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Efficiency of reflection coefficients in the isotropic neutron transport equation and computation of the critical-half thicknesses

Effizienz von Reflektionskoeffizienten in der isotropischen Neutronentransportgleichung und die Berechnung kritischer Halbwertsdicken
A. Bülbül, A. Kara and F. Anlı
From the journal Kerntechnik

Abstract

The critical slab problem of the reflected isotropic one-speed neutron transport equation is solved with the Chebyshev polynomial approximation. The efficiency of the reflection coefficient, R, in the neutron transport equation is obtained for different c values. For the solution, the Mark boundary condition is used. The values obtained from this approximation are compared with results obtained by the spherical harmonics method.

Kurzfassung

Das Kritikalitätsproblem der Eingruppen-Neutronentransportgleichung bei reflektierenden Randbedingungen und isotroper Streuung wird gelöst mit Hilfe von Tschebyscheff-Polynomen. Die Effizienz des Reflektionskoeffizienten R in der Neutronentransportgleichung wird für verschiedene c-Werte erhalten. Für die Lösung der Gleichung wird die Randbedingung nach Mark verwendet. Die aus dieser Näherung erhaltenen Werte werden verglichen mit Ergebnissen nach der Methode der sphärischen Harmonischen.


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References

1 Aspelund, O.: On a New Method for Solving the (Boltzmann) Equation in Neutron Transport Theory. PICG16 (1959) 530534 Search in Google Scholar

2 Conkie, W. R.: Polynomial Approximations in Neutron Transport Theory. Nucl. Scie. Eng.6 (1959) 260266 Search in Google Scholar

3 Yabushita, S.: Tschebyscheff Polynomial Approximation Method of the Neutron Transport Equation. Journ. of Math. Physics.2 (1961) 543549 Search in Google Scholar

4 Garis, N. S.; Sjöstrand, N. G.: Eigenvalues for reflecting boundary conditions in one-speed Neutron Transport Theory. Ann. Nucl. Energy.21 (1994) 6780 Search in Google Scholar

5 Sahni, D. C.; Garis, N. S.; Sjöstrand, N. G.: Trans. Theory Statist. Phys.24 (1995) 62965610.1080/00411459508206019 Search in Google Scholar

6 Siewert, C. E.; Williams, M. M. R.: The effect of anisotropic scattering on the critical slab problem in neutron transport theory using a synthetic kernel. J. Phys. D: Appl. Phys.10 (1977) 20312040 Search in Google Scholar

7 Anlı, F.; Yaşa, F.; Güngör, S.; Öztürk, H.: TN approximation to neutron transport equation and application to critical slab problem. J. Quant. Spectroscopy Radiat. Transfer.101 (2006) 129134 Search in Google Scholar

8 Anlı, F.; Yaşa, F.; Güngör, S.; Öztürk, H.: TN approximation to reflected slab and computation of the critical half thickness. J. Quant. Spectroscopy Radiat. Transfer.101 (2006) 135140 Search in Google Scholar

9 Ozturk, H.; Anlı, F.; Gungor, S.: Application of the UN method to the reflected critical slab problem for one-speed neutrons with forward and backward scattering. Kerntechnik72 (2007) 7476 Search in Google Scholar

10 Ozturk, H.: The reflected critical slab problem for one-speed neutrons with strongly anisotropic scattering, Kerntechnik73 (2008) 6674 Search in Google Scholar

11 Szegö, G.: Orthogonal polynomials, American Society Providence, Rhode Island. 1967 Search in Google Scholar

12 Case, K. M.; Zweifel, P. F.: Linear Transport Theory. Reading MA, Addison Wesley, 1967 Search in Google Scholar

Received: 2009-1-19
Published Online: 2013-04-05
Published in Print: 2010-08-01

© 2010, Carl Hanser Verlag, München