The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation

The effect of anisotropic scattering on the eigenvalues of a multiplying (c >1) and non-multi-plying (c < 1) slab in one-speed neutron transport equation is studied. We have made some calculations, not only for the cases c<1 and 0 < g < 1, but also the cases of c >1 and -1...

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Main Authors: Kacira Kadir, Bilgic Huseyin, Yasa Faruk
Format: Article
Language:English
Published: VINCA Institute of Nuclear Sciences 2014-01-01
Series:Nuclear Technology and Radiation Protection
Subjects:
Online Access:http://www.doiserbia.nb.rs/img/doi/1451-3994/2014/1451-39941402102K.pdf
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spelling doaj-ab85b85053024bca9ddb90840f5b24122020-11-24T21:16:49ZengVINCA Institute of Nuclear SciencesNuclear Technology and Radiation Protection1451-39942014-01-0129210210710.2298/NTRP1402102K1451-39941402102KThe anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equationKacira Kadir0Bilgic Huseyin1Yasa Faruk2Kahramanmaras Sutcu Imam University, Faculty of Arts and Science, Department of Physics, K. Maras, TurkeyKahramanmaras Sutcu Imam University, Faculty of Arts and Science, Department of Mathematics, K. Maras, TurkeyKahramanmaras Sutcu Imam University, Faculty of Arts and Science, Department of Physics, K. Maras, TurkeyThe effect of anisotropic scattering on the eigenvalues of a multiplying (c >1) and non-multi-plying (c < 1) slab in one-speed neutron transport equation is studied. We have made some calculations, not only for the cases c<1 and 0 < g < 1, but also the cases of c >1 and -1<g<0 by using the linear and quadratic approximations of the Henyey-Greenstein scattering kernel. The asymmetry parameter g consists of isotropic, backward and forward bias. An extensive numerical survey is carried out for the eigenvalues in order to provide an accurate evaluation. The numerical results indicate that the discrete eigenvalue increases with forward scattering and decreases with backward scattering in expansions of linear and quadratic anisotropic scattering.http://www.doiserbia.nb.rs/img/doi/1451-3994/2014/1451-39941402102K.pdfHenyey-Greenstein scatteringtransport equationeigenvalue problemdiffusion length
collection DOAJ
language English
format Article
sources DOAJ
author Kacira Kadir
Bilgic Huseyin
Yasa Faruk
spellingShingle Kacira Kadir
Bilgic Huseyin
Yasa Faruk
The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation
Nuclear Technology and Radiation Protection
Henyey-Greenstein scattering
transport equation
eigenvalue problem
diffusion length
author_facet Kacira Kadir
Bilgic Huseyin
Yasa Faruk
author_sort Kacira Kadir
title The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation
title_short The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation
title_full The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation
title_fullStr The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation
title_full_unstemmed The anisotropic approximations of the Henyey-Greenstein phase function for neutron transport equation
title_sort anisotropic approximations of the henyey-greenstein phase function for neutron transport equation
publisher VINCA Institute of Nuclear Sciences
series Nuclear Technology and Radiation Protection
issn 1451-3994
publishDate 2014-01-01
description The effect of anisotropic scattering on the eigenvalues of a multiplying (c >1) and non-multi-plying (c < 1) slab in one-speed neutron transport equation is studied. We have made some calculations, not only for the cases c<1 and 0 < g < 1, but also the cases of c >1 and -1<g<0 by using the linear and quadratic approximations of the Henyey-Greenstein scattering kernel. The asymmetry parameter g consists of isotropic, backward and forward bias. An extensive numerical survey is carried out for the eigenvalues in order to provide an accurate evaluation. The numerical results indicate that the discrete eigenvalue increases with forward scattering and decreases with backward scattering in expansions of linear and quadratic anisotropic scattering.
topic Henyey-Greenstein scattering
transport equation
eigenvalue problem
diffusion length
url http://www.doiserbia.nb.rs/img/doi/1451-3994/2014/1451-39941402102K.pdf
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