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The Use of Density-Law-Invariant Parameters for Criticality Safety Assessment
Song T. Huang and Philip Chou
Lawrence Livermore National Laboratory, P. O. Box 808, Livermore, CA 94551 and huang3@llnl.govINTRODUCTION
The complexity of neutron transport in terms of
space, time, and neutron energy dependence is well
recognized. Through the years, there have been many
attempts to utilize various parameters to characterize
a neutron system to help nuclear engineers to
understand various applications. Parameters such as
kerr, neutron spectrum, average energy of neutrons
causing fissions, and others are used to size up the
types of the problems in a particular application.
From a neutron physics viewpoint, not all the
parameters used are of the same usefulness.
DESCRIPTION OF THE WORK
It is interesting to point out that under the density law
transformation [1,2], some parameters offer better
physics insight than others. For example, parameters
such as the number of mean free paths, nonleakage
fraction, and surface mass density, are invariant
under the density law transformation. Actually, the
transport equation and the diffusion equation are
invariant under the density law transformation. This
means if we use parameters, which are invariant
under the density law, the neutron physics is the same
for various systems with the same parameter value.
The density law is an inherent property of the neutron
transport process. Given the complexity of the
neutron transport process, the density law gives us a
certain physics insight that is very helpful for
practitioners in the criticality safety field. With this in
mind, this paper presents another way of looking at
fissile systems by using parameters that are invariant
under the density law.the geometry and material perspectives. For example,
we use Bg for geometric buckling and BM for
material buckling in a way to help us understand
what parameters are in the material side and what
parameters in the geometry side and how they are
related to criticality assessment. As a matter of fact,
this approach is very powerful in developing many
hand calculation methods such as the J. Thomas's
limiting surface density method [3].
In an infinite medium problem, there is no neutron
leakage. A parameter such as Knf and its associated
four factor formula are used to explain neutron
transport for this type of problems. For a finite
neutron system, the neutron leakage plays an
important role. For example, it is customary to
represent the neutron reproduction factor as follows:
Keff = Kaf * (nonleakage Fraction)
= Kf / (1+M2B2)
where M2 may be interpreted as the migration area
and B 2 as the geometric buckling under the modified
one group model. Although we illustrate the concept
with a modified one group model, the overall concept
of nonleakage fraction is independent of the model
used as the nonleakage fraction may be obtained by
various methods including the Monte Carlo method.
kif vs. M2B2Supercritical Region
-keff
-keff = 1E
C)RESULTS
Use of the Nonleakage Fraction (or the Leakage
Parameter)
In reactor physics and in criticality applications,
various approaches are used to dissect a problem into0
0Subcritical Region
2 3
M2B2Figure 1. keff as a function of M2B2.
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Huang, S & Chou, P. The Use of the Density-Law-Invariant Parameters for Criticality Safety Assessment, article, April 12, 2013; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc840925/m1/3/: accessed April 18, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.