A Closed-Form Formulation for the Build-Up Factor and Absorbed Energy for Photons and Electrons in the Compton Energy Range in Cartesian Geometry
- 1
- 2
- 3
- 4
- 5
Abstract
In this work, we report on a closed-form formulation for the build-up factor and absorbed energy, in one and two di- mensional Cartesian geometry for photons and electrons, in the Compton energy range. For the one-dimensional case we use the LTSN method, assuming the Klein-Nishina scattering kernel for the determination of the angular radiation intensity for photons. We apply the two-dimensional LTSN nodal solution for the averaged angular radiation evaluation for the two-dimensional case, using the Klein-Nishina kernel for photons and the Compton kernel for electrons. From the angular radiation intensity we construct a closed-form solution for the build-up factor and evaluate the absorbed energy. We present numerical simulations and comparisons against results from the literature.
- C. F. Segatto, M. T. Vilhena and R. P. Pazos, “On the Con- vergence of the Spherical Harmonics Approximations,” Nuclear Science and Engineering, Vol. 134, No. 1, 2000, pp. 114-119.
- M. T. Vilhena, C. F. Segatto and L. B. Barichello, “A Par- ticular Solution for the SN Radiative Transfer Problems,” Journal of Quantitative Spectroscopy and Radiative Tran- sfer, Vol. 53, No. 4, 1995, pp. 467-469. doi:10.1016/0022-4073(95)90020-9
- C. Borges and E. W. Larsen, “The Transversely Inte- grated Scalar Flux of a Narrowly Focused Particle Beam,” SIAM Journal on Applied Mathematics, Vol. 55, No. 1, 1995, pp. 1-22.
- C. Borges and E. W. Larsen, “On the Accuracy of the Fokker-Planck and Fermi Pencil Beam Equation for Charged Particle Transport,” Medical Physics, Vol. 23, No. 10, 1996, pp. 1749-1759. doi:10.1118/1.597832
- B. D. A. Rodriguez, M. T. Vilhena, V. Borges and G. Hoff, “A Closed Form Solution for the Two-Dimensional Fokker-Planck Equation for Electron Transport in the Range of Compton Effect,” Annals of Nuclear Energy, Vol. 35, No. 5, 2008, pp. 958-962. doi:10.1016/j.anucene.2007.09.002
- B. D. A. Rodriguez, M. T. Vilhena and V. Borges, “A So- lution for the Two-Dimensional Transport Equation for Photons and Electrons in a Rectangular Domain by the Laplace Transform Technique,” International Journal of Nuclear Energy Science and Technology, Vol. 5, No. 1, 2010, pp. 25-40. doi:10.1504/IJNEST.2010.030304
- H. Hirayama and K. Shin, “Application of the EGS4 Monte Carlo Code to a Study of Multilayer Gamma-Ray Expo- sure Buildup Factors,” Journal of Nuclear Science and Technology, Vol. 35, No. 11, p. 816. doi:10.3327/jnst.35.816
- D. H. Wright, “Physics Reference Manual,” 2001. http://cern.ch/geant4
- G. C. Pomraning, “Flux-Limited Diffusion and Fokker- Planck Equations,” Nuclear Science and Engineering, Vol. 85, No. 2, 1983, p. 116.
- J. Wood, “Computational Methods in Reactor Shielding,” Pergamon Press, Oxford, 1982.
- S. Agostinelli, et al., “Geant4: A Simulation Toolkit,” Nu- clear Instruments and Methods in Physics Research A, Vol. 506, No. 3, 2003, pp. 250-303.
- DOORS 3.1, “One, Two and Three Dimensional Discrete Ordinates Neutron Photon Transport Code System,” Ra- diation Safety Information Computational Center (RSICC), Code Package CCC-650, Oak Ridge, Tennessee, 1996.
- B. D. A. Rodriguez, M. T. Vilhena and V. Borges, “The Determination of the Exposure Buildup Factor Formula- tion in a Slab Using the LTSN Method,” Kerntechnik, Vol. 71, No. 4, 2006, pp. 182-184.