Neutron diffusion in a randomly inhomogeneous multiplying medium with random phase approximation

Journal Article · Fri Jun 15 00:00:00 EDT 2012 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4721650· OSTI ID:22093612

Imre, Kaya ^[1]; Akcasu, A. Ziya ^[2]

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1. Courant Institute of Mathematical Sciences, New York University, New York 10012 (United States)
2. University of Michigan, Ann Arbor, Michigan 48109 (United States)

Neutron diffusion in a randomly inhomogeneous multiplying medium is studied. By making use of a random phase assumption we show that the average neutron density approximately satisfies an integral equation in Fourier space, which is solved using Kummer functions. We used multi-dimensional formulation. In the case of one dimension, we obtain the result of Rosenbluth and Tao for the mean total density for large t. In the three-dimensional case, a closed form of solution is derived for the mean total neutron density. Its asymptotic behavior is also investigated for large t.

• OSTI ID: 22093612
• Journal Information: Journal of Mathematical Physics, Vol. 53, Issue 6; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ASYMPTOTIC SOLUTIONS
DENSITY
FOURIER ANALYSIS
NEUTRON DENSITY
NEUTRON DIFFUSION EQUATION
RANDOM PHASE APPROXIMATION
RANDOMNESS
THREE-DIMENSIONAL CALCULATIONS