analysis of prompt decay experiments for ads reactivity ...€¦ · analysis of prompt decay...
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 1May 21, 2013
Analysis of prompt decay experiments
for ADS reactivity monitoring at VENUS-F
S. Chabod 1, X. Doligez 2, G. Lehaut 3, A. Billebaud 1, J.L. Lecouey 3,
F.R. Lecolley 3, N. Marie 3, A. Kochetkov 4, W. Uyttenhove 4,
G. Vittiglio 4, J. Wagemans 4, F. Mellier 5, G. Ban 3, H.E. Thyébault 1,
D. Villamarin 6
1 LPSC, CNRS-IN2P3/UJF/INPG, France2 IPNO, CNRS-IN2P3/Univ. Paris Sud, France
3 LPC, ENSICAEN/Univ. de Caen/CNRS-IN2P3, France4 SCK-CEN, Belgium
5 CEA DEN/DER/SPEX, France6 CIEMAT, Spain
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 2May 21, 2013
Aim of the kp method
Measure an ADS prompt multiplication factor kp. The method relies on the
(1) monitoring and analysis of decays of the prompt neutron population
(2) programmed short beam interruptions or injections of source neutron pulses
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 3May 21, 2013
Generations of neutrons in a SC reactor
During the FREYA project, we injected pulses of 14 MeV source neutrons
(8×106 at 200 Hz) in the VENUS-F reactor using the GENEPI-3C accelerator
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 4May 21, 2013
Ni(t) = number of generation i neutrons born in the reactor at time tkp = prompt multiplication coefficienttau = time elapsed between two successive fissionsP(tau) = normalized distribution of the times tau
Experimentally, we can not distinguish neutrons of different generations.
At a given time t, we can only observe the sum of all the Ni populations:
tStN
tNPkdtNPktN ip
t
ipi
0
01
Number of neutrons born in a SC reactor – 1/2
0ii tNtN
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 5May 21, 2013
Summing, from i = 0 to i = +, left and right members of previous
equation, we obtain
which leads to an equation giving the number of neutrons born in a SC
reactor at time t
To calculate N(t), we first have to compute the distribution P(tau).
00
01
1
nip
ni
ipi
NPktNtNtN
NPktN
Number of neutrons born in a SC reactor – 2/2
tNPktStN p
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 6May 21, 2013
Distribution P(tau) of VENUS-F SC1 configuration
In Points Kinetics, P(tau) = exp(–tau/L)/L. But at deep subcritical levels,
such as VENUS-F SC1 configuration, this expression is no longer valid.
We computed P(tau) using the MCNP code.
Consequence of thereflector and concrete
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 7May 21, 2013
By solving the equation N = S+kp(P*N) numerically, we can obtain an array
of theoretical curves, Nth(t,kp).
The idea is then to compare Nth(t,kp) with Nexp(t), to determine the kp value.
Problem: experimentally, we don’t have access to the population N(t).
We can only measure count rates in several FCs positioned in the reactor
(cf. Nathalie’s talk). Their count rates, M(t), are nevertheless related to N(t) by
D(tau) is the distribution of the times tau elapsed between
(a) a fission occurring in the reactor
(b) a fission occurring in the fissile deposit of a detector
NDdktNDktMt
pthpth 0
,,
Computation of detector count rates for VENUS-F
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 8May 21, 2013
D(tau) distributions for the FCs used at VENUS-F
NB: for a threshold FC, D(tau) = d(tau) recommended detectors but rare
in core
polyethylene
core boundary
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 9May 21, 2013
Solving our previous equations gives us theoretical count rates, Mth(t,kp), that
can be compared with experimental count rates, Mexp(t), to extract kp value.
Theory vs exp. comparison methodology – 1/3
number of source
neutrons injected
+ detector’s efficiency
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 10May 21, 2013
As the theoretical and exp. count rates Mth(t,kp) and Mexp(t) don’t have the
same normalization, we can not compare them directly.
Use of an intermediate self-normalized estimator required.
Classical kp method (Perdu et al., Prog. in Nucl. Energy 42 2003)
Comparison of Mth(t,kp) and Mexp(t)
done using their log. derivatives :
▲ simple self-normalized estimator
▼ but too sensitive to statistical
fluctuations on M(t) curves.
Theory vs exp. comparison methodology – 2/3
tMtM
t
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 11May 21, 2013
Integral approach of the kp method
Self-normalized integral estimator given by:
▲ Integral = continuous = less sensitive to statistical fluctuations
Time tmin is a cut-off, used to reject the first 10 ms of the curves
(a) weight of the first neutron generations; (b) dead time effects
(corrected but minor errors can still occur); (c) numerical transients.
Theory vs exp. comparison methodology – 3/3
2
'
'
2
min
min
''
''
t
tt
t
tt
dttM
dttM
tW
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 12May 21, 2013
Integral estimator W(t) – 1/2
Arrays of theoretical (lines) and experimental (points) estimators
Wth(t,kp) and Wexp(t) for each FC in the reactor.
Deviation theory vs exp. visible at long times (see ↑ arrows)
Transport of low energy neutrons not perfectly modeled
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 13May 21, 2013
Integral estimator W(t) – 2/2
Errors on Wexp, coming from the statistical errors on Mexp, are calculated
using a Monte-Carlo procedure (Gaussian sampling within the error bars)
(a) The errors on Wexp(t) are Gaussian
(b) No significant deviation observed between the initial Wexp(t) curve and the
mean of the sampled ones integral estimator insensitive to statistics.
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 14May 21, 2013
Determination of the kp value – 1/2
As the errors are Gaussian, we use the least square method to
Quantify the deviation of Wth(t,kp) points from Wexp(t) data
T = time elapsed since the neutron pulse. Since experimental and
theoretical data diverge at long times, we take it as a free parameter.
NB: the error bars eWth(t) were not calculated for this preliminary study.
NB: the center t0 of the Gaussian pulse S(t) is also taken as a free param.
For each detector, the permissible kp values are estimated using:
TttpiWiW
pithi
pi
thktt
ktWtW
nkn
minexp
22
2
exp2
,
,1
ee
1min
22 nkn p
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 15May 21, 2013
Determination of the kp value – 2/2
Examples of reduced 2 obtained for two of the detectors (at a given t0 value)
area (2/n) ≤ (2/n)min + 1
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 16May 21, 2013
Preliminary results of the integral kp method
Application of the kp method to the VENUS-F SC1 configuration
Detector keff = kp/(1–beff) –r ($)
CFUL659 0.9612 – 0.9616 5.52 – 5.58
CFUL658 0.9668 – 0.9687 4.48 – 4.76
CFUL653 0.9694 – 0.9708 4.16 – 4.37
RS-10072 0.9608 – 0.9629 5.34 – 5.65
RS-10071 0.9633 – 0.9645 5.10 – 5.28
RS-10074 0.9618 – 0.9635 5.25 – 5.49
RS-10075 0.9603 – 0.9631 5.31 – 5.72
CFUF34 0.9544 – 0.9624 5.42 – 6.62
CFUM326 0.9578 – 0.9638 5.21 – 6.10
CFUM325 0.9593 – 0.9650 5.03 – 5.87
Mean
(w/o outer FCs)
0.9617 ±0.0003
5.51 ±0.04
MSM0.9631 ±
0.0016
5.30 ±0.23
in core
core boundary
inner reflector
outer
reflector
k1 = 1.8 (n,2n on lead) vs 1/(1–kp) = 22
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 17May 21, 2013
Preliminary results are good, but there remains room for improvement.
Take into account the weight of the first neutron generation(s),
especially for applications at deeper subcritical levels. We demonstrated
that this weight can be accounted for by convoluting S(t) with P1(tau)
Use a high efficiency threshold FC to reduce the systematic errors
coming from the imperfectly-modeled transport of neutrons in the reactor.
(computation of D(tau) no longer needed)
)...'(or
'
621
1
PPPStS
PStS
Conclusion and prospects
d DFC Threshold
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 18May 21, 2013
Thanks to the WP1 FREYA team
Talk ends here
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Analysis of prompt decay experiments at VENUS-F
TCADS-2 Workshop, S. Chabod, Nantes 19May 21, 2013
Low sensitivity of the P(tau) distribution
Courtesy of H.E. Thyébault