Reactivity estimation for source-driven systems using first-order perturbation theory. Page: 1 of 11
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PHYSOR 2002, Seoul, Korea, October 7-10, 2002
REACTIVITY ESTIMATION FOR SOURCE-DRIVEN SYSTEMS
USING FIRST-ORDER PERTURBATION THEORY
Y. Kim*, W. S. Yang, T. A. Taiwo, and R. N. Hill
Argonne National Laboratory
9700 S. Cass Avenue Argonne, Illinois 60439-4842, USA
firstname.lastname@example.org; email@example.com; firstname.lastname@example.org; email@example.com
Applicability of the first-order perturbation (FOP) theory method to reactivity estimation for source-
driven systems is examined in this paper. First, the formally exact point kinetics equations have been
derived from the space-dependent kinetics equations and the kinetics parameters including the
dynamic reactivity have been defined. For the dynamic reactivity, exact and first-order perturbation
theory expressions for the reactivity change have been formulated for source-driven systems. It has
been also shown that the external source perturbation itself does not change the reactivity if the initial
A -mode adjoint flux is used as the weight function. Using two source-driven benchmark problems,
the reactivity change has been estimated with the FOP theory method for various perturbations. By
comparing the resulting reactivity changes with the exact dynamic reactivity changes determined from
the space-dependent kinetics solutions, it has been shown that the accuracy of the FOP theory method
for the accelerator-driven system (ADS) is reasonably good and comparable to that for the critical
reactors. The adiabatic assumption has also been shown to be a good approximation for the ADS
Accelerator-driven systems are currently being proposed for the transmutation of nuclear wastes.
The determination of the safety characteristics of ADSs would require the application of system
analysis codes such as SAS4A/SASSYS. These codes typically use the point kinetics
approximation for solving the neutron kinetics equations. In addition, the point kinetics analyses are
often utilized for the scoping evaluation of the source-driven systems. An issue that arises in the point
kinetics approach is the need to provide appropriate reactivity coefficients that are typically derived
from first-order perturbation (FOP) theory.
In the conventional source-free reactor systems, two concepts of reactivities are used. These are the
static and dynamic reactivities. The static reactivity indicates the off-criticality of a physical state, i.e.,
a distance from the critical state. On the other hand, the dynamic reactivity is related to an actual
transient, thus it is a time-dependent quantity. In a similar way, both static and dynamic reactivities
could be consistently defined for the source-driven system, as discussed in Ref. 3.
The concept of reactivity is required only in lumped parameter models such as the point kinetics
equations. In a point kinetics model for a source-free system, the dynamic reactivity is the primary
driving function that determines the system response during a transient. On the other hand, the
* Korea Atomic Energy Research Institute, Republic of Korea
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Kim, Y.; Yang, W. S.; Taiwo, T. A. & Hill, R. N. Reactivity estimation for source-driven systems using first-order perturbation theory., article, July 2, 2002; Illinois. (digital.library.unt.edu/ark:/67531/metadc734030/m1/1/: accessed December 15, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.