The two-region Milne problem

Journal Article · Wed May 01 04:00:00 EDT 1996 · Nuclear Science and Engineering

OSTI ID:264356

Ganapol, B D ^[1]; Pomraning, G C ^[2]

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1. NASA/AMES Research Center, Moffett Field, CA (United States). Ecosystem Science and Technology Branch
2. Univ. of California, Los Angeles, CA (United States). School of Engineering and Applied Science

The authors consider the two-region Milne problem, defined as the steady-state monoenergetic linear transport problem for two adjoining homogeneous source-free half-spaces, with a particle source coming from infinity in one of the half-spaces. They demonstrate that the asymptotic (Case discrete mode) component of the solution for the scalar flux is easily and explicitly written in terms of Chandrasekhar`s H-function for each medium. This asymptotic solution is shown to exhibit a discontinuity in both the scalar flux and current at the interface between the two half-spaces. Numerical benchmark results for the linear extrapolation distance and the discontinuities are given for various combinations of the mean number of secondaries (c) characterizing the two media. Contact is also made with a variational treatment. In particular, the variational formalism is shown to predict the linear extrapolation distance and these asymptotic discontinuities correct to first order in the difference between the values of c characterizing the two half-spaces.

• OSTI ID: 264356
• Journal Information: Nuclear Science and Engineering, Journal Name: Nuclear Science and Engineering Journal Issue: 1 Vol. 123; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ACCURACY
ASYMPTOTIC SOLUTIONS
MILNE PROBLEM
NEUTRON FLUX
NEUTRON TRANSPORT THEORY
VARIATIONAL METHODS