Diffusion Approximation to Neutron Transport Equation with First Kind of Chebyshev Polynomials

Yıl 2015, Cilt: 10 Sayı: 2, 92 - 96, 22.11.2015

Ökkeş Ege Hakan Öztürk Ahmet Bülbül

Öz

The first kind of Chebyshev polynomials are used for the series expansion of the neutron angular flux in neutron transport theory. The first order approximation known as the diffusion approximation is applied to one-dimensional neutron transport equation to determine the diffusion coefficients of one-speed neutrons for selected values of the scattering parameters

Anahtar Kelimeler

First kind of Chebyshev polynomials, neutron transport equation, diffusion approximation

Birinci Tip Chebyshev Polinomları ile Nötron Transport Denklemine Difüzyon Yaklaşımı

Öz

Nötron transport teorisinde açısal akının seri açılımı için I. Tip Chebyshev polinomları kullanıldı. Tek hızlı nötronların difüzyon katsayılarını belirlemek için difüzyon yaklaşımı olarak bilinen ilk mertebe yaklaşımı saçılma parametrelerinin seçilen değerleri için tek boyutlu nötron transport denklemine uygulanmıştır.

Anahtar Kelimeler

I. tip Chebyshev polinomları, nötron transport denklemi, difüzyon Yaklaşımı

Kaynakça

• Lamarsh J.R., Baratta A.J., 2001. Introduction to nuclear engineering. Prentice Hall, Inc.
• Davison B., 1958. Neutron transport theory. London, Oxford University Press.
• Case K.M, Zweifel P.F., 1967. Linear transport theory. Addison-Wesley Publishing Company.
• Aspelund O., 1958. On a new method for solving the (Boltzmann) equation in neutron transport theory, PICG, 16: 530.
• Conkie W.R., 1959. Polynomial approximations in neutron transport theory, Nuclear Science and Engineering. 6: 260-266.
• Yabushita S., 1961. Tschebyscheff polynomials approximation method of the neutron transport equation, Journal of Mathematical Physics, 2: 543-549.
• Anlı F., Yaşa F., Güngör S., Öztürk H., 2006. TN approximation to neutron transport equation and application to critical slab problem, Journal of Quantitative Spectroscopy and Radiative Transfer, 101: 129-134.
• Öztürk H., Anlı F., Güngör S., 2007. TN method for the critical thickness of one-speed neutrons in a slab with forward and backward scattering, Journal of Quantitative Spectroscopy and Radiative Transfer, 105: 211-216.
• Öztürk H., Bülbül A., Kara A., 2010. U1 approximation to the neutron transport equation and calculation of the asymptotic relaxation length, Kerntechnik, 75: 375-376.
• Tıraş M., Öztürk H., Bülbül A., 2014. T1 and U1 approximations to neutron transport equation in one- dimensional spherical geometry, Kerntechnik, 79: 163-166.
• Yıldırım S., Öztürk H., 2014. Diffusion length calculations for one-speed neutrons in a slab with backward, forward and linear anisotropic scattering, Kerntechnik, 79: 243-246.
• Bell G.I., Glasstone, S., 1970. Nuclear reactor theory. New York, VNR Company, 619 p.
• Hakan Öztürk e-mail: [e-mail]
• Ahmet Bülbül e-mail: [e-mail]