Yuanzineng kexue jishu (Mar 2024)
Correlated Sampling Method for Point Detector Sensitivity Calculation
Abstract
In reactor radiation shielding design, the shielding scheme often needs to be optimized by changing shielding body size, material density and isotope atomic fractions. The knowledge of radiation dose rate's difference can help a lot. Besides, the uncertainty of the nuclear data itself affects the accuracy of the radiation shielding simulating results, which also needs to be considered in the evaluation of the shielding scheme. When the difference of radiation dose rate is small, perturbation method can be used. Perturbation is especially useful in Monte Carlo calculation in which statistic error masks the inherent difference between two schemes. In Monte Carlo radiation shielding calculation, point detector tally has great efficiency by using next event estimator. In order to calculate the sensitivity of point detector tally, correlated sampling algorithm was introduced in JMCT software. Random walk was assumed the same for both perturbated and original systems. Instead, dose difference was expressed only in particle weight. Perturbation caused by material and nuclear data propagated in the entire random walk. General particle weight correction was calculated in colliding and flying events, and virtual particle weight correction was calculated in source sampling and colliding events. Weight correction was deduced for every process considering transportation biasing, often used in deep penetrating problem simulation. System with single perturbation was introduced to encapsulate weight correction calculation. Within one perturbated system, only perturbation in one energy region, isotope and reaction type was considered. Meanwhile, the perturbated system had the same number of tallies with original system, and the sensitivity tallies could be built by cloning from original system's point detector tallies. This feature avoids a lot of underlying mistakes in memory allocation and tally initialization. Multiply perturbation can be considered in one Monte Carlo simulation without interference with each other. Weight correction of descendant is managed in form of particle extended property so that no history retrieving is needed. This makes the algorithm compatible with variance reduction techniques such as weight window or cell importance. Validation was performed on Livermore pulsed sphere experiment and NURGE/CR-6115 benchmark. Good agreement is found in time-of-flight leakage spectra in 2.9 mean free paths carbon sphere with results published by R. L. Perel which uses differential operator method. For the perturbation of inelastic scattering cross section in specified energy range, difference below 5% is achieved in both source direct leakage peak and single scattering leakage peak compared with reference results. In NUREG/CR-6115 benchmark, consistent adjoint driven importance sampling was used to reduce the statistical variance. Comparing with the result from analogy Monte Carlo, qualitative agreement is found. However, time consuming in correlated sampling method is 4.1 CPU hours compared with 4 286.2 CPU hours in analogy Monte Carlo method, which makes the correlated sampling method is applicable in shielding design optimization.
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