Session: 08-02: New Facility Planning/ Environmental Management (EM)/ Health & Safety

Paper Number: 109852

109852 - Application and Improvement of Chebyshev Rational Approximation Method in Activation Calculation of Materials 

In recent years, with the development of new reactors and the application of new nuclear materials, to ensure the radiation protection of workers, it is necessary to accurately and efficiently analyze the activation of materials suffering from neutron irradiation. Through the activation calculation of materials, the changes in nuclide composition and atom inventory of materials with running time during irradiation can be analyzed. The essence of activation calculation is to solve the equations of equilibrium for nuclides, which are mainly divided into analytical methods (trajectory transmutation analysis) and numerical methods (time difference method, matrix exponential solution, etc.). The Chebyshev rational approximation method (CRAM), as one of the numerical methods, has comprehensive advantages in terms of computational accuracy and efficiency. Compared with other numerical methods (such as the truncated Taylor series approach), this method can directly calculate the matrix exponent without preprocessing, and it can still obtain high accuracy with large time steps. In this paper, the basic theory of the CRAM method is described firstly, the traditional PFD (Partial Fraction Decomposition) form for CRAM of order 14 is derived, and then some typical cases are selected to test and verify. The results showed that the accuracy of order 14 CRAM is greatly affected by the time steps in dealing with the decay calculation problem of short-lived nuclides, which has a problem with time step selection. Aiming at this problem, the order 14 CRAM is optimized, a new IPF (Incomplete Partial Fractions) form of CRAM with higher-order is introduced, and the influence of the expansion order of CRAM on the time step selection is analyzed systematically. Further calculations show that, compared with order 14 PFD, the higher-order CRAM of IPF form is more efficient and accurate in calculating the decay problem of short-lived nuclides, and the selection process of time steps can be omitted. This paper extends the application range of CRAM in the activation calculation of materials by overcoming the difficulty of time step selection.

Presenting Author: Xiao Yu North China Electric Power University

Presenting Author Biography: Xiao Yu, male, born in 1998, graduated from North China University of Water Resources and Power with a bachelor’s degree in 2021, and is currently studying at the School of Nuclear Science and Engineering, North China Electric Power University, focusing on the calculation of fuel depletion/material activation.
This work is supported by National Magnetic Confinement Fusion Program of China under Grant Nos. 2019YFE03110000 and 2019YFE03110003.