Prompt Time Constants of a Reflected Reactor
Tao YeChaobin ChenWeili Sun

Benai Zhang

Dongfeng Tian

Institute of Applied Physics and Computational Mathematics, Beijing, China
Time eigenvalue of transportation equation, alpha, is defined to describe all neutrons’ time
behavior (increasing or decreasing) in a nuclear reactor. Its number reflects the criticality also. The
time constant, especially prompt time constant, had been studied for 60 years. Lots of reflectedreactor’s experimental data cannot be satisfactorily explained using the standard point kinetic
model 1. And multiple decay modes near delayed critical were also observed, which of course
cannot be described by standard point kinetic model.
The existing numerical transportation codes, such as MCNP4C 2 and TART 3, 4 , can do the job
well with only the fundamental mode calculated. By using alpha static criticality method,
MCNP4C is a good tool if keff is close 1, which means the reactor is near delayed critical. But
MCNP4C’s calculation may be very difficult and time-consuming if the reactor has more negative
reactivity or reflector contains hydrogen, or both.
In the region of analytical method, many works contains too much mathematics, which are noteasy to calculate and compare with experimental data. G. D. Spriggs’ one-group, two-region
kinetic model based on Avery-Cohn model is simple, calculable. The model introduces simple
probability relationships essential to calculating the coupling parameters between core andreflector,1 and derives the reflected-core inhour equation which contains multiple decay modes.
However, Spriggs model cannot well describe multiple time constants of the thermal reflectedreactor. In this kind of reactor, thermal neutrons with long lifetime contribute much to the time
constant. Because of importance of thermal neutrons in such fast-thermal reactor, we present a
simplified two-group, two-region kinetic model (2G2R) based on Spriggs model, and rewrite thereflected-core inhour equation. With the help of MCNP code, we calculated the coupling
parameters, neutron lifetimes and first and secondary time constant of a spherical benchmark
reactor, PU-MET-FAST-024.6 Because we don’t have experimental data, the results of time
constants are also compare with 3 different models, MCNP time fitting method, alpha staticmethod (MCNP4C), and Spriggs model. The results of 2G2R model agree well with MCNP time
fitting method which can be thought as an experiment in computer.

REFERENCES
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G. D. Spriggs et al., “Two-Region Kinetic Model for Reflected Reactor”, Ann. Nucl. Energy, 24, 205, (1997).
Judith F. Briesmeister, “MCNPTM-A General Monte Carlo N – Particle Transport Code”, LA-13709-M, Arpi.
10, (2001).
Dermott E. Cullen, “TART 2002: A Coupled Neutron-Photon 3-D Combinatorial Geometry, Time DependentMonte Carlo Transport Code”, UCRL-ID-126455, Rev. 4, June (2003).
Dermott E. Cullen et al., “Static and Dynamic Criticality: Are They Different?”, UCRL-TR-201506, Nov. 22,(2003).
G. I. Bell, S. Glasstone, Nuclear Reactor Theory, Van Nostrand, Princeton, N. J., (1970).
M. V. Gorbatenko et al., “Polyethylene-Reflected Spherical Assembly of 239PU(δ, 98%)”, Vol. I,
NEA/NSC/DOC/(95).

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