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Steady-state solutions for the one-dimensional energy-dependent neutron transport equation in an infinite medium

Conference · · Trans. Am. Nucl. Soc.; (United States)
OSTI ID:5500009
;
Recent work by the authors has resulted in the development of a reliable computer code that provide highly accurate numerical (benchmark) solutions to the one-dimensional monoenergetic steady-state neutron transport equation in an infinite medium. The method employed is application of the standard Fourier transformation to the transport equation in order to arrive at an analytical representation that can be numerically evaluated. The technique is applicable to beam and isotropic sources, anisotropic scattering, and distributed sources. Additional work has resulted in the extension of the code to provide multigroup neutron transport solutions. The purpose of this paper is to further extend the monoenergetic method to the energy-dependent neutron transport equation in an infinite medium for isotropic scattering and source in the laboratory frame of reference. This is done by taking a Laplace transform with respect to lethargy in addition to the spatial Fourier transform. The resulting expression is expanded in an infinite series for which the inverse Laplace transform can be analytically determined. After further manipulation, a numerically tractable expression for the flux in transform space is achieved. The numerical evaluation of the transformed flux is accomplished in a manner identical to that for the monoenergetic case.
Research Organization:
Univ. of Arizona, Tucson
OSTI ID:
5500009
Report Number(s):
CONF-870601-
Conference Information:
Journal Name: Trans. Am. Nucl. Soc.; (United States) Journal Volume: 54
Country of Publication:
United States
Language:
English

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Related Subjects

654003* -- Radiation & Shielding Physics-- Neutron Interactions with Matter
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACCURACY
ALGORITHMS
BENCHMARKS
BOLTZMANN EQUATION
COMPUTER CODES
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL LOGIC
NEUTRON TRANSPORT THEORY
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
STEADY-STATE CONDITIONS
TRANSPORT THEORY