• Nuclear Engineering and Technology
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• v.54 no.1
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• pp.275-282
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• 2022

The aim of this work is to develop the fractional Bateman equations, which can model memory effects in successive isotopes transformations. Such memory effects have been previously reported in the alpha decay, which exhibits a non-Markovian behavior. Since there are radioactive decay series with consecutive alpha decays, it is convenient to include the mentioned memory effects, developing the fractional Bateman Equations, which can reproduce the standard ones when the fractional order is equal to one. The proposed fractional model preserves the mathematical shape and the symmetry of the standard equations, being the only difference the presence of the Mittag-Leffler function, instead of the exponential one. This last is a very important result, because allows the implementation of the proposed fractional model in burnup and activation codes in a straightforward way. Numerical experiments show that the proposed equations predict high decay rates for small time values, in comparison with the standard equations, which have high decay rates for large times. This work represents a novelty approach to the theory of successive transformations, and opens the possibility to study properties of the Bateman equation from a fractional approach.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.239-246
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• 2021

In this article, a study of generalized Bateman's matrix polynomials is presented. We obtained partial differential equations by using differential operators in the generalized Bateman's matrix polynomials for two variables. Then we introduced some different recurrence relationships of the generalized Bateman's matrix polynomials. Finally present the relationship between the generalized Bateman's matrix polynomials of one and two variables.

• Nuclear Engineering and Technology
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• v.51 no.4
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• pp.949-953
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• 2019

The burnup equation of nuclides is one of the most equations in nuclear reactor physics, which is generally coupled with transport calculations. The burnup equation describes the variation of the nuclides with time. Because of its very stiffness and the need for large time step, this equation is solved by special methods, for example transmutation trajectory analysis (TTA) or the matrix exponential methods where the matrix exponential is approximated by CRAM. However, TTA or CRAM functions well when the flux is constant. In this work, a new method is proposed when the flux changes. It's an improved method compared to TTA or CRAM. Furtherly, this new method is based on TTA or CRAM, and it is more accurate than them. The accuracy and efficiency of this method are investigated. Several cases are used and the results show the accuracy and efficiency of this method are great.

• Nuclear Engineering and Technology
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• v.54 no.7
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• pp.2690-2701
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• 2022

In this paper, we select important fission products for the estimation of the source term during a severe accident of a PWR. The selection is based on the numerical results obtained from depletion calculations for the typical PWR fuel via the in-house code named DEGETION (Depletion, Generation, and Transmutation of Isotopes on Nuclear Application), release fractions of the fission products derived from NUREG-1465, and effective dose conversion coefficients from ICRP 119. Then, for the selected fission products, we obtain the adjoint solutions of the Bateman equations for radioactive decay in order to determine the importance of precursors producing the aforementioned fission products via radioactive decay, which would provide insights into the assumption used in MACCS 2 for a level 3 PSA analysis in which up to six precursors are considered in the calculations of radioactive decays for the fission product after release from the reactor.

• Nuclear Engineering and Technology
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• v.53 no.6
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• pp.1893-1908
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• 2021

In light of the importance of helium production in influencing the behaviour of fast reactor fuels, in this work we present a burn-up module with the objective to calculate the production of helium in both in-pile and out-of-pile conditions tracking the evolution of 23 alpha-decaying actinides. This burn-up module relies on average microscopic cross-section look-up tables generated via SERPENT high-fidelity calculations and involves the solution of the system of Bateman equations for the selected set of actinide nuclides. The results of the burn-up module are verified in terms of evolution of actinide and helium concentrations by comparing them with the high-fidelity ones from SERPENT, considering two representative test cases of (U,Pu)O₂ fuel in fast reactor conditions. In addition, a code-to-code comparison is made with the independent state-of-the-art module TUBRNP (implemented in the TRANSURANUS fuel performance code) for the same test cases. The herein presented burn-up module is available in the SCIANTIX code, designed for coupling with fuel performance codes.