Heuristic geometric “eigenvalue universality” in a one-dimensional neutron transport problem with anisotropic scattering
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G. A. Gonçalves
Abstract
In the present work we propose a heuristic construction of a transport equation for neutrons with anisotropic scattering considering only the radial cylinder dimension. The eigenvalues of the solutions of the equation correspond to the positive values for the one dimensional case. The central idea of the procedure is the application of the SN method for the discretisation of the angular variable followed by the application of the zero order Hankel transformation. The basis the construction of the scattering terms in form of an integro-differential equation for stationary transport resides in the hypothesis that the eigenvalues that compose the elementary solutions are independent of geometry for a homogeneous medium. We compare the solutions for the cartesian one dimensional problem for an infinite cylinder with azimuthal symmetry and linear anisotropic scattering for two cases.
Kurzfassung
In der vorliegenden Arbeit schlagen wir eine heuristische Konstruktion für eine Neutronentransportgleichung mit anisotroper Streuung vor und ziehen nur die radiale Zylinderdimension in Betracht. Die Eigenwerte der Lösungen der Gleichung entsprechen den positiven Werten für den eindimensionalen Fall. Die zentrale Idee des Verfahrens ist die Anwendung der SN-Methode für die Diskretisierung der Winkelvariable, gefolgt von der Anwendung der Hankel-Transformation nullter Ordnung. Die Grundlage der Erstellung der Streuterme in Form einer Integro-Differentialgleichung für den stationären Transport folgt der Hypothese, dass die Eigenwerte, die die elementaren Lösungen bestimmen, unabhängig sind von der Geometrie für ein homogenes Medium. Wir vergleichen für zwei Fälle die Lösungen für kartesische eindimensionale Probleme mit denen eines unendlichen Zylinders mit azimutaler Symmetrie und linear anisotroper Streuung.
References
1 Altaç, Z.; Spinrad, B. I.: The SKN Method I: A High-Order Transport Approximation to Neutron Transport Problems, Nuclear Science and Engineering106 (1990) 471–479Suche in Google Scholar
2 Arfken, G. B.; Weber, H. J.: Mathematical Methods for Physicists, 6th edition, Harcourt, San Diego (2005)Suche in Google Scholar
3 Case, K. M.; Zweifel, P. F.: Linear Transport Theory, Addison-Wesley Publishing Company Inc. (1967)Suche in Google Scholar
4 Mitsis, G. J.: Transport Solutions to the Monoenergetic Critical Problems. PhD. Thesis, Report ANL-6787, Argone National Laboratory, Chicago (1963) 10.2172/4118021Suche in Google Scholar
5 Siewert, C. E.; Thomas, J. R.: Neutron Transport Calculations in Cylindrical Geometry. Nuclear Science and Engineering87 (1984) 107–112Suche in Google Scholar
6 Vilhena, M. T.; Velho, H. F. de Campos; Segatto, C. F.; Gonalves, G. A.: Analytical Solution of the One-Dimensional Discrete Ordinates Equation by the Laplace and Hankel Integral Transform. In: Constanda, M. A.; Largillier, A. (Org.), Integral Methods in Science and Engineering, Cambridge, Birkhauser Boston (2004) 267–272Suche in Google Scholar
7 Watson, G. N.: A Treatise on the Theory of Bessel Functions, Second Edition, Cambridge University Press (1995)Suche in Google Scholar
© 2010, Carl Hanser Verlag, München
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
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- Chebyshev polynomials expansion method for solving the one-dimensional transport equation in spherical geometry
- Heuristic geometric “eigenvalue universality” in a one-dimensional neutron transport problem with anisotropic scattering
- An analytical solution for the one-dimensional time-dependent SN transport equation for bounded and unbounded domains in cartesian geometry
- Accurate critical slab calculations for various degrees of anisotropy and for different reflection coefficients
- Technical Notes/Technische Mitteilungen
- The boundary problem in the 1D-CANDLE burn-up reactor
Artikel in diesem Heft
- Contents/Inhalt
- Contents
- Summaries/Kurzfassungen
- Summaries
- Technical Contributions/Fachbeiträge
- European clearinghouse on nuclear power plants operational experience feedback
- Investigation on primary side oriented accident management measures in a hypothetical station blackout scenario for a VVER-1000 pressurized water reactor
- Heat transfer to the building structures of the Ignalina NPP accident localisation system
- Algorithmic determination of fuel rod cladding burst time at elevated temperatures
- Development of a decommissioning strategy for the MR research reactor
- Neutron transmutation doping conceptual design
- Design optimization of shell-and-tube heat exchangers using single objective and multiobjective particle swarm optimization
- Chebyshev polynomials expansion method for solving the one-dimensional transport equation in spherical geometry
- Heuristic geometric “eigenvalue universality” in a one-dimensional neutron transport problem with anisotropic scattering
- An analytical solution for the one-dimensional time-dependent SN transport equation for bounded and unbounded domains in cartesian geometry
- Accurate critical slab calculations for various degrees of anisotropy and for different reflection coefficients
- Technical Notes/Technische Mitteilungen
- The boundary problem in the 1D-CANDLE burn-up reactor
