The Half-Space Albedo Calculations with the Linear-Quadratik Anisotropic Scattering with Singular Eigenfunction Method

Year 2018, Volume: 13 Issue: 2, 144 - 153, 30.11.2018

R. Gökhan Türeci

https://doi.org/10.29233/sdufeffd.460420

Abstract

In this study the infinite medium Green’s function is derived for linear-quadratic
anisotropic scattering in one-speed neutron transport theory and, it is used for the half-space
albedo calculations with Singular eigenfunction method. The calculated numerical results
completely conformed to Modified FN (HN) method the results.

Keywords

Linear-Quadratic anisotropic scattering, the infinite medium Green’s function, CN Equations, Singular Eigenfunction method, Half-space albedo

Singüler Özfonksiyonlar Yöntemi ile Lineer-Kuadratik Anizotropik Saçılmalı Yarı-Uzay Albedo Hesaplamaları

Abstract

Bu çalışmada tek-hızlı nötron transport teoride çalışılan lineer-kuadratik anizotropik
saçılma fonksiyonu için sonsuz ortam Green fonksyionu elde edilmiş ve yarı-uzay albedo
hesaplamaları için Singüler özfonksiyonlar yönteminde kullanılmıştır. Elde edilen sayısal
sonuçlar Modified FN (HN) yöntemi sonuçları ile tamamen uyumludur

Keywords

Lineer-kuadratik anizotropik saçılma, CN denklemleri, Singüler özfonksiyonlar yöntemi, Yarı-uzay albedo, Sonsuz ortam Green fonksiyonu, Yarı-uzay albedo

References

• B. Davison, Neutron Transport Theory. London: Oxford University Press, 1958, ch. 1-8.
• K. M. Case, “Elementary solutions of the transport equation and their applications,” Ann. Physics, vol. 9, no. 1, pp. 1-23, 1960.
• K. M. Case, and P. F. Zweifel, Linear Transport Theory. Reading Mass: Addition-Wesley, 1967, ch. 4-6.
• M. M. R. Williams, Mathematical Methods in Particle Transport Theory. New York: Wiley-Interscience, 1971, ch. 3-8.
• G. I. Bell, and S. Glasstone, Nuclear Reactor Theory. New York: Von Nostrand Reinhold, 1972, ch. 1-3.
• W. M. Stacey, Neutron Transport Theory. 2nd ed., Weinheim: Wiley-VCH Verlag GmbH & Co. KGaA, 2007. ch. 9.
• J. Mika, “Neutron transport with anisotropic scattering,” Nucl. Sci. Eng., vol. 11, no. 4, pp. 415-427, 1961.
• N. J. McCormick, and I. Kuščer, “Half‐space neutron transport with linearly anisotropic scattering,” J. Math. Phys., vol. 6, no. 2, pp. 1939-1945, 1965.
• N. J. McCormick, and I. Kuščer, “Singular eigenfunction expansions in neutron transport theory,” Adv. Nucl. Sci. Tech., vol. 7, pp. 181-282, 1973.
• V. Protopopescu, and N. G. Sjöstrand, “On the solution of the dispersion equation for monoenergetic neutron transport with linearly anisotropic scattering,” Prog. Nucl. Energ., vol. 7, no. 1, pp. 47-58, 1981.
• C. E. Siewert, and P. Benoist, “The FN method in neutron-transport theory, Part I: Theory and applications,” Nucl. Sci. Eng., vol. 69, no. 2, pp. 156-160, 1979.
• P. Grandjean, and C. E. Siewert, “The FN method in neutron-transport theory, Part II: Applications and numerical results,” Nucl. Sci. Eng., vol. 69, no. 2, pp. 161-168, 1979.
• A. Kavenoky, “The CN method of solving the transport equation: Application to plane geometry,” Nucl. Sci. Eng., vol. 65, no. 2, pp. 209-225, 1978.
• C. Tezcan, A. Kaşkaş, M. Ç. Güleçyüz, “The H-N method for solving linear transport equation: theory and applications,” J. Quant. Spectrosc. Ra.., vol. 78, no. 2, pp. 243-254, 2003.
• N. G. Sjöstrand, “Complex eigenvalues for neutron transport equation with quadratically anisotropic scattering,” J. Nucl. Sci. Technol., vol. 18, no. 1, pp. 1-5, 1981.
• R. G. Türeci, and D. Türeci, “Time dependent albedo problem for quadratic anisotropic scattering,” Kerntechnik, vol. 72, no. 1-2, pp. 59-65, 2007.
• R. G. Türeci, and M.Ç. Güleçyüz, “The slab albedo and criticality problem for the quadratic scattering kernel with the H-N method,” Kerntechnik, vol. 73, no. 4, pp. 171-175, 2008.
• R. G. Türeci, “Solving the criticality problem with the reflected boundary condition for the triplet anisotropic scattering with the Modified FN method,” Kerntechnik, vol. 80, no. 6, pp. 583-591, 2015.
• R. G. Türeci, and D. Türeci, “Half-space albedo problem with Modified FN method for linear and quadratic anisotropic scattering,” Kerntechnik, vol. 82, no. 2, pp. 239-245, 2017.
• R. G. Türeci, and D. Türeci, “Slab albedo for linearly and quadratically anisotropic scattering kernel with Modified FN method,” Kerntechnik, vol. 82, no.5, pp. 605-611, 2017.
• R.G. Türeci, “Half-space albedo problem for the (İnönü, Linear and Quadratic) anisotropic scattering,” Kerntechnik, submitted for publication.
• K. M. Case, F. de Hoffmann, and G. Placzek, Introduction to the Theory of Neutron Diffusion. Los Alamos (N.M.) Scientific Laboratory, New Mexico, 1953.
• C. Tezcan, M. Ç. Güleçyüz, and F. Erdoğan, “A new approach of solving the third form of the transport equation in plane geometry: Half-space albedo problem,” J. Quant. Spectrosc. Ra.., vol. 55, no. 2, pp. 251-258, 1996.
• F. Erdoğan, M. Ç. Güleçyüz, A. Kaşkaş and C. Tezcan “Solution of the CN equations using singular eigenfunctions and applications,” Ann. Nucl. Energy., vol. 23, no. 6, pp. 553-541, 1996.
• M. Ç. Güleçyüz, A. Kaşkaş, and C. Tezcan, “Slab albedo problem for anisotropic scattering using singular eigenfunction solution of the CN equations J. Quant. Spectrosc. Ra.., vol. 61, no. 3, pp. 329-338, 1999.
• R. G. Türeci “Half-space albedo problem for linear-quadratic anisotropic scattering according to moments of ıncoming neutron distribution,” International Conference on Theoretical and Experimental Studies in Nuclear Applications and Technology, in Conf. Rec. 2017 TESNAT 2017, Adana, Turkey.