Exact solution of the neutron transport equation in spherical geometry
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F. Anlı
, A. Akkurt , H. Yıldırım and K. Ateş
Abstract
Solution of the neutron transport equation in one dimensional slab geometry construct a basis for the solution of neutron transport equation in a curvilinear geometry. Therefore, in this work, we attempt to derive an exact analytical benchmark solution for both neutron transport equations in slab and spherical medium by using PN approximation which is widely used in neutron transport theory.
Kurzfassung
Die Lösung der Neutronentransportgleichung in eindimensionaler Plattengeometrie bildet die Grundlage für die Lösung der Neutronentransportgleichung in kurvenförmiger Geometrie. Deshalb wird in dem vorliegenden Beitrag eine exakte analytische Benchmark-Lösung sowohl für die Neutronentransportgleichung in eindimensionaler Plattengeometrie wie auch in einem kugelförmigen Medium mit Hilfe der in der Neutronentheorie häufig verwendeten PN-Approximation abgeleitet.
References
1 Baranov, A. S.: On Series Containing Products of Legendre Polynomials. Mat. Zametki80 (2006) 17110.1007/s11006-006-0124-5Search in Google Scholar
2 Larsen, E. W.; Pomraning,G. C.: PN theory as an asymptotic limit of transport theory in planar geometry – I: Analysis. Nuclear Science and Engineering109 (1991) 4910.13182/NSE91-A23844Search in Google Scholar
3 Lee, C. E.; Dias, M. P.: Analytical solutions to the moment transport equations – I: One group one region slab and sphere criticality. Annals of Nuclear Energy11 (1984) 51510.1016/0306-4549(84)90076-8Search in Google Scholar
4 Prudnikov, A. P.; Brychkov,Yu. A.; Marichev, O. I.: Integrals and series. Vol. 2. Gordon & Breach Science Publishers, New York1988Search in Google Scholar
5 Wang, Z. X.; Guo, D. R.: Special Functions. World Scientific Publishing Co., NJ198910.1142/0653Search in Google Scholar
6 Anli, F.; Gungor, S.: Some useful properties of Legendre polynomials and its applications to neutron transport equation in slab geometry. Applied Mathematical Modelling31 (2007) 72710.1016/j.apm.2005.12.005Search in Google Scholar
7 Bell, W. W.: Special Function for Scientist and Engineer. D. Van Nostrand Company London, 1967Search in Google Scholar
8 Bell, G. I.; Glasstone, S.: Nuclear Reactor Theory. Van Nostrand Reinhold Company, New York, 1970Search in Google Scholar
9 Davidson, B.; Sykes, J. B.: Neutron Transport Theory. The Clarendon Press, Oxford, 1957Search in Google Scholar
10 Mitsis, G. J.: Transport solutions to the monoenergetic critical problems, Ph.D. Dissertation, Argonne National Lab., 196310.2172/4118021Search in Google Scholar
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