Generalization of Spatial Channel Theory to Three-Dimensional x-y-z Transport Computations

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Spatial channel theory, initially introduced in 1977 by M. L. Williams and colleagues at ORNL, is a powerful tool for shield design optimization. It focuses on so called ''contributon'' flux and current of particles (a fraction of the total of neutrons, photons, etc.) which contribute directly or through their progeny to a pre-specified response, such as a detector reading, dose rate, reaction rate, etc., at certain locations of interest. Particles that do not contribute directly or indirectly to the pre-specified response, such as particles that are absorbed or leak out, are ignored. Contributon fluxes and currents are computed based on ... continued below

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Abu-Shumays, I. K.; Hunter, M. A.; Martz, R. L. & Risner, J. M. March 12, 2002.

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  • Bettis Atomic Power Laboratory
    Publisher Info: Bettis Atomic Power Lab., West Mifflin, PA (United States)
    Place of Publication: West Mifflin, Pennsylvania

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Spatial channel theory, initially introduced in 1977 by M. L. Williams and colleagues at ORNL, is a powerful tool for shield design optimization. It focuses on so called ''contributon'' flux and current of particles (a fraction of the total of neutrons, photons, etc.) which contribute directly or through their progeny to a pre-specified response, such as a detector reading, dose rate, reaction rate, etc., at certain locations of interest. Particles that do not contribute directly or indirectly to the pre-specified response, such as particles that are absorbed or leak out, are ignored. Contributon fluxes and currents are computed based on combined forward and adjoint transport solutions. The initial concepts were considerably improved by Abu-Shumays, Selva, and Shure by introducing steam functions and response flow functions. Plots of such functions provide both qualitative and quantitative information on dominant particle flow paths and identify locations within a shield configuration that are important in contributing to the response of interest. Previous work was restricted to two dimensional (2-D) x-y rectangular and r-z cylindrical geometries. This paper generalizes previous work to three-dimensional x-y-z geometry, since it is now practical to solve realistic 3-D problems with multidimensional transport programs. As in previous work, new analytic expressions are provided for folding spherical harmonics representations of forward and adjoint transport flux solutions. As a result, the main integrals involve in spatial channel theory are computed exactly and more efficiently than by numerical quadrature. The analogy with incompressible fluid flow is also applied to obtain visual qualitative and quantitative measures of important streaming paths that could prove vital for shield design optimization. Illustrative examples are provided. The connection between the current paper and the excellent work completed by M. L. Williams in 1991 is also discussed.

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INIS; OSTI as DE00797087

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  • ANS Radiation Protection and Shielding Topical Meeting, Santa Fe, NM (US), 04/14/2002--04/17/2002; Other Information: Supercedes report DE00797087; PBD: 12 Mar 2002

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  • Report No.: B-T-3410
  • Grant Number: AC11-98PN38206
  • Office of Scientific & Technical Information Report Number: 797087
  • Archival Resource Key: ark:/67531/metadc738251

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  • March 12, 2002

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  • Oct. 19, 2015, 7:39 p.m.

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  • March 30, 2016, 12:44 p.m.

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Abu-Shumays, I. K.; Hunter, M. A.; Martz, R. L. & Risner, J. M. Generalization of Spatial Channel Theory to Three-Dimensional x-y-z Transport Computations, article, March 12, 2002; West Mifflin, Pennsylvania. (digital.library.unt.edu/ark:/67531/metadc738251/: accessed November 20, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.