Large Perturbation Calculation Method For Monte Carlo Simulation Of Fixed-source Problems

Monte Carlo(MC)method has the advantages of strong geometric adaptability and accurate calculation results,which is widely used in nuclear system design and safety analysis.In nuclear design,the calculation model needs to be iteratively modified,such as material replacement and geometric size adjustment.Traditional nuclear design uses multiple independent MC calculations,which is time-consuming and inefficient.Perturbation calculation method can obtain the results of multiple different models through one-time calculation.However,the accuracy and speed of the perturbation calculation method have been affected by the expansion order,which can only deal with low-order perturbations,i.e.,the problem of changes in materials,geometry in a small area.Thus,it is difficult to solve the problem of changes in the material nuclide composition such as material replacement,geometry changes in a large area(large perturbation).In this work,large perturbation for fixed source problem was carried out based on the Super Multi-functional Calculation Program for Nuclear Design and Safety Evaluation(SuperMC).A reference model and perturbation models that approximate real model are established,and the small change between the perturbation model and the real model is used to transform the large perturbation calculation problem into a perturbation problem between the perturbation model and the real model.Combined with the relevant sampling calculation method,MC transport calculation is carried out in the reference model;the perturbation weight factor is derived from the neutron transport equation.After obtaining the corresponding calculation results in the perturbation model,fitting extrapolation and error delivery methods are used to calculate the result and the variance of the perturbation model,which realizes the large perturbation calculation.A naked ball model,the Ueki model of the international typical shielding benchmark and the HCPB mock-up model of the fusion reactor cladding experiment are used to verify the correctness and effectiveness of the developed method.For the naked ball model,the impact of different reference models on the calculation results is analyzed,and the accuracy of the particle distribution in space and energy of the large perturbation calculation is verified.For the shielding benchmark,the results of 3 materials or 6 geometric sizes are obtained in a single transport calculation by using the large perturbation calculation method.Compared with independent MC calculations,the maximum deviations are less than 0.4%and 2.8%,respectively and the perturbation calculation efficiencies are 3.5 and 4 times of independent MC calculation.For the fusion reactor cladding example,the large perturbation calculation method is used to obtain the reaction rate results of 8 materials in a single transport calculation.Compared with the independent MC calculation,the maximum deviation is less than 0.1%,and the perturbation calculation efficiency is 5 times of independent MC calculation.All the results show that the large perturbation calculation method developed in this work can improve the efficiency of nuclear design and analysis.