In recent years, the Monte Carlo (MC) methods have become an extensive and reference tool for criticality calculations. Despite the high precision that could be reached in MC modeling, the criticality calculations are still faced with the problem of fission source convergence leading, thereby, in some cases to false convergences and, in particular, to an erroneous effective multiplication factor. This is a challenging issue from a criticality safety point of view. Thus, to prevent from these specific issues and to obtain correct results, a convergence assessment has been carried out, for the first time, in this work, to the MC model of the NUR research reactor initial core.

To this end, both effective multiplication factor (keff) and Shannon entropy of the fission source (Hsrc) were evaluated for various M, the number of neutrons per cycle, and for different locations of the initial fission source in the reactor core.

From the obtained results, it reveals that: a number of 10000 neutrons/cycles (or more) are needed to reduce bias on keff and at least 30 inactive cycles are required to allow keff convergence. Whereas, the choice of a point source in each fuel element or in each fuel plate are the most preferred assumptions. As for the number of active cycles, it can be fixed according to the reasonable uncertainty that a user may accept for the effective multiplication factor, keff.

1.
Ruaridh
Macdonald
.
Investigation of Improved Methods for Assessing Convergence of Models in MCNP Using Shannon Entropy
.
BACHELOR OF SCIENCE IN NUCLEAR SCIENCE AND ENGINEERING AT THE MASSACHUSETTS INSTITUTE OF TECHNOLOGY
, June
2012
.
2.
Yoshitaka
Naito
,
Toshihiro
Yamamoto
,
Tsuyoshi
Misawa
and
Yuichi
Yamane
.
Review of studies on criticality safety evaluation and criticality experiment methods
.
Journal of Nuclear Science and Technology
,
2013
. Vol.
50
, No.
11
,
1045
1061
, .
3.
Forrest B.
Brown
,
On the Use of Shannon Entropy of the Fission Distribution for Assessing Convergence of Monte Carlo Criticality Calculations
. PHYSOR
2006
,
ANS Topical Meeting on Reactor Physics.
4.
Forrest B.
Brown
,
K-effective of the World” and Other Concerns for Monte Carlo Eigenvalue Calculations
,
Progress in Nuclear Science and Technology
, Vol.
2
, pp.
738
742
(
2011
).
5.
Forrest B.
Brown
,
A Review of Monte Carlo Criticality Calculations Convergence, Bias and Statistics.
American Nuclear Society Mathematics & Computation Topical Meeting Saratoga
,
NY May 3-7
,
2009
.
6.
Forrest B.
Brown
,
Brian
Nease
,
Jesse
Cheatham
,
Convergence Testing for MCNP5 Monte Carlo Eigenvalue Calculations
,
M&C+SNA-2007, ANS Mathematics & Computation Topical Meeting Monterey, CA, 15-19 April
2007
.
7.
Michel
Nowak
,
Jilang
Miao
,
Eric
Dumonteil
,
Benoit
Forget
,
Anthony
Onillon
,
Kord S.
Smith
,
Andrea
Zoia
.
Monte Carlo power iteration: Entropy and spatial correlations
.
Annals of Nuclear Energy
94
(
2016
)
856
868
.
8.
Taro
Ueki
and
Forrest B.
Brown
, Informatics Approach To stationarity Diagnostics of the Monte Carlo Fission Source Distribution.
Applied Physics Division
,
Los Alamos National Laboratory, MS F663, Los Alamos, NM 87545
, November
2003
.
9.
C. E.
Shannon
,
A Mathematical Theory of Communication Reprinted with corrections from The Bell System
.
Technical Journal
, Vol.
27
, pp.
379
423
, 623–656, July, October,
1948
.
10.
MCNP5 Manuel
A General Monte Carlo N-Particle Transport Code
, Version 5, Volume
II
:
User’s Guide
.
2003
.
11.
Kaur
Tuttelberg
,
Jan
Dufek
,
Neutron batch size optimization methodology for Monte Carlo criticality calculations
.
Annals of Nuclear Energy
75
(
2015
)
620
626
.
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