The planar Green`s function in an infinite multiplying medium

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Throughout the history of neutron transport theory, the study of simplified problems that have analytical or semi-analytical solutions has been a foundation for more complicated analyses. Analytical transport results are often used as benchmarks or in pedagogical settings. Benchmark problems in infinite homogeneous media have been studied continually, beginning with the monograph by Case, DeHoffmann, and Placzek. A fundamental problem considered in this work is the Green`s function in an infinite medium. The Green`s function problem considers an infinite planar source emitting neutral particles in the single directions`. Recently, this Green`s function has been used to obtain solutions for finite ... continued below

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10 p.

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Kornreich, D.E. & Ganapol, B.D. October 1, 1996.

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  • Kornreich, D.E. Los Alamos National Lab., NM (United States)
  • Ganapol, B.D. Univ. of Arizona, Tucson, AZ (United States). Dept. of Aerospace and Mechanical Engineering

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Description

Throughout the history of neutron transport theory, the study of simplified problems that have analytical or semi-analytical solutions has been a foundation for more complicated analyses. Analytical transport results are often used as benchmarks or in pedagogical settings. Benchmark problems in infinite homogeneous media have been studied continually, beginning with the monograph by Case, DeHoffmann, and Placzek. A fundamental problem considered in this work is the Green`s function in an infinite medium. The Green`s function problem considers an infinite planar source emitting neutral particles in the single directions`. Recently, this Green`s function has been used to obtain solutions for finite media. These solutions, which hinge on accurate and fast evaluation of the infinite medium Green`s function, use Fourier and Laplace transform inversion techniques for the evaluation. Until now, only absorbing media have been considered, and applications were therefore limited to non-multiplying media. In an effort to relax this limitation, the infinite medium Green`s function is numerically evaluated for an infinite multiplying medium using the double-sided Laplace transform inversion. Of course, no steady-state mathematical solution exists for an infinite multiplying medium with a source present; however, the non-physical solution in an infinite medium can be used in finite media problems where the solution is physically realizable.

Physical Description

10 p.

Notes

INIS; OSTI as DE96014038

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  • Winter meeting of the American Nuclear Society (ANS) and the European Nuclear Society (ENS), Washington, DC (United States), 10-14 Nov 1996

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  • Other: DE96014038
  • Report No.: LA-UR--96-1952
  • Report No.: CONF-961103--14
  • Grant Number: W-7405-ENG-36
  • Office of Scientific & Technical Information Report Number: 385560
  • Archival Resource Key: ark:/67531/metadc680022

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  • October 1, 1996

Added to The UNT Digital Library

  • July 25, 2015, 2:20 a.m.

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  • March 2, 2016, 1:25 p.m.

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Kornreich, D.E. & Ganapol, B.D. The planar Green`s function in an infinite multiplying medium, article, October 1, 1996; New Mexico. (digital.library.unt.edu/ark:/67531/metadc680022/: accessed August 18, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.