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      Application of the Chebyshev polynomial ( T N and U N ) approximation to reflected slab geometry in the neutron transport equation and computation of critical half thicknesses

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      1 , * , , 2
      Kerntechnik
      Carl Hanser Verlag

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          Abstract

          The transport of one-speed neutrons has been studied in isotropically scattering slab using ultraspherical polynomial approximation whose sub-cases are spherical harmonics approximation and Chebyshev polynomial approximation of first and second kind with reflective boundaries. An integral equation for the total flux has been derived and solved numerically for different values of c and reflection coefficients. In the solution, Marshak type vacuum boundary conditions were used. The critical thicknesses obtained by the Chebyshev polynomial method are in good agreement with literature values. Computations were made by using the T N, U N and P N approximations for comparison.

          Kurzfassung

          Anwendung der Tschebyscheff-Polynom-Approximation (T N und U N) auf reflektierende Stabgeometrie in der Neutronentransportgleichung und Berechnung kritischer Halbwertsdicken. Der Transport von Ein-Gruppen-Neutronen wurde bei isotroper Streuung in Stabgeometrie untersucht mit Hilfe ultraspärischer Polynom Approximation, die klassische polynomiellen Folgen, wie sphärische harmonische Approximation und Tschebyscheff-Polynom-Approximation erster und zweiter Ordnung mit reflektierenden Randbedingungen vereinheitlicht. Eine Integralgleichung für den gesamten Strahlungsfluss wurde hergeleitet und numerisch gelöst für verschiedene Werte von c und Reflektionskoeffizienten. Für den Lösungsweg wurden Vakuum-Randbedingungen vom Marshak-Typ verwendet. Die mit Hilfe der Tschebyscheff-Polynom-Approximation erhaltenen kritischer Halbwertsdicken stimmen gut mit Werten aus der Literatur überein. Zum Vergleich wurden Berechnungen mit T N, U N and P N Approximationen durchgeführt.

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          TN approximation to reflected slab and computation of the critical half thicknesses

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            Application of the U N method to the reflected critical slab problem for one-speed neutrons with forward and backward scattering

            The U N method is used to solve the critical slab problem for reflecting boundary conditions in one-speed neutron transport theory. The isotropic scattering kernel with the combination of forward and backward scattering is chosen for the neutrons in a uniform finite slab. It is shown that the method converges rapidly with easily executable equations. The presented numerical results are compared with the results available in the literature.
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              Solution of one-speed neutron transport equation for strongly anisotropic scattering by TN approximation: Slab criticality problem

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                Author and article information

                Journal
                kt
                Kerntechnik
                Carl Hanser Verlag
                0932-3902
                2195-8580
                2010
                : 75
                : 5
                : 282-287
                Affiliations
                1 Osmaniye Korkut Ata University, Faculty of Arts and Science, Department of Physics Osmaniye, Turkey
                2 Kahramanmaras Sutcu Imam University, Faculty of Arts and Science, Department of Physics, Kahramanmaras, Turkey
                Author notes
                Article
                KT110104
                10.3139/124.110104
                6b18f904-f444-4749-be15-ce1bec981532
                © 2010, Carl Hanser Verlag, München
                History
                : 8 June 2010
                Page count
                References: 17, Pages: 6
                Categories
                Technical Contributions/Fachbeiträge

                Materials technology,Materials for energy,Nuclear physics
                Materials technology, Materials for energy, Nuclear physics

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