次临界的 ,但从ADS整体来看只要质子加速器与次临界反应堆匹配得当 ,ADS系统是可以像通常临界反应堆那样 ,维持自持的链式反应的 (或临界的 )。给出了ADS系统维持自持链式反应的匹配条件 (广义临界条件 )。最后根据ADS系统的特点探讨了ADS在核废物处理 (嬗变 )、提高核燃料增殖效率及核能开发中的作用。