Title: A solution for the two-dimensional transport equation for photons and electrons in a rectangular domain by the Laplace transform technique

Authors: Barbara D. do Amaral Rodriguez, Marco Tullio Vilhena, Volnei Borges

Addresses: Instituto de Matematica, Estatistica e Fisica, Universidade Federal do Rio Grande – FURG, Campus Carreiros Av. Italia Km 8, s/n, Rio Grande, Rio Grande do Sul, Brazil. ' Pure and Applied Mathematics Department, Universidade Federal do Rio Grande do Sul – UFRGS, Avenida Bento Goncalves 9500, Porto Alegre, Rio Grande do Sul, Brazil. ' Mechanical Engineering Post-Graduation Program, Universidade Federal Rio Grande do Sul – UFRGS, Rua Sarmento Leite, 425 – sala 314 Porto Alegre, Rio Grande do Sul, Brazil

Abstract: In the first part of this paper, we describe a review in the Laplace transform technique applied to S_N two-dimensional transport equation in a rectangular domain considering Compton scattering. In Compton scattering the incident photon interacts with an electron of the irradiated medium, giving the electron kinetic energy, and also producing a scattered photon. In order to track that electron, in the second part of this paper, we apply the P_N approximation to X,Y-geometry electron transport problems. In this derivation, the energy deposited by the free electron is taken into account. To reach this objective we solve two model problems: the first one for the transport of photons, assuming the Klein-Nishina scattering kernel as the scattering differential cross-section as well as the multigroup model in the energy variable; and the second one for the transport of free electrons considering the screened Rutherford scattering kernel. The results are presented under absorbed energy form in several points of interest. We report numerical simulations and comparisons with results obtained by using the Geant4 version 9.1 program which applies the Monte Carlo|s technique to low energy libraries for both two-dimensional problems.

Keywords: Klein-Nishina scattering kernel; Rutherford scattering kernel; multigroup modelling; rectangular domain; Laplace transform technique; 2D transport equation; Compton scattering; photons; electrons.

DOI: 10.1504/IJNEST.2010.030304

International Journal of Nuclear Energy Science and Technology, 2010 Vol.5 No.1, pp.25 - 40

Published online: 14 Dec 2009 *

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