Analysis of prompt decay experiments for ADS reactivity ...€¦ · Analysis of prompt decay...

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



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



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



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



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



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such as VENUS-F SC1 configuration, this expression is no longer valid.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



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



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



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



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.


tMtM

t



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.


2

'

'

2

min

min

''

''

t

tt

t

tt

dttM

dttM

tW



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



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.



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



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



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



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



Thanks to the WP1 FREYA team

Talk ends here



Low sensitivity of the P(tau) distribution

Courtesy of H.E. Thyébault

Analysis of prompt decay experiments for ADS reactivity ...€¦ · Analysis of prompt decay...

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