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

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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