**M. I. Holiuk, O. M. Khotiaintseva, V. M. Khotiaintsev,
A. V. Nosovskyi, V. I. Gulik**

Institute for Safety Problems of Nuclear Power Plants,

NAS of Ukraine, 12, Lysogirska st., Kyiv, 03028, Ukraine

**DOI: doi.org/10.31717/2311-8253.21.3.3**

**Abstract**

The radiation protection is an important issue in the operation of nuclear power plants and artificial radioactive sources, which include spent nuclear fuel storage facilities. The Monte-Carlo codes are the effective instruments for calculation of radiation shielding properties and radiation field characteristics for complex geometries. However, achieving

a satisfactory statistical error of the results in modeling the passage of neutrons and photons through biological protection may require excessively long calculation time. To solve this problem, Monte-Carlo codes use methods to reduce the variance to direct particles to regions with detectors to improve statistical accuracy. Our paper presents the application of the variance reduction function based on weight windows in the Monte-Carlo Serpent code, the function is investigated on the example of a simplified 2D model of the spent nuclear fuel storage container HI-STORM 190. The simple approach option of variance reduction with fixed cartesian and cylindrical meshes was investigated for different mesh nodes and for different dimensions of nodes. Also, global variance reduction option with fixed cartesian and cylindrical meshes was analyzed for case of achieving satisfactory results for the entire simulated volume. For a qualitative assessment of the variance reduction function, the indicator — figure of merit (FOM) used in our paper which proposed by the developers of the Serpent Monte-Carlo code. It is shown that the use of the variance reduction function leads to a significant decrease of statistical error and decrease of the calculation time, and therefore can be useful for biological protection calculations. As conclusions we can note that: the cylindrical mesh is not as effective in terms of FOM compared to Cartesian mesh; for both cylindrical and Cartesian meshes it is possible to find the recommended grain (node) size; the use of azimuthal partition of the cylindrical mesh together with radial partition leads to an increase in FOM; the application of global variance reduction is useful in the case of asymmetric biological protection geometries, while the FOM decreases.

* Keywords:* Monte Carlo Serpent code, container HI-STORM 190, radiation protection, variance reduction, global variance reduction, figure of merit.

**References**

1. Leppänen J. (2019). Response matrix method-based importance solver and variance reduction scheme in the Serpent 2 Monte Carlo code. Nuclear Technology, vol. 205, no. 11, pp. 1416–1432.

2. Shi T., Huang H. Qiu Y., Li Z., Qian D. (2017). A new global variance reduction technique based on pseudo flux method. Nuclear Engineering and Design, vol. 324, pp. 18–26.

3. Lux I., Koblinger L. (1991). Monte Carlo particle transport methods: neutron and photon calculations. Boca Raton: CRC Press, 529 p. doi: 10.1201/9781351074834.

4. Leppänen J., Viitanen T., Hyvönen O. (2017). Development of a variance reduction scheme in the Serpent 2 Monte Carlo code. Proceedings of the Int. Conf. on Mathematics

and Computational Methods Applied to Nuclear Science and Engineering, M&C2017 (Jeju, Republic of Korea, April 16–20, 2017).

5. Leppänen J., Aufiero M. (2015). Development of an unstructured mesh based geometry model in the Serpent 2 Monte Carlo code. Proceedings of the Int. Conf. on Physics

of Reactors, PHYSOR2014 (Kyoto, Japan, September 28 — October 3, 2014), 1101586.

6. Leppänen J. (2015). CAD-based geometry type in Serpent 2 — Application in fusion neutronics. Proceedings of the Mathematics and Computations, Supercomputing

in Nuclear Applications and Monte Carlo Int. Conf. (Nashville, U. S., April 19–23, 2015). Curran Associates Inc., pp. 1635–1646.

7. Kaltiaisenaho T., Leppänen J. (2016). Expanding the use of Serpent 2 to fusion applications: Shut-down dose rate calculations. Proceedings of the Int. Conf. on the Physics of

Reactors, PHYSOR2016 (Sun Valley, U. S., May 1–5, 2016).

8. Leppänen J., Kaltiaisenaho T., Valtavirta V., Metsälä M. (2017). Development of a coupled neutron/photon transport mode in the Serpent 2 Monte Carlo code. Proceedings of

the Int. Conf. on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C2017 (Jeju, Republic of Korea, April 16–20, 2017).

9. Leppänen J., Viitanen T., Hyvönen O. (2017). Development of a variance reduction scheme in the serpent 2 Monte Carlo code. Proceedings of the International Conference

on Mathematics and Computational Methods Applied to Nuclear Science and Engineering, M&C2017 (Jeju, Republic of Korea, April 16–20, 2017).

10. Updated preliminary report on the safety analysis of CSFSF. Kyiv: SE “State Scientific and Engineering Center for Control Systems and Emergency Response”, 2018.

(in Russ.)

11. Leppänen J. (2017). On the use of delta-tracking and the collision flux estimator in the Serpent 2 Monte Carlo particle transport code. Annals of Nuclear Energy, vol. 105,

pp. 161–167

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