Izvestiya vuzov. Yadernaya Energetika

The peer-reviewed scientific and technology journal. ISSN: 0204-3327

Multigroup Importance Function Calculation Method in the MCU Code

12/10/2025 2025 - #04 Modelling processes at nuclear facilities

Arkhangelsky D.M. Daichenkova Yu.S. Kalugin M.A. Oleynik D.S. Shkarovsky D.A.

DOI: https://doi.org/10.26583/npe.2025.4.11

UDC: 621.039.51

The calculation of neutron kinetics functionals, including the effective fraction of delayed neutrons (βeff) and the prompt neutron generation time (Λ), by the Monte Carlo method is known to be challenging due to the complexities involved in calculating the adjoint function. In the context of the Monte Carlo method, it is optimal to represent the importance function as the asymptotic number of descendants of a neutron placed at a given point in phase space. In practice, it is possible to consider only a finite number of generations. This limitation forms the basis of the Iterated Fission Probability (IFP) method. However, this approach is associated with several disadvantages, including the convergence of the adjoint source through a given number of generations, the appearance of statistical noise, and high requirements for memory space. It is demonstrated that reducing the IFP to one generation, known as the Next Fission Probability (NFP), facilitates the attainment of favorable agreement with experimental results. The potential exists for further reduction in RAM usage through the calculation of the importance function a priori and its subsequent tabulation into the program. In this regard, both the IFP and matrix methods can be applied. In this paper, we present a methodology for calculating the multigroup importance function using the matrix method implemented in the MCU code. The computational model is partitioned into a finite number of registration objects and energy groups. During the modeling process, the elements of the fission matrix are registered, and the neutron importance function for each energy group of each object is calculated at the post-processing stage. The methodology was validated by calculating βeff and Λ for 6 ICSBEP handbook experiments. The one- and 14-group approximation of the importance function yielded almost identical results, with a negligible difference (less than 1%), due to the minor change in importance in the energy range where most neutrons are generated.

References

  1. Hoogenboom J. Methodology of Continuous-Energy Adjoint Monte Carlo for Neutron, Photon, and Coupled Neutron-Photon Transport. Nuclear Science and Engineering. 2003;143(2):99–120. DOI: https://doi.org/10.13182/NSE03-A2322
  2. Hurwitz H. Physical Interpretation of the Adjoint Flux: Iterated Fission Probability. Naval Reactor Physics Handbook. 1964;1:864–869.
  3. Frank-Kamenetsky A.D., Yudkevich M.S. Raschet vremeni zhizni mgnovennykh neitronov v reaktore metodom Monte-Karlo. Preprint IAE-2155, Moscow, 1971 (in Russian).
  4. Kiedrowski B., Brown F., Wilson, P. Adjoint-Weighted Tallies for k-Eigenvalue Calculations with Continuous-Energy Monte Carlo. Nuclear Science and Engineering. 2011;168(3):226–241. DOI: https://doi.org/10.13182/NSE10-22
  5. Leppänen J., Aufiero M., Fridman E., Rachamin R., van der Marck S. Calculation of effective point kinetics parameters in the Serpent 2 Monte Carlo code. Annals of Nuclear Energy. 2014; 65:272–279. DOI: https://doi.org/10.1016/j.anucene.2013.10.032
  6. Qiu Y., Wang Z., Li K., Yuan Y., Wang K., Fratoni M. Calculation of adjoint-weighted kinetic parameters with the reactor Monte Carlo code RMC. Progress in Nuclear Energy. 2017;101:424–434. DOI: https://doi.org/10.1016/j.pnucene.2017.03.023
  7. Perfetti C., Rearden T., Martin W. SCALE Continuous-Energy and Eigenvalue Sensitivity and Coefficient Calculations. Nuclear Science and Engineering. 2016;182:332–353. DOI: https://doi. org/10.13182/NSE15-12
  8. Belousov V.I., Gomin E.A., Davidenko V.D., Dyachkov I.I., Ioannisian M.V., Raskach K.F., Pisarev A.N. Algorithms for Calculating the Effective Parameters of the Point Kinetics Equations Based on the Monte Carlo Method, their Verification and Validation. Voprosy atomnoy nauki i tekhniki. Serya: Fizika yadernikh reaktorov. 2024;1:19–31 (in Russian).
  9. Peng X., Liang J., Forget B., Smith K. Calculation of adjoint-weighted reactor kinetics parameters in OpenMC. Annals of Nuclear Energy. 2019;128:231–235. DOI: https://doi.org/10.1016/j.anucene.2019.01.007
  10. Peng X., Liang J., Alhajri A., Forget B., Smith K. Development of continuous-energy sensitivity analysis capability in OpenMC. Annals of Nuclear Energy. 2017;110:362–383. DOI: https://doi.org/10.1016/j.anucene.2017.06.061
  11. Meulekamp R., Marck S. Calculating the Effective Delayed Neutron Fraction with Monte Carlo. Nuclear Science and Engineering. 2006;152(2):142–148. DOI: https://doi.org/10.13182/NSE03-107
  12. Nauchi Y., Kameyama T. Development of Calculation Technique for Iterated Fission Probability and Reactor Kinetic Parameters Using Continuous-Energy Monte Carlo Method. Journal of Nuclear Science and Technology. 2010;47(11):977–990. DOI: https://doi.org/10.1080/18811248.2010.9711662
  13. Nagaya Y., Chiba G., Mori T., Irwanto D., Nakajima K. Comparison of Monte Carlo calculation methods for effective delayed neutron fraction. Annals of Nuclear Energy. 2010;37(10):1308–1315. DOI: https://doi.org/10.1016/j.anucene.2010.05.017
  14. Carney S., Brown F., Kiedrowski B., Martin W. Theory and applications of the fission matrix method for continuous-energy Monte Carlo. Annals of Nuclear Energy. 2014;73:423–431. DOI: https://doi.org/10.1016/j.anucene.2014.07.020
  15. Gurevich M.I., Kalugin M.A., Oleynik D.S., Shkarovsky D.A. Estimation of some neutron physics characteristics by Monte-Carlo method using the importance function. Annals of Nuclear Energy. 2019;130:388–393. DOI: https://doi.org/10.1016/j.anucene.2019.02.047
  16. Bell D., Glasstone S. Teoriya yadernikh reaktorov. Moscow, Aromizdat, 1974, 496 p. (in Russian).
  17. Ilyin V.A., Poznyak E.G. Lineynaya algebra. Izd. 4. Moscow, Nauka, Fizmatlit, 1999, 296 p. ISBN 5-211-04843-1 (in Russian).
  18. Paxton H. Fast critical experiments. Progress in Nuclear Energy. 1981;7(3):151–174. DOI: https://doi.org/10.1016/0149-1970(81)90030-5
  19. Arkhangelsky D.M., Daichenkova Yu.S., Kalugin M.A., Oleynik D.S., Shkarovsky D.A. The effect of the importance function resolution on the accuracy of calculating the functionals of the neutron kinetics in water critical assemblies by Monte Carlo method. Nuclear Energy and Technology. 2023;9(3):171–175. DOI: https://doi.org/10.3897/nucet.9.112165
  20. Abagyan L.P., Bazazyanz N.O., Nikolaev M.N., Tsybulya A.M. Gruppovie konstanty dlya rascheta reaktorov i zaschity. Moscow, Energoizdat, 1981, 232 p. (in Russian).

Monte Carlo method neutron importance function matrix method MCU kinetic parameters

Link for citing the article: Arkhangelsky D.M., Daichenkova Yu.S., Kalugin M.A., Oleynik D.S., Shkarovsky D.A. Multigroup Importance Function Calculation Method in the MCU Code. Izvestiya vuzov. Yadernaya Energetika. 2025, no. 4, pp. 148-159; DOI: https://doi.org/10.26583/npe.2025.4.11 (in Russian).

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