Analytic Solution for Time-Dependent Neutron Transport with Delayed Neutrons via Singular Eigenfunction Expansion

Journal Article · Fri Jul 01 04:00:00 EDT 2016 · Transactions of the American Nuclear Society

OSTI ID:23042665

Densmore, Jeffery D. ^[1]

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1. Bettis Atomic Power Laboratory, P.O. Box 79, West Mifflin, PA 15122 (United States)

An important way to verify the proper functioning of a computer code, and its underlying numerical schemes, is by comparing numerical results generated with the code to an analytic solution. To this end, we present an analytic solution for time-dependent neutron transport with delayed neutrons, which can be used to verify computer codes for modeling reactor kinetics phenomena. To develop our analytic solution, we use the singular eigenfunction expansion method. Ganapol et al. have also developed a solution to this problem, but by using the multiple collision technique. Our approach has certain advantages with respect to this previous work, in particular that it yields a closed form (i.e., in terms of an integral rather than an infinite series) explicit expression for the angular flux (i.e., instead of just the scalar flux or the angular flux at a single spatial point). In addition, Su and Olson have presented an analytic solution for a very similar problem: non-equilibrium radiative transfer. Their approach involves a Laplace transform, which they invert by showing there are no singularities in the right complex plane of the Laplace transform parameter and then simply choosing the Bromwich contour as the imaginary axis. To extend this previous work to our case, we would further need to exclude supercritical problems in order to use the same contour. The resulting analytic solution would then be of limited interest. In contrast, our analytic solution is completely general with respect to sub, delayed super, or prompt supercriticality. (authors)

• OSTI ID: 23042665
• Journal Information: Transactions of the American Nuclear Society, Journal Name: Transactions of the American Nuclear Society Vol. 115; ISSN 0003-018X
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
97 MATHEMATICS AND COMPUTING
ANALYTICAL SOLUTION
COMPUTER CODES
COMPUTERIZED SIMULATION
DELAYED NEUTRONS
EIGENFUNCTIONS
LAPLACE TRANSFORMATION
NEUTRON TRANSPORT
RADIANT HEAT TRANSFER
REACTOR KINETICS
SCALARS
SINGULARITY
TIME DEPENDENCE