S4 Solution of the Transport Equation for Eigenvalues: Isotropic, Forward and Backward Scattering in a Slab

Abstract

Abstract: The neutron transport equation is solved numerically for monoenergetic neutrons in a finite homogeneous slab with backward and forward scattering for the eigenvalue spectrum. The forward-backward-isotropic (FBI) scattering kernel is chosen for representing the neutron scattering in transport equation. Then, the transport equation is converted into a discrete ordinates form by using the integral transform technique with the even-order Gauss-Legendre quadrature set. Finally, the eigenvalues are calculated for a medium from weakly absorbing to highly scattering condition using various values of the scattering, backward and forward scattering parameters. Gauss-Legendre quadrature sets are used for all calculations and the calculated eigenvalues are given in the tables.

Keywords

• Transport Equation,Forward and Backward Scattering,Discrete Ordinates,Eigenvalues

Transport Denkleminin Özdeğerler için S4 Çözümü: Dilimde İzotropik, İleri ve Geri Saçılma

Abstract

Özet: İleri ve geri saçılmalı sonlu homojen bir dilimde tek enerjili nötronların özdeğer spektrumu için nötron transport denklemi nümerik olarak çözülmüştür. Transport denklemindeki nötron saçılmasını temsilen, ileri-geri-izotropic (FBI) saçılma fonksiyonu tercih edilmiştir. Daha sonra, çift-mertebeli Gauss-Legendre kuadratür seti ile integral dönüşüm tekniği kullanılarak transport denklemi diskret-ordinatlar haline dönüştürülmüştür. Son olarak, faklı saçılma, ileri ve geri saçılma parametreleri kullanılarak zayıf yutulmalı bir ortamdan kuvvetli saçılmalı bir ortama kadar özdeğerler hesaplanmıştır. Bütün hesaplamalarda Gauss-Legendre kuadratür setleri kullanılmış ve hesaplanan özdeğerler çizelgelerde verilmiştir.

Keywords

• Transport Denklemi,İleri ve Geri Saçılma,Diskret Ordinatlar,Özdeğerler

References

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