Improvement of Monte Carlo Lattice Burnup Calculation Performance with the Correlated Sampling Method

For next generation reactor designs, which are attempting wide variations of assembly configurations, the flexibility Monte Carlo method holds is attractive, but still costly for repetitive design study works. This paper presents an advanced correlated sampling (ACS) method which was developed to speed up Monte Carlo lattice burnup calculations. The ACS method is the combination of the correlated sampling method and a pseudo-scattering technique. All burnup steps are considered as consecutive perturbed problems using the same neutron collision history, which is pre-calculated based on a selected unperturbed problem. Since neutron weights can be adjusted on every collision point, rather than along paths between them, the perturbed calculation is very fast and the neutron collision history is light enough to be stored in memory or physical storage, which is an indispensable feature for consecutive perturbed calculations. The presented theory shows that the ACS method has good potential to work for a wide range of neutron absorption variations, the dominant perturbation in the lattice burnup. In an example calculation on a BWR lattice, the ACS calculation results of 600,000 neutrons/step agree well with the independent Monte Carlo runs of 20,000,000 neutrons/step within 0.1%dk/k in terms of k_? throughout 95 steps (~50GWd/t). Average calculation time of neutron tracking with the former method is 3.4 s/step with 600,000 neutron histories on a single processor of an Alpha21164-600 MHz, and the speed-up factor against the Monte Carlo calculation turns out to be about 100.     

Improvement of Correlated Sampling Monte Carlo Methods for Reactivity Calculations

Two correlated Monte Carlo methods, the similar flight path and the identical flight path methods, have been improved to evaluate up to the second order change of the reactivity perturbation. Secondary fission neutrons produced by neutrons having passed through perturbed regions in both unperturbed and perturbed systems are followed in a way to have a strong correlation between secondary neutrons in both the systems. These techniques are incorporated into the general purpose Monte Carlo code MORSE, so as to be able to estimate also the statistical error of the calculated reactivity change.

The control rod worths measured in the FCA V-3 assembly are analyzed with the present techniques, which are shown to predict the measured values within the standard deviations. The identical flight path method has revealed itself more useful than the similar flight path method for the analysis of the control rod worth.     

基于中子首次裂变的MC/S_N耦合输运算法

外源驱动次临界系统是一类广泛存在且重要的核能系统。固有的射线效应和存在空间局部源,使得离散纵标(SN)法难以精确计算该类系统内的中子注量率。虽然蒙特卡罗(MC)方法可有效地模拟局部源问题,但存在计算效率较低的不足。因此,单一的SN方法或MC方法难以兼顾计算精度和效率。为充分发挥两种方法的优点,提出了以中子首次裂变为耦合点的MC/SN耦合算法。首先,采用MC方法模拟源中子在发生裂变反应之前的输运过程,并统计出首次裂变中子源;其次,采用SN方法求解对应于首次裂变中子源的输运方程;最后叠加两种方法计算的中子注量率,得到最终结果。算例表明,该耦合算法可有效地模拟外源驱动次临界系统的中子输运过程。     

Improvement of Neutron Source Introduction Method for Absolute Measurements of Low Reactor Power

The neutron source introduction method was applied to absolute measurements of low reactor power at the Static Experiment Critical Facility STACY. To obtain the effective neutron source intensity more accurately, which is a key parameter for the source introduction method, the neutron source is newly defined as fission neutrons from the first fission reaction caused by neutrons emitted from the external neutron source. To obtain the newly defined effective neutron source intensity, the probability that a neutron from the external neutron source causes a fission reaction is calculated using the Monte Carlo code MCNP. This calculation took into consideration the three-dimensional complicated core structures. Furthermore, the fission reaction distribution, fundamental mode forward and adjoint flux distribution in a critical state were calculated using the three-dimensional transport code THREEDANT. Following the principle of the neutron source introduction method, an external neutron source was inserted near the STACY core tank and the reactor power was measured. The reactor powers by the neutron source introduction method were in good agreement with the ones from the analyses of the FP activity generated by high power operation.     

New Sampling Method in Continuous Energy Monte Carlo Calculation for Pebble Bed Reactors

A pebble bed reactor generally has double heterogeneity consisting of two kinds of spherical fuel element. In the core, there exist many fuel balls piled up randomly in a high packing fraction. And each fuel ball contains a lot of small fuel particles which are also distributed randomly. In this study, to realize precise neutron transport calculation of such reactors with the continuous energy Monte Carlo method, a new sampling method has been developed. The new method has been implemented in the general purpose Monte Carlo code MCNP to develop a modified version MCNP-BALL. This method was validated by calculating inventory of spherical fuel elements arranged successively by sampling during transport calculation and also by performing criticality calculations in ordered packing models. From the results, it was confirmed that the inventory of spherical fuel elements could be reproduced using MCNP-BALL within a sufficient accuracy of 0.2%. And the comparison of criticality calculations in ordered packing models between MCNP-BALL and the reference method shows excellent agreement in neutron spectrum as well as multiplication factor.

MCNP-BALL enables us to analyze pebble bed type cores such as PROTEUS precisely with the continuous energy Monte Carlo method.     

Vectorization of Continuous Energy Monte Carlo Method for Neutron Transport Calculation

The vectorization method was studied to achieve a high efficiency for the precise physics model used in the continuous energy Monte Carlo method. The collision analysis task was reconstructed on the basis of the event based algorithm, and the stack-driven zone-selection method was applied to the vectorization of random walk simulation. These methods were installed into the vectorized continuous energy MVP code for general purpose uses. Performance of the present method was evaluated by comparison with conventional scalar codes VIM and MCNP for two typical problems. The MVP code achieved a vectorization ratio of more than 95% and a computation speed faster by a factor of 8–22 on the FACOM VP-2600 vector supercomputer compared with the conventional scalar codes.     

Analysis of a multigroup stylized CANDU half-core benchmark

An 8-group cross section library is provided to augment a previously published 2-group 3D stylized half-core Canadian deuterium uranium (CANDU) reactor benchmark problem. Reference eigenvalues and selected pin and bundle fission rates are also included. This benchmark is intended to provide computational reactor physicists and methods developers with a stylized model problem in more than two energy groups that is realistic with respect to the underlying physics. In addition to transport theory code verification, the 8-group energy structure provides reactor physicist with an ideal problem for examining cross section homogenization and collapsing effects in a full-core environment. To this end, additional 2-, 4- and 47-group full-core Monte Carlo benchmark solutions are compared to analyze homogenization-free transport approximations incurred as a result of energy group condensation.     

Neutronics shielding analysis for the end plug of a tandem mirror fusion reactor

A neutronics analysis using the Monte Carlo method is carried out for the end-plug penetration and magnet system of a tandem mirror fusion reactor. Detailed penetration and the magnets' three-dimensional configurations are modeled. A method of position dependent angular source biasing is developed to adequately sample the DT fusion source in the central cell region and obtain flux contributions at the penetration components.To assure cryogenic stability, the barrier cylindrical solenoid is identified as needing substantial shielding of about 1 m of a steel-lead-boron-carbide-water mixture. Heating rates there would require a thermal-hydraulic design similar to that in the central cell blanket region. The transition coils, however, need a minimal 0.2 m thickness shield. The leakage neutron flux at the direct converters is estimated at 1.3×10¹⁵ n/(m²·s), two orders of magnitude lower than that reported at the neutral beam injectors for tokamaks around 10¹⁷ n/(m²·s) for a 1 MW/m² 14 MeV neutron wall loading. This result is obtained through a coupling between the nuclear and plasma physics designs in which hydrogen ions rather than deuterium atoms are used for energy injection at the end plug, to avoid creating a neutron source there. This lower and controllable radiation leakage problem is perceived as a potential major advantage of tandem mirrors compared to tokamaks and laser reactor systems.     

Calculation of Electron Swarm Parameters of SF6/N2 in a Uniform Field Using an Improved Monte Carlo Collision Simulation Method

The electron swarm parameters of SF6/N2 are calculated in the present study using an improved Monte Carlo collision simulation method （MCS）. And some improved sampling techniques are also adopted. The simulation results show that the improved simulation method can provide more accurate results.     

蒙特卡罗共轭输运法计算反应堆压力容器快中子注量率

为了保证压力容器（RPV）在核电厂寿期内的安全,通过理论方法准确评估其受到的快中子积分注量率非常重要。本文提出了一种应用共轭输运理论解决深穿透问题的计算方法,并将该方法的计算结果与基准题HBR-2给出的实测值及确定论方法的结果进行了比较。结果表明：本文计算结果与基准题给出的实测数据吻合良好,大多反应率计算相对误差小于10%,最大相对误差不超过35%;70%以上的计算结果准确性优于确定论方法,表明本文提出的解决蒙特卡罗深穿透问题的方法是有效且准确的。     

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.     

MC法模拟重金属氧化物玻璃屏蔽性能

论文旨在验证采用MCNP软件获得的模拟实验结果真实性。利用MCNP粒子输运模拟软件计算不同重金属氧化物玻璃以及铅在不同能量γ射线下的质量衰减系数,平均自由程,使用XCOM程序预测计算γ射线能量在0.001~100 000 Me V的质量衰减系数以及平均自由程,通过将两种MC法模拟软件获得的计算结果与实验值对比,证明了采用MC法进行模拟计算的可靠性。研究结果表明,基于MC法的MCNP程序可用于计算重金属氧化物玻璃的屏蔽性能。     

MC法模拟核部件自发裂变中子活化瞬发γ能谱

在分析中子活化瞬发γ产生机理及瞬发γ射线强度计算方法基础上,提出了应用MCNP程序计算模拟核部件自发裂变中子活化放出瞬发γ能谱的直接模拟与分步模拟方法,对两种方法的计算结果及特点进行了比较分析。计算了模拟核部件核材料自发衰变产生的γ能谱,并与瞬发γ能谱进行了比较分析。本文结果可为核部件认证技术研究提供参考。     

D-T Neutron Measurements on Gekko XII Laser Inertial Fusion Plasmas by Multi-Activation Foil Method

The Criticality Safety Benchmark Evaluation Project (CSBEP) was initiated in 1992 by the United States Department of Energy. The project quickly became an international effort as scientists from other interested countries became involved. The International Criticality Safety Benchmark Evaluation Project (ICSBEP) is now an official activity of the Organization for Economic Cooperation and Development-Nuclear Energy Agency (OECD-NEA).

“International Handbook of Criticality Safety Benchmark Experiments” was prepared and is updated yearly by the working group of the project. This handbook contains criticality safety benchmark specifications that have been derived from experiments that were performed at various nuclear criticality facilities around the world. However, the handbook lacks criticality data of 20 wt%-enriched uranium fuel. The author proposes to make benchmark specifications derived from, modern research reactors in Asia. Future evaluations of these reactors will facilitate to fill the “enrichment gap”.     

Biased Selection of Particle Flight Directions as a Variance Reduction Technique in Monte Carlo Calculations

As a practical variance reduction technique applicable to Monte Carlo shielding calculations, the present article shows a new simple biased sampling technique on particle flight directions. Scattered particles not directed towards the detector positions are killed if they are not so important, that is, if the particle weights are sufficiently small compared to the source weight. In this way, we can reduce the sample size required for obtaining an accurate estimate for the detector response.

The present technique was incorporated into the multigroup neutron and γ-ray transport code MORSE, and sample calculations were performed on spherical fast neutron systems. The results have shown that this biased technique is effective for dealing with neutron multiplication as well as neutron transmission problems. The neutron flux or the effective multiplication factor of a nuclear reactor is estimated more accurately than from the method of path-length stretching with about the same computation time. In addition, it is shown that the flight-direction biasing can further effectively be used by combining it with other variance reduction techniques.     

A 3D stylized half-core CANDU benchmark problem

A 3D stylized half-core Canadian deuterium uranium (CANDU) reactor benchmark problem is presented. The benchmark problem is comprised of a heterogeneous lattice of 37-element natural uranium fuel bundles, heavy water moderated, heavy water cooled, with adjuster rods included as reactivity control devices. Furthermore, a 2-group macroscopic cross section library has been developed for the problem to increase the utility of this benchmark for full-core deterministic transport methods development. Monte Carlo results are presented for the benchmark problem in cooled, checkerboard void, and full coolant void configurations.     

基于MC方法的小型压水堆全堆计算分析

使用蒙卡计算程序MCNP,建立小型压水堆四分之一堆芯几何模型,计算小型压水堆首循环初始装料冷态(20℃)、常压(1.01 bar)下的堆芯反应性、径向功率和轴向功率分布,并与输运+扩散方法程序SCIENCE-V2程序包的计算结果进行对比。结果表明:MCNP程序适用于小型堆堆芯核设计计算,并可与SCIENCE-V2程序包互相验证。