Neutron spectrum unfolding based on the detection of Bonner multi-sphere spectrometer
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摘要: 在中子辐射领域，中子解谱问题备受关注。邦纳多球谱仪常用于中子能谱探测，最大熵法可针对多球谱仪探测数据进行中子解谱。基于此原理，建立包含邦纳多球谱仪的仿真模型，以蒙特卡罗方法的模拟结果作为先验谱，使用基于最大熵原理的最大熵反卷积（MAXED）方法进行中子解谱，与文献数据对比验证后，证明了方法的有效性和准确性。通过增加蒙特卡罗方法的随机粒子数，获得了精确度不同的多组先验谱，对于不同的先验谱，最终解谱结果均可获得统计学显著性，解谱结果有效。经过对比，先验谱越精准，最终解谱结果准确度越高，说明通过合适的降方差方法获得准确的蒙特卡罗计算结果至关重要，可为后续研究和实验提供参考。同步使用了基于迭代算法的GRAVEL方法进行中子解谱，两种解谱方法计算结果对比进一步证明了MAXED方法解谱的优越性能。Abstract: In the field of neutron radiation, the problem of neutron spectrum unfolding has attracted much attention. The Bonner sphere spectrometer is often used for neutron spectrum detection, and the maximum entropy method can be used to analyze the neutron spectrum of the Bonner sphere spectrometer. Based on this principle, this paper establishes a simulation model including the Bonner sphere spectrometer with reference to the neutron shielding experiment in 2014. The simulation results of Monte Carlo method are used as the prior spectrum, and the MAXED based on the principle of maximum entropy is used for neutron spectrum unfolding. The effectiveness and accuracy of the method are verified by comparing with the literature data. By increasing the number of random particles in Monte Carlo method, multiple groups of prior spectrum with different accuracy are obtained. For different prior spectrum, the final spectral solution results can be statistically significant and the spectral solution results are effective. After comparison, the more accurate the prior spectrum is, the higher the accuracy of the final spectral solution results, indicating that it is important to obtain accurate Monte Carlo calculation results through appropriate variance reduction method, which can provide reference for subsequent research and experiments. In this paper, the GRAVEL method based on iterative algorithm is used to solve the neutron spectrum simultaneously, and the comparison of the calculation results of the two methods further proves the superior performance of the solution spectrum of the MAXED method.
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Key words:
- neutron detector /
- neutron spectrum unfolding /
- Maximum entropy method /
- prior spectrum
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图 1 仿真模型示意图
Figure 1. Simulation model diagram (Section view, ① concrete, ② air, ③ Bonner ball, ④ neutron source)
图 2 邦纳球模型示意图
Figure 2. Model diagram of Bonner spectrometer (Section view, ① polyethylene layer, ② aluminum shell, ③ LiI scintillator)
图 5 不同先验谱情况下MAXED解谱结果
Figure 5. The results of MAXED spectral decomposition under different prefabricated spectra
图 6 MAXED与GRAVEL解谱结果对比
Figure 6. Comparison of spectral results between MAXED and GRAVEL
表 1 材料元素构成
Table 1. Composition of material elements
Name Density/(g/cm3) Element (weight fraction) concrete 2.30 H(2.2%), C(0.3%), O(57.5%), Na(1.5%), Mg(0.1%), Al(2%), Si(30.5%), K(1%), Ca(4.3%), Fe(0.6%) polythene 0.95 C(86%), H(14%) Al shell 2.70 Al(100%) LiI scintillator 3.84 6Li(5%), I(95%) air 1.20×10−3 C(0.01%), N(76.52%), O(23.47%) 
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表 2 不同随机粒子数情况下可信结果占比
Table 2. The proportion of reliable results under different random particle numbers
Random particle population Percentage of credible results 2.2×107 34.92% 2.2×108 52.38% 3.0×108 55.56% 5.0×108 60.32% 1.0×109 74.60%
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表 3 不同迭代次数情况下GRAVEL解谱结果χ2-PDF值
Table 3. χ2-PDF values of GRAVEL solution results under different iterations
iterations χ2-PDF 50 1.34 100 1.18 150 1.08 207 0.99
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