A power spectrum approach to tally convergence in Monte Carlo criticality calculation

In Monte Carlo criticality calculation, confidence interval estimation is based on the central limit theorem (CLT) for a series of tallies from generations in equilibrium. A fundamental assertion resulting from CLT is the convergence in distribution (CID) of the interpolated standardized time series (ISTS) of tallies. In this work, the spectral analysis of ISTS has been conducted in order to assess the convergence of tallies in terms of CID. Numerical results obtained indicate that the power spectrum of ISTS is equal to the theoretically predicted power spectrum of Brownian motion for tallies of effective neutron multiplication factor; on the other hand, the power spectrum of ISTS of a strongly correlated series of tallies from local powers fluctuates wildly while maintaining the spectral form of fractional Brownian motion. The latter result is the evidence of a case where a series of tallies are away from CID, while the spectral form supports normality assumption on the sample mean. It is also demonstrated that one can make the unbiased estimation of the standard deviation of sample mean well before CID occurs.     

Monte Carlo criticality analysis under material distribution uncertainty

Analysis framework under material distribution uncertainty is not yet established for the Monte Carlo (MC) criticality calculation of continuously mixed media formed via molten core concrete interaction. To approach this issue, one group cross-sections have specifically been prepared for burned fuel, stainless steel and concrete, and the effect of spatially continuous variation of volume fractions is inspected. Trigonometric functions and randomized Weierstrass functions (RWFs) are utilized to represent the spatially continuous variation. Here, trigonometric functions enable the amount of each material to be exactly preserved, and RWF is a randomized trigonometric series that can be generated within specified upper and lower bounds. With these functions, one can assess the influence of indeterminate material distribution. MC particle transport is conducted using the delta-tracking. Numerical results indicate that the effective multiplication factor (k_eff) under RWF variation can depart significantly from the k_eff of a reference uniform medium. These numerical results also show that the deterministic modeling of spatial variation provides a bound measure for extreme results from random realizations.     

基于双向遍历的蒙特卡罗临界计算并行方法

在基于蒙特卡罗粒子输运方法的反应堆模拟中,如裂变堆、聚变裂变混合堆等,达到可接受的统计误差需要大量的计算时间,这已成为蒙特卡罗方法的挑战问题之一,需通过并行计算技术解决。为解决现有方法中通信死锁的问题并保证负载均衡性,设计了基于双向遍历的临界计算并行算法。该方法基于超级蒙特卡罗核计算仿真软件系统SuperMC进行实现,以池式钠冷快堆BN600基准模型进行验证,并与MCNP进行对比。测试结果表明,串行和并行计算结果一致,且SuperMC并行效率高于MCNP。     

Fractal dimension analysis for run length diagnosis of Monte Carlo criticality calculation

In Monte Carlo criticality calculation (MCCC), each output quantity of interest is a series of tallies under autocorrelation. As a consequence from the functional central limit theorem, the stepwise interpolation of standardized tallies (SIST) converges in distribution to Brownian bridge (BB). Here, the standardization of tallies is a functional version of the statistic in the central limit theorem with the sample mean at each generation and the true mean replaced by the sample mean at the final generation. Fractional Brownian motion (FBM) is a family of stochastic processes including Brownian motion and assumes a unique value of the box-counting dimension (BCD) in fractal geometry. This work shows that the BCD of SIST is an effective diagnostic measure for the run length of MCCC. The sufficiency of the number of generations run can be judged by relating the BCD of FBM to that of BB. Numerical results are presented for the tallies of representative autocorrelation characteristics in a three-dimensional model of a pressurized water reactor and the effective multiplication factor (k_eff) tallies of the criticality problem by D. Mennerdahl.     

用蒙特卡罗方法进行核临界安全计算

本文介绍了蒙特卡罗程序ＡＭＰＸ－ＫＥＮＯ系统的铀富集厂核临界安全计算机中的应用,并为此作了大量临实验数据的验证计算和可用于实际生产的临界安全参数计算。     

表面峰强度的Monte Carlo模拟计算

本文介绍用Monte Carlo模拟方法对入射He~+离子能量在0.1—2.OMeV范围内,硅、铝单晶在几种不同表面结构条件下的表面峰强度进行了计算。讨论了离子入射能量、入射角度、晶格原子热振动幅度、相关系数、表面增强因子、原子位移和吸附原子等因素对计算结果的影响。     

蒙特卡罗临界计算粒子并行动态负载均衡调权算法研究

本文针对蒙特卡罗临界计算,提出了一种具有动态负载平衡能力的粒子权重调节算法。该算法在每次源迭代初始,将模拟粒子总权重均分到每个进程上,在保证每个进程本地权重恒定的前提下,分别调节不同进程的粒子出生权重,实现了源迭代过程中进程间计算的动态负载平衡。与Master Slave、Nearest Neighbor等算法进行比对,发现此算法加速效果更好。将此算法集成到JMCT程序中,通过BEAVRS基准题测试了并行效率,相对于128进程,4 800进程弱可扩和强可扩展并行效率分别可达92.54%和81.47%。     

基于改进多区delta-tracking方法的蒙特卡罗中子输运跟踪与临界计算验证

传统蒙特卡罗程序进行中子输运跟踪时,当中子穿越不同材料边界时需频繁大量地计算中子到材料边界的距离,若中子平均自由程大于局部模型的宏观尺寸,则大量的距离计算会显著降低中子输运跟踪效率。为弥补传统中子输运跟踪方法带来的潜在效率降低的缺陷,本文提出了改进多区delta-tracking中子输运跟踪方法,通过引入虚截面来对模型进行多区的虚拟均匀化处理,进而在中子输运跟踪时可不考虑材料边界穿越问题,理论上可提高中子输运跟踪效率。将改进多区delta-tracking中子输运跟踪方法在多功能辐射输运模拟仿真平台MOSRT系统中进行了程序实现。利用基准题和全堆芯模型开展了临界计算验证,证明了本文方法及程序的正确性和有效性。     

Comparison of Monte Carlo calculation methods for effective delayed neutron fraction

Monte Carlo calculation methods to estimate the effective delayed neutron fraction β_eff are investigated: one is proposed by Meulekamp et al. and the other is by Nauchi et al. It is revealed that both the methods calculate the delayed neutron fraction weighted with the importance functions defined by Kobayashi. The accuracy of the methods are also examined for several simple benchmark systems. Consequently, it is found that Meulekamp’s method causes ∼5% discrepancies in the β_eff values for fast systems; Nauchi’s method gives good results for fast bare systems but ∼10% discrepancies for fast reflected systems. Both the methods calculate the β_eff values approximately within the accuracy of ∼2% for thermal systems.     

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.     

用光子源敷贴治疗时血管瘤中剂量分布的蒙特卡罗计算

用蒙特卡罗法计算了用10-366keV的光子源敷贴治疗时一种简化血管瘤模型中的剂量分布。计算结果表明,临床治疗时,光子能量应选在30keV附近,这样既有很好的治疗效果,又可适当减少对正常组织的照射。用~(125)I对30余例混合型、海绵状血管瘤进行的治疗疗效显著,随访中没有发现皮肤溃烂等现象。同时给出了10Gy的瘤体平均剂量对应的各种能量下的光子数。     

Secondary electron emission yield calculation performed using two different Monte Carlo strategies

The secondary electron emission yield in Al₂O₃ and polymethylmethacrylate (PMMA) is calculated using two different Monte Carlo approaches, one based on the energy straggling strategy (ES), the other one on the continuous-slowing-down (CSD) approximation. This work is aimed at comparing the secondary electron emission yields calculated by these two Monte Carlo strategies with the available experimental data. The results of both methods are in good agreement with experimental data. The CSD strategy is about 10 times faster than the ES strategy.     

基于复杂接续面的蒙特卡罗接续计算方法研究

为了提高大型复杂问题的计算效率,提出一种适用于具有多个空间区域表面与复杂曲面型表面结构体的蒙特卡罗接续计算方法。该方法以结构体外边界面作为接续面源进行接续计算,将写源过程的计算结果与接续过程的计算结果之和作为计算的最终结果;该方法通过一次写源计算与多次接续计算,避免直接计算过程中对相同结构的重复计算,大大提升了计算效率。以MCNP程序建立典型反应堆结构计算模型,以该接续计算方法进行4种结构方案的计算,并与直接计算方法的计算结果进行对比。结果表明,该接续计算方法的计算结果与直接计算的计算结果一致,且使用该方法比直接计算方法在效率上取得了约3倍的提升效果。因此,本研究提出的蒙特卡罗接续计算方法对于涉及大量重复计算的大型复杂问题可以取得显著的效率提升。     

Brownian bridge and statistical error estimation in Monte Carlo reactor calculation

Brownian bridge (BB) is an effective vehicle in processing an output series in Monte Carlo (MC) simulation. However, most estimators based on BB cost the capability of on-the-fly monitoring. Here, on-the-fly implies that statistical error can be computed at every generation except some initial generations. In this work, on-the-fly estimation of standard deviation by the way of BB, which maintains a fixed storage size of tallies, has been investigated within a framework of the iterated integration of simulation output (IISO). Numerical tests on the MC power distribution calculation of a pressurized water reactor core reveal that the IISO approach with a relatively few number of integrations performs fairly well on average. The bias of statistical error can be managed to be about 10% or less.     

CT图像的体元大小对EGSnrc蒙特卡罗剂量计算的影响

目前的放射治疗计划系统采用经验或半经验常规剂量算法,计算得到的剂量分布不够精确,而蒙特卡罗剂量算法是一种精确的剂量计算方法,但其计算时间冗长问题最终影响临床的应用.本文基于一例病人头部电子计算机体层成像(Computer Tomography,CT)数据,应用EGSnrc(Electron Gamma Shower NRC,EGSnrc)蒙特卡罗程序,研究不同体元大小对剂量分布计算精度和计算时间等的影响.     

Decay heat analysis of VHTR cores by Monte Carlo core depletion calculation

In this study, a decay heat analysis was performed for prism type VHTR cores by combining Monte Carlo depletion calculation with McCARD code and the decay cooling calculation with ORIGEN-2 code. In the Monte Carlo depletion approach, the McCARD multi-cycle core depletion calculation was performed up to an equilibrium cycle, involving a great details of core geometry and material inventory. ORIGEN-2 performs only the decay cooling calculation with the full scope of ORIGEN-2 nuclides inventory provided by the McCARD depletion calculation. The accuracy of the decay heat analysis procedure developed in the previous work by using HELIOS and ORIGEN-2 codes was also verified. The HELIOS/ORIGEN-2 procedure showed a good accuracy for a short period of cooling time. However, a relatively large discrepancy between the two was observed for a long period of cooling time. As expected, the decay heat of a TRU fueled DB-MHR core was much higher than that of uranium fueled PMR200 core due to the fuel composition difference, which means that more attention for effective removal of the decay heat should be paid in designing the TRU fueled deep burn cores to ensure the safety of the deep burn core during the conduction cooling events.     

组合方法改进Monte Carlo计算中的伪随机数发生器

针对随机数产生基本方法的局限性．提出了一种高品质的组合随机数产生方法。使用此方法改进MCNP程序中的随机数发生器．能大大增加随机数周期的长度,显著改善伪随机数的品质,并使随机数的产生速度有明显提高．能有效地满足各种问题的计算要求。     

A batch size selection strategy by checking stability of fission source distribution for Monte Carlo eigenvalue calculations

The power iteration method is generally used for Monte Carlo eigenvalue calculations. In the process, the fission sources at each cycle are not independently sampled by the iteration scheme. This dependency of the sampled fission source can cause underestimation of response uncertainty. To solve these issues, previous studies have recommended the selection of large-size batches, which nonetheless, would require large calculation cost. This study proposes a method for selecting a reference criterion of batch size avoiding significant biases in the local responses, and mainly emphasizing the maintenance of the stability of fission source distribution. To determine the criterion for the diagnostics of stability, real-to-apparent standard deviations are analyzed with the stability of fission source distribution. The results show that the batch sizes determined by the proposed method allow the evaluation of local responses without large biases. The proposed method is expected to contribute to improving the reliability of the Monte Carlo criticality calculations.     

基于计数辅助树的蒙特卡罗粒子输运计算大规模计数方法

传统的蒙特卡罗粒子输运计算程序在粒子每一步模拟结束后,通过遍历所有计数器来判断当前粒子所在栅元是否需要进行计数,该过程耗时随计数器数量的增加近似线性增长,当计数器数量较大时,计数耗时远高于输运耗时。本文发展了一种基于计数辅助树的大规模计数加速方法,建立了与几何栅元一一对应的树形结构,并在节点中存储了相应栅元的计数信息,通过当前粒子所在栅元的几何信息从树中快速读出对应的计数器。为了验证该方法的有效性,基于Hoogenboom全堆基准例题测量了不同计数器数量下的计算耗时。测试结果显示本文方法能有效地提高大规模计数问题的计算效率。     

高气压电离室能量响应的模拟计算

高气压电离室因其能量响应好而被广泛应用于环境γ本底测量。电离室外壳形状及材料的选择对其能量响应的影响非常大,本文采用蒙特卡罗方法对AGM-5型电离室的能量响应做了模拟计算,计算结果与实验刻度值吻合得比较好。