Langevin equation approach to reactor noise analysis: stochastic transport equation

Journal Article · Fri Jan 01 04:00:00 EST 1993 · Nuclear Science and Engineering; (United States)

OSTI ID:6503798

Akcasu, A Z ^[1]; Stolle, A M ^[2]

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1. Univ. Konstanz (Germany)
2. Univ. of Michigan, Ann Arbor (United States)

The application of the Langevin equation method to the study of fluctuations in the space- and velocity-dependent neutron density as well as in the detector outputs in nuclear reactors is presented. In this case, the Langevin equation is the stochastic linear neutron transport equation with a space- and velocity-dependent random neutron source, often referred to as the noise equivalent source (NES). The power spectral densities (PSDs) of the NESs in the transport equation, as well as in the accompanying detection rate equations, are obtained, and the cross- and auto-power spectral densities of the outputs of pairs of detectors are explicitly calculated. The transport-level expression for the R([omega]) ratio measured in the [sup 252]Cf source-driven noise analysis method is also derived. Finally, the implementation of the Langevin equation approach at different levels of approximation is discussed, and the stochastic one-speed transport and one-group P[sub 1] equations are derived by first integrating the stochastic transport equation over speed and then eliminating the angular dependence by a spherical harmonics expansion. By taking the large transport rate limit in the P[sub 1] description, the stochastic diffusion equation is obtained as well as the PSD of the NES in it. This procedure also leads directly to the stochastic Fick's law.

• DOE Contract Number: FG02-86NE37969
• OSTI ID: 6503798
• Journal Information: Nuclear Science and Engineering; (United States), Journal Name: Nuclear Science and Engineering; (United States) Vol. 113:1; ISSN NSENAO; ISSN 0029-5639
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
220100* -- Nuclear Reactor Technology-- Theory & Calculation
DATA ANALYSIS
EQUATIONS
LANGEVIN EQUATION
MEASURING INSTRUMENTS
NEUTRAL-PARTICLE TRANSPORT
NEUTRON DENSITY
NEUTRON DETECTORS
NEUTRON SOURCES
NEUTRON TRANSPORT
PARTICLE SOURCES
RADIATION DETECTORS
RADIATION SOURCES
RADIATION TRANSPORT
REACTOR COMPONENTS
REACTOR CORES
REACTOR NOISE
SPACE DEPENDENCE
STOCHASTIC PROCESSES
VARIATIONS