Point-Kernel Code Development for Gamma-Ray Shielding Applications
Source abstract
Abstract
The point-kernel (PK) technique has a long history in applied radiation shielding, originating from the early days of digital computers. The PK technique applied to gamma-ray attenuation is one of many successful applications, based on the linear superposition principle applied to distributed radiation sources. Mathematically speaking, the distributed source will produce a detector response equivalent to the numerical integration of the radiation received from an equivalent number of point sources. In this treatment, there is no interference between individual point sources, while inherent limitations of the PK method are its inability to simulate gamma scattering in shields and the usage of simple boundary conditions. The PK method generally works for gamma-ray shielding with corrective B-factor for scattering and only specifically for fast neutron attenuation in a hydrogenous medium with the definition of cross section removal. This paper presents theoretical and programming aspects of the PK program developed for a distributed source of photons (line, disc, plane, sphere, slab volume, etc.) and slab shields. The derived flux solutions go beyond classical textbooks as they include the analytical integration of Taylor B-factor, obtaining a closed form readily suitable for programming. The specific computational modules are unified with a graphical user interface (GUI), assisting users with input/output data and visualization, developed for the fast radiological characterization of simple shielding problems. Numerical results of the selected PK test cases are presented and verified with the CADIS hybrid shielding methodology of the MAVRIC/SCALE6.1.3 code package from the ORNL.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Radiation Shielding Materials Analysis · Graphite, nuclear technology, radiation studies · Nuclear Physics and Applications
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Applied Physics, University of Zagreb Faculty of Electrical Engineering and Computing, Unska 3, 10000 Zagreb, Croatia
Department of Energy and Power Systems, University of Zagreb Faculty of Electrical Engineering and Computing, Unska 3, 10000 Zagreb, Croatia
Funding
Croatian Science Foundation
References (35)
Show source-provided references
1. Schaeffer, N.M. (1976). Reactor Shielding for Nuclear Engineers, U.S. Atomic Energy Commission Office of Information Services.
2. Glasstone, S., and Sesonske, A. (1994). Nuclear Reactor Engineering—Reactor Design Basics, Chapman & Hall. [4th ed.].10.1007/978-1-4615-7525-2 ↗
3. Goldstein, H. (1959). Fundamental Aspects of Reactor Shielding, Addison-Wesley Publishing Company, Inc.
4. Trubey, D.K. (1992, January 15–20). Early Test Facilities and Analytic Methods for Radiation Shielding; History and Evolution of Buildup Factors. Proceedings of the a Special Session for the Radiation Protection and Shielding Division at the American Nuclear Society Winter Meeting, Chicago, IL, USA.
5. Development of Point Kernel Shielding Analysis Computer Program Implementing Recent Nuclear Data and Graphic User Interfaces
6. Support vector regression model for the estimation of γ-ray buildup factors for multi-layer shields10.1016/j.anucene.2007.05.001 ↗
7. IGSHIELD: A new interactive point kernel gamma ray shielding code10.1016/j.anucene.2008.09.007 ↗
8. U-Shielder—an open source software for the estimation of gamma shielding using depleted uranium10.1051/radiopro/2017033 ↗
9. A gamma-ray dose rate assessment method for arbitrary shape geometries based on voxelization algorithm10.1016/j.radphyschem.2019.02.015 ↗
10. MIGSHIELD: A new model-based interactive point kernel gamma ray shielding package for virtual environment10.1016/j.net.2019.12.026 ↗
11. 3DGShield: A new 3D gamma ray shielding code for arbitrary source and shield geometry based on point kernel technique10.1016/j.anucene.2021.108352 ↗
12. A Novel and High-Precision Method for Calculating the γ-Ray Build-Up Factor for Multilayer Shields
13. A GPU-based point kernel gamma dose rate computing code for virtual simulation in radiation-controlled area10.1016/j.net.2023.03.018 ↗
14. NPTS-PK: A new point kernel code for fast calculation of 3D gamma radiation field10.1016/j.radphyschem.2024.112329 ↗
15. POKER: A new point kernel 3D radiation field characterization code with stratified and deep shielding capabilities
16. Spent Fuel Pool Dose Rate Calculations Using Point Kernel and Hybrid Deterministic-Stochastic Shielding Methods
17. Monte Carlo Codes for Neutron Buildup Factors
18. Point Kernel Modification Including Support Vector Regression Neutron Buildup Factor Models
19. (2025, May 26). Scale: A Comprehensive Modeling and Simulation Suite for Nuclear Safety Analysis and Design, ORNL/TM-2005/39, Version 6.1, June 2011, Available from Radiation Safety Information Computational Center at Oak Ridge National Laboratory as CCC-785, Available online: https://www.ornl.gov/scale.
20. Lewis, E.E., and Miller, W.F. (1993). Computational Methods of Neutron Transport, American Nuclear Society, Inc.
21. An Approximation of Gamma-Ray Buildup Factors by Modified Geometrical Progression10.13182/NSE83-A18222 ↗
22. An Historical Review and Current Status of Buildup Factor Calculations and Applications10.1016/0969-806X(93)90317-N ↗
23. Wood, J. (1982). Computational Methods in Reactor Shielding, Pergamon Press. [1st ed.].
24. Compact Tables of Functions for Use in Shielding Calculations10.13182/NSE75-A26623 ↗
25. Kernighan, B.W., and Ritchie, D.M. (1988). The C Programming Language, Prentice Hall PTR. [2nd ed.].
26. (2025, May 26). The GNU C Compiler. Available online: https://gcc.gnu.org/.
27. (2025, May 26). The GNU C Language Intro and Reference Manual. Available online: https://www.gnu.org/software/c-intro-and-ref/manual/.
28. Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (1992). Special Functions. Numerical Recipes in C—The Art of Scientific Computing, Cambridge University Press. [2nd ed.].
29. Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P. (1992). Root Finding and Nonlinear Sets of Equations. Numerical Recipes in C—The Art of Scientific Computing, Cambridge University Press. [2nd ed.].
30. Stroustrup, B. (2013). The C++ Programming Language, Pearson Education, Inc.. [4th ed.].
31. (2025, May 10). Qt documentation. Available online: https://doc.qt.io/.
32. Matijević, M., Kaselj, A., and Trontl, K. (2024, January 9–12). Calculation of Sievert Integral for Point-Kernel Shielding Applications. Proceedings of the 14th International Conference of the Croatian Nuclear Society, Zadar, Croatia.
33. Automated Variance Reduction of Monte Carlo Shielding Calculations Using the Discrete Ordinates Adjoint Function10.13182/NSE98-2 ↗
34. Denovo: A new three-dimensional parallel discrete ordinates code in SCALE10.13182/NT171-171 ↗
35. Bell, G.I., and Glasstone, S. (1970). Nuclear Reactor Theory, Van Nostrand Reinhold Company, Litton Educational.