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3D modelling of unpolarized photon diffusion using the integral form of the transport equation
Author(s) -
Fernández J. E.,
Molinari V. G.,
Teodori F.
Publication year - 1999
Publication title -
x‐ray spectrometry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 45
eISSN - 1097-4539
pISSN - 0049-8246
DOI - 10.1002/(sici)1097-4539(199909/10)28:5<327::aid-xrs373>3.0.co;2-x
Subject(s) - physics , photon , photon diffusion , diffusion equation , compton scattering , monte carlo method for photon transport , convection–diffusion equation , scalar (mathematics) , photon transport in biological tissue , diffusion , integral equation , boundary value problem , momentum (technical analysis) , computational physics , optics , geometry , quantum mechanics , mathematical analysis , mechanics , monte carlo method , economy , mathematics , service (business) , dynamic monte carlo method , direct simulation monte carlo , hybrid monte carlo , markov chain monte carlo , light source , statistics , finance , economics
The 3D scalar transport equation for unpolarized photons is used to give a detailed description of the fluorescence photon diffusion from a homogeneous slab. As an example, the paper considers, with a complete 3D spatial description in plane geometry, the distribution both in physical and momentum space of the primary photons induced by a narrow radiation beam crossing the slab. Then it is shown how the 3D geometry influences the shape of the continuous spectra due to a second Compton collision which modifies the distribution of the primaries due to photoelectric effect. The possibility of isolating the effect of a particular interaction is one of the strengths of the multiple‐scattering scheme in the framework of transport techniques, which allows a better understanding of photon diffusion. In order to evaluate the effects of boundary conditions, the integral transport equation is used instead of the integro‐differential equation, which has the advantage of treating the flow of photons from the outer space as an external source. The results are compared with those obtained for a half‐infinite medium uniformly irradiated with a plane infinite slant source of monochromatic photons previously solved in 1D. Copyright © 1999 John Wiley & Sons, Ltd.