A Conventional Phase Function with the Chebyshev Polynomials of Second Kind for the Criticality Problem in Transport Theory

Year 2017, Volume: 7 Issue: 2, 121 - 132, 04.01.2018

Hakan Öztürk

Abstract

The
criticality calculations for one-speed neutrons in a finite homogenous slab are
done using the conventional Henyey-Greenstein (HG) phase function in transport theory.
After defining the phase function in transport equation, the neutron angular
flux is expanded in terms of the Chebyshev polynomials of second kind (U_N method). Then, the
critical half-thicknesses of the slab are calculated for various values of the
scattering parameters. The numerical results obtained from the present method
are given in the tables together with the ones obtained using an alternative
phase function (Anlı-Güngör, AG) for comparison.

Keywords

Henyey-Greenstein Function, Critical Slab, UN Method, Transport Equation

Transport Teoride Kritiklik Problemi için İkinci Tip Chebyshev Polinomları ile Konvansiyonel Bir Faz Fonksiyonu

Abstract

Transport
teoride konvansiyonel Henyey-Greenstein (HG) faz fonksiyonu kullanılarak sonlu
homojen bir dilimdeki nötronlar için kritiklik hesaplamaları yapılmıştır. Transport denkleminde faz fonksiyonu tanımlandıktan
sonra, açısal nötron akısı ikinci tip Chebyshev polinomları cinsinden seriye
açılmıştır (U_N metodu). Daha sonra, saçılma parametrelerinin farklı
değerleri için dilimin yarı-kalınlıkları hesaplanmıştır. Mevcut metotla elde
edilen nümerik sonuçlar, alternatif faz fonksiyonu (Anlı-Güngör, AG) kullanılarak
elde edilen sonuçlar ile karşılaştırma yapmak için tablolarda verilmiştir.

Keywords

Henyey-Greenstein Fonksiyonu, Kritik Dilim, UN Metodu, Transport Denklemi

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