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

Year 2018, , 144 - 153, 30.11.2018
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.

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.

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

Year 2018, , 144 - 153, 30.11.2018
https://doi.org/10.29233/sdufeffd.460420

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

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.
There are 26 citations in total.

Details

Primary Language Turkish
Subjects Metrology, Applied and Industrial Physics
Journal Section Makaleler
Authors

R. Gökhan Türeci 0000-0001-6309-6300

Publication Date November 30, 2018
Published in Issue Year 2018

Cite

IEEE R. G. Türeci, “Singüler Özfonksiyonlar Yöntemi ile Lineer-Kuadratik Anizotropik Saçılmalı Yarı-Uzay Albedo Hesaplamaları”, Süleyman Demirel University Faculty of Arts and Science Journal of Science, vol. 13, no. 2, pp. 144–153, 2018, doi: 10.29233/sdufeffd.460420.