Home Technology Application of the Henyey-Greenstein and Anlı-Güngör phase functions for the solution of the neutron transport equation with Legendre polynomials: Reflected critical slab problem
Article
Licensed
Unlicensed Requires Authentication

Application of the Henyey-Greenstein and Anlı-Güngör phase functions for the solution of the neutron transport equation with Legendre polynomials: Reflected critical slab problem

  • H. Öztürk
Published/Copyright: November 23, 2013
Become an author with De Gruyter Brill

Abstract

The criticality problem for one-speed neutrons in a uniform homogeneous slab with reflecting boundary conditions is studied using Henyey-Greenstein (HG) and Anlı-Güngör (AG) phase functions. The critical half-thicknesses of the slab are performed with traditional spherical harmonics (PN) method for various values of the cross-section parameter, reflection coefficient and the scattering parameters of HG and AG phase functions. The numerical results obtained in case of using both HG and AG phase functions are tabulated in the tables and they are compared with each other.

References

1 Davison, B.: Neutron transport theory. London, Oxford University Press, 195810.1063/1.3062414Search in Google Scholar

2 Case, K. M; Zweifel, P. F.: Linear transport theory. Addison-Wesley Publishing Company, 1967Search in Google Scholar

3 Bell, G. I.; Glasstone, S.: Nuclear reactor theory. New York, VNR Company, 1972Search in Google Scholar

4 Sahni, D. C.; Sjöstrand, N. G.; Garis, N. S.: Criticality and time eigenvalues for one-speed neutrons in a slab with forward and backward scattering. J. Phys. D: Appl. Phys.25 (1992) 1381Search in Google Scholar

5 Henyey, L. G.; Greenstein, J. L.: Diffuse radiation in the galaxy. Astrophys. J.93 (1941) 70Search in Google Scholar

6 Reynolds, L. O.; McCormic, N. J.: Approximate two parameter phase function for light scattering. J. Op. Soc. Am.70 (1980) 1206Search in Google Scholar

7 Williams, M. M. R.: A synthetic scattering kernel for particle transport in absorbing media with anisotropic scattering. J. Phys. D: Appl. Phys.11 (1978) 2455Search in Google Scholar

8 Liu, P.: A new phase function approximating to Mie scattering for radiative transport eqyations. Phys. Med. Biol.39 (1994) 1025Search in Google Scholar

9 Anlı, F.; Yaşa, F.; Güngör, S.: General eigenvalue spectrum in a one-dimensional slab geometry transport equation. Nucl. Sci. Eng.150 (2005) 72Search in Google Scholar

10 Anlı, F.; Güngör, S.: Some useful properties of Legendre polynomials and its applications to neutron transport equation in slab geometry. Appl. Math. Mod.31 (2007) 727Search in Google Scholar

11 Yaşa, F.; Anlı, F.: A model for calculation of forward isotropic scattering with application to transport equation in slab geometry. Kerntechnik74 (2009) 320Search in Google Scholar

12 Öztürk, H.; Anlı, F.: Diffusion approximation for certain scattering parameters of the Anli-Güngör phase function. Kerntechnik77 (2012) 381Search in Google Scholar

13 Yıldız, C.: Variation of the critical slab thickness with the degree of strongly anisotropic scattering in one-speed neutron transport theory. Ann. Nucl. Energy25 (1998) 529Search in Google Scholar

14 Lee, C. E.; Dias, M. P.: Analytical solutions to the moment transport equations-I; one-group one-region slab and sphere criticality. Ann. Nucl. Energy11 (1984) 515Search in Google Scholar

15 Arfken, G.: Mathematical methods for physicists. London, Academic Press, Inc.: 1985Search in Google Scholar

16 Sahni, D. C.; Sjöstrand, N. G.: Non-monotonic variation of the criticality factor with the degree of anisotropy in one-speed neutron transport. Transp. Theory Statist. Phys.20 (1991) 339Search in Google Scholar

Received: 2012-12-24
Published Online: 2013-11-23
Published in Print: 2013-11-14

© 2013, Carl Hanser Verlag, München

Downloaded on 14.2.2026 from https://www.degruyterbrill.com/document/doi/10.3139/124.110328/html
Scroll to top button