Neutron Number Probability Distributions in a Subcritical System Using the Forward Master Equation

Journal Article · Wed Jun 15 04:00:00 EDT 2016 · Transactions of the American Nuclear Society

OSTI ID:22991994

O'Rourke, Patrick F.; Prinja, Anil K. ^[1]; Fichtl, Erin D. ^[2]

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1. Department of Nuclear Engineering, University of New Mexico, Albuquerque, NM 87131 (United States)
2. Computational Physics and Methods, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, NM, 87545 (United States)

The subject of this paper is the determination of the equilibrium probability distribution function (PDF) of the neutron population within a subcritical multiplying system in the presence of an intrinsic random source as a result of spontaneous fission (SF). Such systems are strongly stochastic and low order moments such as the mean and variance of the neutron number are not sufficient to characterize the true state of the neutron population. We base our work on the forward Master equation in a lumped model formulation for P{sub n} (t), n = 0, 1, 2,..., the probability of there existing η neutrons at time t and obtain solutions for the steady state distributions. The key parameters in this model, neutron lifetime and fission probability, are rigorously obtained by numerically solving the k-eigenvalue problem in a one-dimensional spherical system and using standard definitions of lumped parameters in terms of production and loss rates in finite systems. Previous work has examined single-chain PDFs (a single fission and the resulting progeny) for neutrons, uncoupled neutron-photon single-chain PDFs, both using a lumped backward Master equation formulation, as well as neutron PDFs in supercritical systems. In this paper, we analyze strictly subcritical systems, for which we compare analytically derived solutions with numerical computations for different multiplicity distribution models. For subcritical systems where the neutron population remains finite at steady state, we show that the forward Master equation can be very efficiently solved numerically to obtain the equilibrium distributions. Finally, this work is motivated by potential application to passive interrogation for detection of diverted nuclear materials as well to criticality safety. The equilibrium neutron number probability distribution in subcritical systems has been numerically investigated for several models of the induced and spontaneous fission multiplicity distribution. A well known approximate but closed form solution, namely the quadratic model, was shown to be unacceptably accurate for subcritical media. The matrix inversion and the recursion methods agree well and were benchmarked with the binary fission model, but the recursion formulation proves far more computationally efficient. A qualitative change in the shape of the neutron PDF is observed for increasing source strength, as expected, and a transition from a stochastic to a deterministic system is expected for a sufficiently strong source. We are currently extending this approach to obtain the equilibrium joint distribution of neutrons within the system and those that have leaked, to explicitly represent the neutron PDF as observed by an external detector. (authors)

• OSTI ID: 22991994
• Journal Information: Transactions of the American Nuclear Society, Journal Name: Transactions of the American Nuclear Society Journal Issue: 1 Vol. 114; ISSN 0003-018X
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
97 MATHEMATICS AND COMPUTING
BINARY FISSION
CRITICALITY
EIGENVALUES
EQUATIONS
EQUILIBRIUM
NEUTRONS
POPULATIONS
PROBABILITY
SAFETY
SPONTANEOUS FISSION
STOCHASTIC PROCESSES