Analysis of prompt decay experiments for ADS reactivity monitoring at VENUS-F

Transcription

1 Analysis of romt decay exeriments for ADS reactivity monitoring at VENUS-F S. Chabod 1, X. Doligez, 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-INP3/UJF/INPG, France IPNO, CNRS-INP3/Univ. Paris Sud, France 3 LPC, ENSICAEN/Univ. de Caen/CNRS-INP3, France 4 SCK-CEN, Belgium 5 CEA DEN/DER/SPEX, France 6 CIEMAT, Sain TCADS- Worksho, S. Chabod, Nantes 1

2 Aim of the k method Measure an ADS romt multilication factor k. The method relies on the (1) monitoring and analysis of decays of the romt neutron oulation () rogrammed short beam interrutions or injections of source neutron ulses TCADS- Worksho, S. Chabod, Nantes

3 Generations of neutrons in a SC reactor During the FREYA roject, we injected ulses of 14 MeV source neutrons ( at 00 Hz) in the VENUS-F reactor using the GENEPI-3C accelerator TCADS- Worksho, S. Chabod, Nantes 3

4 Number of neutrons born in a SC reactor 1/ N i (t) k tau P(tau) = number of generation i neutrons born in the reactor at time t = romt multilication coefficient = time elased between two successive fissions = normalized distribution of the times tau N N i1 0 t k P N t d k P N t t S t t 0 i i Exerimentally, we can not distinguish neutrons of different generations. At a given time t, we can only observe the sum of all the N i oulations: N t i0 N i t TCADS- Worksho, S. Chabod, Nantes 4

5 Number of neutrons born in a SC reactor / Summing, from i = 0 to i = +, left and right members of revious equation, we obtain N i1 t n0 N k i1 P N i t Nt N t k P 0 which leads to an equation giving the number of neutrons born in a SC reactor at time t t St k P Nt N n0 N i To calculate N(t), we first have to comute the distribution P(tau). TCADS- Worksho, S. Chabod, Nantes 5

6 Distribution P(tau) of VENUS-F SC1 configuration In Points Kinetics, P(tau) = ex( tau/l)/l. But at dee subcritical levels, such as VENUS-F SC1 configuration, this exression is no longer valid. We comuted P(tau) using the MCNP code. Consequence of the reflector and concrete TCADS- Worksho, S. Chabod, Nantes 6

7 Comutation of detector count rates for VENUS-F By solving the equation N = S+k (P*N) numerically, we can obtain an array of theoretical curves, N th (t,k ). The idea is then to comare N th (t,k ) with N ex (t), to determine the k value. Problem: exerimentally, we don t have access to the oulation N(t). We can only measure count rates in several FCs ositioned in the reactor (cf. Nathalie s talk). Their count rates, M(t), are nevertheless related to N(t) by M th t t, k D N t, k 0 th d D N D(tau) is the distribution of the times tau elased between (a) a fission occurring in the reactor (b) a fission occurring in the fissile deosit of a detector TCADS- Worksho, S. Chabod, Nantes 7

8 D(tau) distributions for the FCs used at VENUS-F olyethylene in core core boundary NB: for a threshold FC, D(tau) = d(tau) recommended detectors but rare TCADS- Worksho, S. Chabod, Nantes 8

9 Theory vs ex. comarison methodology 1/3 Solving our revious equations gives us theoretical count rates, M th (t,k ), that can be comared with exerimental count rates, M ex (t), to extract k value. number of source neutrons injected + detector s efficiency TCADS- Worksho, S. Chabod, Nantes 9

10 Theory vs ex. comarison methodology /3 As the theoretical and ex. count rates M th (t,k ) and M ex (t) don t have the same normalization, we can not comare them directly. Use of an intermediate self-normalized estimator required. Classical k method (Perdu et al., Prog. in Nucl. Energy 4 003) Comarison of M th (t,k ) and M ex (t) done using their log. derivatives : t M M t t simle self-normalized estimator but too sensitive to statistical fluctuations on M(t) curves. TCADS- Worksho, S. Chabod, Nantes 10

11 Theory vs ex. comarison methodology 3/3 Integral aroach of the k method Self-normalized integral estimator given by: W t t t' t t t' t M min M min t' t' dt' dt' Integral = continuous = less sensitive to statistical fluctuations Time t min 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. TCADS- Worksho, S. Chabod, Nantes 11

12 Integral estimator W(t) 1/ Arrays of theoretical (lines) and exerimental (oints) estimators W th (t,k) and W ex (t) for each FC in the reactor. Deviation theory vs ex. visible at long times (see arrows) Transort of low energy neutrons not erfectly modeled TCADS- Worksho, S. Chabod, Nantes 1

13 Integral estimator W(t) / Errors on W ex, coming from the statistical errors on M ex, are calculated using a Monte-Carlo rocedure (Gaussian samling within the error bars) (a) The errors on W ex (t) are Gaussian (b) No significant deviation observed between the initial W ex (t) curve and the mean of the samled ones integral estimator insensitive to statistics. TCADS- Worksho, S. Chabod, Nantes 13

14 Determination of the k value 1/ As the errors are Gaussian, we use the least square method to Quantify the deviation of W th (t,k) oints from W ex (t) data nk 1 n t min t i T e W W ex ex ti Wtht i, k t e t, k i W th i T = time elased since the neutron ulse. Since exerimental and theoretical data diverge at long times, we take it as a free arameter. NB: the error bars e Wth (t) were not calculated for this reliminary study. NB: the center t 0 of the Gaussian ulse S(t) is also taken as a free aram. For each detector, the ermissible k values are estimated using: nk n 1 min TCADS- Worksho, S. Chabod, Nantes 14

15 Determination of the k value / Examles of reduced obtained for two of the detectors (at a given t 0 value) area ( /n) ( /n) min + 1 TCADS- Worksho, S. Chabod, Nantes 15

16 Preliminary results of the integral k method Alication of the k method to the VENUS-F SC1 configuration Detector k eff = k /(1 b eff ) r ($) CFUL CFUL outer reflector CFUL RS RS RS RS CFUF CFUM CFUM Mean (w/o outer FCs) ± ± 0.04 in core inner reflector core boundary MSM ± ± 0.3 k 1 = 1.8 (n,n on lead) vs 1/(1 k ) = TCADS- Worksho, S. Chabod, Nantes 16

17 Conclusion and rosects Preliminary results are good, but there remains room for imrovement. Take into account the weight of the first neutron generation(s), esecially for alications at deeer subcritical levels. We demonstrated that this weight can be accounted for by convoluting S(t) with P 1 (tau) S' (or t S P S' 1 t S P P... P ) 1 6 Use a high efficiency threshold FC to reduce the systematic errors coming from the imerfectly-modeled transort of neutrons in the reactor. (comutation of D(tau) no longer needed) Threshold FC D d TCADS- Worksho, S. Chabod, Nantes 17

18 Thanks to the WP1 FREYA team Talk ends here TCADS- Worksho, S. Chabod, Nantes 18

19 Low sensitivity of the P(tau) distribution Courtesy of H.E. Thyébault TCADS- Worksho, S. Chabod, Nantes 19