Browse > Article
http://dx.doi.org/10.1016/j.net.2019.10.008

Half-space albedo problem for İnönü, linear and quadratic anisotropic scattering  

Tureci, R.G. (Kirikkale University, Kirikkale Vocational School, Center Campus)
Publication Information
Nuclear Engineering and Technology / v.52, no.4, 2020 , pp. 700-707 More about this Journal
Abstract
This study is concerned with the investigation of the half-space albedo problem for "İnönü-linear-quadratic anisotropic scattering" by the usage of Modified FN method. The method is based on Case's method. Therefore, Case's eigenfunctions and its orthogonality properties are derived for anisotropic scattering of interest. Albedo values are calculated for various linear, quadratic and İnönü anisotropic scattering coefficients and tabulated in Tables.
Keywords
${\dot{I}}n{\ddot{o}}n{\ddot{u}}$-linear-quadratic anisotropy; Half-space albedo; Forward-linear-quadratic anisotropy; Backward-linear-quadratic anisotropy;
Citations & Related Records
연도 인용수 순위
  • Reference
1 B. Davison, Neutron Transport Theory, Oxford University Press, London, 1958.
2 M.M.R. Williams, Mathematical Methods in Particle Transport Theory, Oxford University Press, London, 1971.
3 G.I. Bell, S. Glasstone, Nuclear Reactor Theory, Von Nostrand Reinhold, New York, 1972.
4 K.M. Case, Elementary solutions of the transport equation and their applications, Ann. Phys. 9 (1) (1960) 1-23, https://doi.org/10.1016/0003-4916(60)90060-9.   DOI
5 K.M. Case, P.F. Zweifel, Linear Transport Theory, Addition-Wesley, MA, 1967.
6 C.E. Siewert, P. Benoist, The FN method in neutron-transport theory, Part I: theory and applications, Nucl. Sci. Eng. 69 (1979) 156.   DOI
7 P. Grandjean, C.E. Siewert, The FN method in neutron-transport theory, Part II: applications and numerical results, Nucl. Sci. Eng. 69 (1979) 161.   DOI
8 A. Kavenoky, The CN method of solving the transport equation: application to plane geometry, Nucl. Sci. Eng. 65 (1978) 209-225.   DOI
9 C. Tezcan, A. Kaskas, M.C. Gulecyuz, The H-N method for solving linear transport equation: theory and Applications, J. Quant. Spectrosc. Radiat. Transfer 78 (2) (2003) 243-254.   DOI
10 K.M. Case, F. de Hoffmann, G. Placzek, Introduction to the Theory of Neutron Diffusion, Los Alamos, New Mexico, 1953.
11 A. Kavenoky, The CN Method of solving the transport equation: application to plane geometry, Nucl. Sci. Eng. 65 (1978) 209.   DOI
12 J. Mika, Neutron transport with anisotropic scattering, Nucl. Sci. Eng. 11 (1961) 415.   DOI
13 N.J. McCormick, I. Kuscer, Half-space neutron transport with linearly anisotropic scattering, J. Math. Phys. 6 (12) (1965) 1939.   DOI
14 V. Protopopescu, N.G. Sjostrand, On the solution of the dispersion equation for monoenergetic neutron transport with linearly anisotropic scattering, Prog. Nucl. Energy 7 (1) (1981) 47.   DOI
15 D.C. Sahni, N.G. Sjostrand, N.S. Garis, Criticality and time eigenvalues for onespeed neutrons in a slab with forward and backward scattering, J. Phys. D Appl. Phys. 25 (10) (1992) 1381.   DOI
16 Mathematica Software, Wolfram researches, UK.
17 R.G. Tureci, D. Tureci, Slab albedo for linearly and quadratically anisotropic scattering kernel with Modified FN method, Kerntechnik 82 (5) (2017) 693-699.   DOI
18 R.G. Tureci, The Half-Space Albedo Calculations with the Linear-Quadratic Anisotropic Scattering with Singular Eigenfunction Method, vol. 13, Suleyman Demirel University Faculty of Arts and Sciences Journal of Science, 2018, pp. 144-153 (2).
19 R.G. Tureci, Lineer-Kuadratik Anizotropik Sacilma Icin Kritiklik Probleminde Yansitici Ozdegerleri, vol. 14, Suleyman Demirel University Faculty of Arts and Sciences Journal of Science, 2019, pp. 1-15 (1).
20 R.G. Tureci, D. Türeci, Time dependent albedo problem for quadratic anisotropic scattering, Kerntechnik 72 (1-2) (2007) 59.   DOI
21 R.G. Tureci, The albedo problem for pure-quadratic anisotropic scattering with Inonu scattering, Kerntechnik 75 (5) (2010) 292.   DOI
22 E. Inonu, A theorem on anisotropic scattering, Transp. Theory Stat. Phys. 3 (1973) 137-147.   DOI
23 E. Inonu, Scalar and time inversion of the linear mono-energetic Boltzmann equation, Phys. Fluids 19 (1976) 1332-1335.   DOI
24 C.E. Siewert, M.M.R. Williams, The effect of anisotropic scattering on the critical slab problem in neutron transport theory using a synthetic kernel, J. Phys. D Appl. Phys. 10 (15) (1977) 2031-2040.   DOI
25 M.M.R. Williams, A synthetic scattering kernel for particle transport in absorbing media with anisotropic scattering, J. Phys. D Appl. Phys. 11 (18) (1978) 2455-2463.   DOI
26 C. Tezcan, C. Yildiz, The effect of forward, backward and linear anisotropic scattering on the critical slab thickness, J. Quant. Spectrosc. Radiat. Transfer 53 (6) (1995) 687-691.   DOI
27 D.C. Sahni, N.G. Sjostrand, Criticality eigenvalues of the one-speed transport equation with strong forward-backward scattering-relationship with rod model, Transp. Theory Stat. Phys. 27 (2) (1998) 137-158.   DOI
28 C. Devaux, C.E. Siewert, Y. Yener, The effect of forward and backward scattering on the spherical albedo for a finite plane-parallel atmosphere, J. Quant. Spectrosc. Radiat. Transfer 21 (6) (1979) 505-509.   DOI
29 C. Tezcan, R. Sever, The critical slab with the backward-forward-isotropic scattering model, Ann. Nucl. Energy 12 (10) (1985) 573-576.   DOI
30 M.M.R. Williams, The energy-dependent backward-forward-isotropic scattering model with some applications to the neutron transport equation, Ann. Nucl. Energy 12 (4) (1985) 167-176.   DOI
31 C. Yildiz, E. Alcan, The effect of strong anisotropic scattering on the critical sphere problem in neutron transport theory using a synthetic kernel, Ann. Nucl. Energy 22 (10) (1995) 671-679.   DOI
32 C. Yildiz, Variation of the albedo and the transmission factor with forward and backward scattering in neutron transport theory- the FN method, Ann. Nucl. Energy 27 (9) (2000) 831-840.   DOI
33 F.S. de Azevedo, E. Sauter, P.H.A. Konzen, M. Thompson, Numerical results for the transport equation with strongly anisotropic scattering in a slab, Ann. Nucl. Energy 79 (2015) 61-67.   DOI
34 R.G. Tureci, D. Tureci, Half-space albedo problem with Modified FN method for linear and quadratic anisotropic scattering, Kerntechnik 82 (2) (2017) 239-245.   DOI