Delayed gamma power measurement for sodium-cooled fast reactors

Nuclear Engineering and Design 241 (2011) 339–348

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Delayed gamma power measurement for sodium-cooled fast reactors R. Coulon a,∗ , S. Normand a,1 , G. Ban b,1 , E. Barat e , T. Montagu e , T. Dautremer e , H.-P. Brau c , V. Dumarcher d , M. Michel a , L. Barbot a , T. Domenech a , K. Boudergui a , J.-M. Bourbotte a , P. Jousset g , G. Barouch e , S. Ravaux e , F. Carrel e , N. Saurel f , A.-M. Frelin-Labalme a , H. Hamrita a , V. Kondrasovs a a

CEA, LIST, Laboratoire Capteurs et Architectures Electroniques, F-91191 Gif-sur-Yvette, France ENSICAEN, 6 Boulevard Maréchal Juin, F-14050 Caen Cedex 4, France c ICSM, Centre de Marcoule, BP 17171 F-30207 Bagnols sur Cèze, France d AREVA NP, SET, F-84500 Bollène, France e CEA, LIST, Laboratoire Modélisation Simulation et Systèmes, F-91191 Gif-sur-Yvette, France f CEA, DAM, Laboratoire Mesure de Déchets et Expertise, F-21120 Is-sur-Tille, France g CEA, LIST, Département des Capteurs, du Signal et de l’Information, F-91191 Gif-sur-Yvette, France b

a r t i c l e

i n f o

Article history: Received 30 June 2010 Received in revised form 23 September 2010 Accepted 16 October 2010

a b s t r a c t Previous works on pressurized water reactors show that the nitrogen 16 activation product can be used to measure thermal power. Power monitoring using a more stable indicator than ex-core neutron measurements is required for operational sodium-cooled fast reactors, in order to improve their economic efficiency at the nominal operating point. The fluorine 20 and neon 23 produced by (n,˛) and (n,p) capture in the sodium coolant have this type of convenient characteristic, suitable for power measurements with low build-up effects and a potentially limited temperature, flow rate, burn-up and breeding dependence. This method was tested for the first time during the final tests program of the French Phénix sodiumcooled fast reactor at CEA Marcoule, using the ADONIS gamma pulse analyzer. Despite a non-optimal experimental configuration for this application, the delayed gamma power measurement was prevalidated, and found to provide promising results. © 2010 Elsevier B.V. All rights reserved.

1. Introduction In a sodium-cooled fast reactor (SFR), power is monitored by ex-core neutron measurements using fission chambers located at the bottom of the primary vessel, covering more than 11 decades of neutron flux. This measurement provides instantaneous estimations of the power, but requires temperature corrections and periodic re-calibrations with the heat balance measurement. This thermodynamic calibration is used to set the nominal operating point, from the point of view of reactor safety and thermal efficiency. It should also be noted that this measurement can only be applied after thermo-hydraulic stability of the primary to secondary and steam generator circuits has been reached. Drifts in the normally constant relationship between ex-core neutron flux and instantaneous released thermal power (fission rate) are mainly due to temperature changes, isotopic composition changes of the fuel, variations in residual power magnitude

during fuel burn-up, and poor axial and radial representativeness of the measurement. Thus, between each heat balance calibration, the reactor may not be functioning sufficiently close to its nominal operating point, thus leading to a degradation in safety and thermodynamic efficiency. Various studies have been carried out to improve this measurement. For example, high dynamic range and high temperature fission chambers are under development, to achieve improved axial representativeness of the neutron flux measurement (Vaux and Vuillemin, 1991). The present paper introduces a method based on the measurement of the gamma activity of activation products, in order to estimate the instantaneous neutron power. This approach has been already used in pressurized water reactors (PWR), using 16 N as a power tagging agent (Papin and Bernard, 1981; Papin, 1981, 1984).

2. Methods 2.1. Practicability of the power measurement method

∗ Corresponding author. Tel.: +33 169082527. E-mail addresses: [email protected] (R. Coulon), [email protected] (S. Normand), [email protected] (G. Ban). 1 Tel.: +33 169086863. 0029-5493/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2010.10.002

In a SFR, the primary sodium coolant contains corrosion, fission and activation products. Under normal conditions, only those activation products produced from direct activation of the sodium

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Table 1 Neutron activation reactions in the sodium coolant. Nuclear reaction Activation product Decay period Cross-section JEFF3.1.1 (␮b) Energy (MeV) Emission probability

23

23

23

23

40

24

23

20

22

41

Na (n,) Na 15 h 1400 1.369; 2.754 1; 1

Na (n,p) Ne 37.2 s 355 0.440; 1.636 0.33; 0.01

coolant by a fast neutron flux are experimentally measurable. The practicability of the power measurement depends on the availability of activation products, which can be used as power tagging agents. Several characteristics are needed for these tagging agents to be suitable for power measurements:

Na (n,˛) F 11.03 s 230 1.634 1

The main neutron activation reactions producing gamma emitters are listed in Table 1. The cross-sections given in this table are weighted by the fast neutron spectrum (Williamson, 1961; Bass et al., 1966; Young and Arthur, 1977). Dissolved argon from the cover gas is also taken into account (concentration of about 0.02 ppm) (Costa and Devaux, 1974). The primary cycle time is about 2 min for the Phénix SFR. We consider a build-up rate equal to e− /, where  is the decay constant and  is the mean cycle time. A build-up correction using the signal recorded at t − , and weighted by an exponential decay factor, can be determined only if the condition  ≈ 1 is respected. Hence, neither 22 Na nor 24 Na can be used, due to their excessively long decay periods, when compared to the primary cycle time. Conversely, 24m Na, with a decay period of 2.2 ms, immediately disappears outside the reactor core. 20 F and 23 Ne are thus more convenient candidates, in view of their decay periods of respectively 11 s and 37 s. It can thus be seen that there are power tagging candidates, which could be exploited for power measurements in a SFR. It is important to note here that there are two such power tagging candidates for a SFR, whereas there is only one tagging agent (the 16 N) suitable for use in a PWR. When compared with the 16 N measurements implemented in water coolants, the use of 20 F and 23 Ne for SFR power measurements leads to additional instrumental challenges. 16 N has a high production rate and emits high-energy photons (6.13 and 7.12 MeV), with no other radionuclides being measured at higher energies. 20 F emits 1.634 MeV photons and 23 Ne emits 0.440 MeV photons, whereas 24 Na emits at 2.754 MeV, inducing a high-energy background noise due to the Compton scattering effect. This scattering signal induces statistical difficulties when measurements of the 20 F signal, and especially the 23 Ne signal, are made. The main requirement for a power monitoring system is its ability to measure power over a large dynamic range, with good accuracy and a fast response time. To monitor the power, a random error P/P of not more than several percent, and a response time t of several seconds must be achieved. As expressed in Eq. (1), two conditions are set, relating to the detection limit in the presence of a Compton background, and to the expected random error associated to the

Ar (n,) Ar 1.8 h 818 1.294 1

Poisson statistic of the counting measurement:

⎧ PM ⎪ ⎨P = m

Se−d SM t √ 8.8 B · FWHM

⎪ ⎩ P = √ P

• The cross-section of the reaction producing the tagging agent must be sufficiently high to produce a significant concentration in the coolant. • The second requirement is the radioactive constant. The decay period has to be short in comparison with the primary cycle time, in order to limit the build-up effect. This period should however not be too short, when compared to the sampling transit time taken to reach the measurement sample. • Finally, high energy gamma emission is preferable; in order to increase the signal-to-noise ratio achieved with gamma spectrometry measurements.

Na (n,2n) Na 2.6 y 6 1.275 1

1

(1)

Se−d SM t

where PM and Pm are the maximal and minimal measurable thermal power levels, S is the magnitude of the tagging agent signal, SM is the maximal total input gamma signal,  d is the mean dead time for a photon event, P/P is the statistical error associated with the power measurement, B is the background noise level, and FWHM is the full width at half maximum of the photo-peak of the power tagging agent (Millies-Lacroix, 1994). The maximum system throughput corresponds to the maximum input count rate, producing the maximal rate of processed signal events. The first equation shows that the dynamic range of measured power increases as a function of maximum throughput, and of the inverse square root of the product of background noise and energy resolution. The second equation shows that the random error decreases as a function of maximum throughput. The energy resolution and the upper count rate capacity of the gamma spectrometry system thus determine the potential performance of the power measurement system. In view of the above considerations, the gamma spectrometry system used for delayed gamma power measurements must have high energy resolution and counting rate capabilities. For these reasons, a cryogenic Hyper Pure Germanium diode (HPGe), and a metrology-grade, high count-rate analyzer need to be used. 2.2. The ADONIS system Conventional gamma spectrometry systems have limitations when it comes to performing this kind of measurement, for which high input count rates as well as optimal energy resolution and metrological stability must be maintained. The ADONIS system allows all of these instrumental requirements to be met. ADONIS (Algorithmic Development framewOrk for Nuclear Instrumentation and Spectrometry) is a project under development at the CEA-LIST, and is dedicated to high resolution, high count rates and on-line applications. It offers greater stability and flexibility than conventional gamma spectrometry measurement techniques. Filtering methods are usually based on a triangular or trapezoidal impulse response. The parameters of the linear filter are adjusted to the pre-requirement pulse shapes in order to optimize the resulting spectral resolutions and dynamic ranges (Radeka, 1971). Pile-up rejection and life-time correction units are also implemented, to increase the system’s high count rate ability. For time-varying activity measurements, conventional systems use loss-free counting methods in which the count rates are corrected in real time, using an instantaneous evaluation of the system’s dead time (Ortec, in press). These methods are complex to adjust and are intrinsically limited in terms of the instantaneous lifetime accuracy associated with signal filtering based on linear shaping filters. For this reason, a new filtering and smoothing method for HPGe diode signals was developed for the ADONIS system (Barat et al., 2006). The Kalman bimodal smoother makes use of the intrinsic statistical properties of nuclear signals, to obtain an energy resolution

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and a count rate estimation which are always optimal, whatever the instantaneous experimental conditions, and variations thereof. The ADONIS analyzer generates an event stream which, for each pulse, is comprised of an accurate value for the collected charge quantity, the charge collection duration, and the time separation with respect to the previous event. This triplet allows an accurate and robust estimation to be made of the real count rate. The system is then able to measure count rates above 1 Mcps without incurring pile-up rejection units, and has a maximum throughput rate of 600 kcps. This system is also optimal for time-domain analysis of the gamma spectrometry measurement (Plagnard et al., 2004). ADONIS is currently being developed for use together with the PING system (Normand et al., 2009), as well as other new spectrum analysis techniques (Barat et al., 2007; Trigano, 2005; Barat et al., 2009).

2.3. The experimental test The challenges of the experimental test were to implement gamma spectrometry of the Phénix sodium coolant, using the ADONIS prototype, and to demonstrate the feasibility of the 20 F and 23 Ne signal measurements. This experiment was classed as test no. 103, in the “final tests” program of the Phénix reactor, before its definitive closure in January 2010 (Martin et al., 2009; Coulon, 2009a; Vasile et al., 2010). The Global Delayed Neutron Detection cell (DND/G) was considered to be the best available location at the Phénix nuclear power plant. The DND/G system was chosen in order to detect cladding failures via the measurement of delayed neutron emitters (Phénix, 1974). Although this location was not optimal for the purposes of our experiment, it was retained for two main reasons: • The sodium transit time from the core outlet to the measurement sample is the shortest at the pool-type Phénix reactor (about 30 s), thereby increasing the probability of achieving suitable measurements of the 20 F and 23 Ne signals. • Despite a core outlet to sampling area distance of 1.5 m, the 6 sampling points located near to each intermediary heat exchanger allow the influence of sodium flow heterogeneities to be limited. Fig. 1 illustrates the principle of the DND/G system. The gamma spectrometry system is composed of a coaxial germanium detector with reverse electrodes and an efficiency of 10% (CANBERRA REGe1020). It is coupled to a reset transistor preamplifier, and a hybrid cryostat. This setup is convenient for remote measurements (Canberra, 2010; Safe and Effective Alternatives to Liquid Nitrogen, 2008). The HPGe diode signals were processed and recorded using the ADONIS analyzer. The disadvantage of the chosen location was related to the presence of lead shielding, which led to an attenuation of the order of 10−19 for 23 Ne photons, and approximately 10−7 for 20 F photons, such that the high count rate capability of the ADONIS system could not be used to advantage.

Fig. 1. Schematic diagram of the DND/G system.

balance conservation equation: ∂Nj ∂t

 + div(Nj v) = Ni

j (E)(E)dE − j Nj

(2)

E

where Ni is the nuclear concentration of the target nucleus i, Nj is the nuclear concentration of activation product j,  j (E) is the reaction cross-section producing the activation product j, j is the decay constant of the activation product j, v is the velocity field of the sodium coolant, and (E) is the neutron flux. To solve this equation, the core geometry is radially meshed into three cylindrical components (dash c of equal neutron flux magnitude, sodium velocity and 23 Na atomic density), namely: the fissile area, the fertile area and the reflector area. The axial flux distribution is modeled by a sinusoidal function c (E, z) = ¯ sin( z/h), where z is the axial ordinate and h is the height c (E, h) of the fissile column. This approximation is usually used as a firstorder model for the axial flux distribution in a PWR. However, in the case of a SFR this model could be far from the reality, due to fertile blanket enrichment effects. The analytical solution for Nj from Eq. (2) can be written in the form:

2.4. Measurement simulations In order to optimize the measurement configuration in a preexisting location, simulation studies are useful since they allow the magnitudes of the signal to be estimated. The following activation model was used to obtain the order of magnitude of each activation product concentration at the reactor–core outlet. The concentration Nj of an activation product j, at any location in the sodium core, is calculated using the nuclear

 z Nj,c (z) = 0

Ni,c (s)

 E

j (E)c (E, s)dE

vc (s)

−

×e

z s

(j +(∂vc (u))/∂z)/(vc (u))du

ds

(3)

This equation can be solved numerically by Riemann sums (discretization of the z axis), using at each increment k the released heat calculation, and taking the conservation of mass flow rate into

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Fig. 4. Activation product concentrations (build-up effect). Fig. 2. Sodium activation in the fissile area.

Finally, the mean activation product concentrations at the reactor core outlet (z = h) are weighted in order to obtain a global value:

account:



⎧ c,f (k)εf ⎪ Qc (k) = ⎪ ⎪ vc (k)Sc c (Tc (k − 1)) ⎪ ⎪ ⎪ ⎪ ⎪ Qc (k − 1) ⎪ ⎨ Tc (k) = Tc (k − 1) + ⎪ ⎪ ⎪ Ni,c (k) = ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ vc (k) =

Cpc (Tc (k − 1))

Nj,0 =

where k is the z axis increment, Qc is the heat quantity absorbed per sodium mass unit,  f is the fission rate, Tc is the sodium temperature, εf is the mean energy released per fission, Cpc is the specific heat of sodium, NA is Avogadro’s number, and A is the chemical atomic weight of sodium. Fig. 2 shows the computed production of radionuclides in the fertile area, and Fig. 3 shows the computed production of 20 F in each area c.

20

F concentration in each area.

Nj,c (h)Sc vc



(5) Sc vc

c

(4)

c (Tc (k))NA A c (Tc (k − 1))vc (k − 1) c (Tc (k))

Fig. 3.

c

where c is the area indicator (fissile, fertile, reflector), Sc is the equivalent sodium surface of each area c, and Nj,0 is the global concentration of each activation product j at the core outlet. During the sodium coolant cycle, radionuclides are diluted in the primary coolant, and could undergo a complete coolant cycle if their decay period was sufficiently long. This build-up effect is modeled by:

⎧  n

⎪ ⎪ −mj x ⎪ e ⎪ ⎨ Nj,n = Nj,0 1 + ⎪ ⎪ ⎪ ⎪ ⎩ Nj,∞ =

Nj,0

m=1

e−j x 1+ j x



(6)

where n is the cycle number and  x is the mean cycle time. Fig. 4 illustrates the computed variations in activation product concentration resulting from a 350 MWth power step. 23 Ne is found to have a 5% build-up magnitude with a transient state lasting 4 min, and 20 F is found to have negligible build-up impact (below 0.01%). Direct measurements of 23 Ne and 20 F could thus be used to implement fast and accurate power measurements. In comparison to PWR configuration, the build-up correction is not useful for the 20 F power measurement. A transfer function is then used to link the activation product concentration at the core outlet to the activity of each radionuclide contained in the measurement sample of the DND/G system. Experimental data extracted from the COLCHIX Phénix hot pool physical model (1:8 scale) were used to simulate the sodium flow (Rion and Roux, 1989). Tagging agents were injected into each core assembly in the model, and analyzed using laser fluorimetry at each DND/G sampling point. This allows the thermal hydraulic impulse response Fj to be evaluated (see Eq. (7) and Fig. 5). The shunt peak is modeled using experimental data Rie,ass (t) from each sub-assembly ass and each intermediate exchanger ie. Then the function is adjusted by means of a perfect mixing model, where ˛ is an experimentally

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Pulse height tally simulations for the HPGe sensor have been validated experimentally (Michel, 2009). Charge carrier quantification and electronic noise effect is added by a convolution of Y(E) with a Gaussian function. The standard deviation (ε,  Y) is experimentally determined with ε is the energy and Y = E y(E)dE is the total input count rate.



y (E) =



y(ε)

2

2 (ε, Y )e−((E−ε)

)/(2 2 (ε,Y ))

dε

(11)

ε

Fig. 5. Sodium activation products impulse response.

determined constant.

⎧ ⎪ ⎨t ∈ ⎪ ⎩

→ Fj (t)

[0; 20]s

=

1

Rie,ass (t)e−j t nass nie ass

t

∈

[20; ∞]s

→ Fj (t)

=

ie

(7)

˛e−(˛+j )t

The activation products’ transit through the sampling tubes is considered as a plug flow, with a constant transit time  m . The activation products’ activity is then given by:

The ADONIS system gives the guaranty that the energy of a pileup event is exactly the sum of the energy of each independent event. Piled-up phenomenon are then simulated by a lot of random selections on the distribution y (E)/Y and a random summation test based on the pile-up probability 1 − e−Y d . Our simulations showed that because of the lead shielding of the DND/G system, a minimal collimator hole surface and thickness is needed to measure the 20 F or 23 Ne signals. Various operations were thus required. The HPGe sensor was then shielded with a lead castle, in order to increase the source-signal to scattered-signal ratio. In addition, a collimation hole was designed to increase the incident flux from the source, and to mitigate any undesirable influence on the security level of the DND/G system (safety system) (Coulon, 2009b; Jeannot, 2005; Molliex and Dirat, 2009). Table 2 shows the results obtained from this simulation, and Fig. 7 provides a simulation of the spectrum produced by the experiment. The gamma signal is composed mainly of the 24 Na signal with photoelectric peaks at 2.754 MeV and 1.369 MeV, and escape peaks at 2.243 MeV and 1.732 MeV. Although the probability of measuring the 20 F signal was increased by the collimator, its statistical accuracy is still far



−j m

Aj = j Nj,∞ e

Fj (t)dt

(8)

t

The gamma spectrometry measurement is then simulated using MCNP particle transport code, which has been validated in this field (Sood et al., 2003). Since the lead shielding thickness leads to difficulties with the Monte-Carlo simulation, the simulation was separated into two parts. The first part of the simulation consists in computing a flux point tally (F5) to simulate the incident gamma flux yield MC, (E) at the HPGe detector (see Fig. 6). These simulations were strongly accelerated using variance reduction techniques to compensate for statistical losses in the DND/G lead shielding. The exponential transform, spanning the pathlength between collisions, was used to simulate particle tracks into the internal lead shielding, thus increasing the rate of photon events outside the DND/G device. Moreover, geometry splitting and Russian roulette techniques were used to increase the rate of photon events in the direction of the detector. Due to the sample complexity, a partial gamma flux yield MC, (E) is simulated for each part of the sample volume to obtain absolute gamma emission rates A (E): A (E) = ς



[Aj



j MC, (E)V ]

(9)

j

j

where j is the emission rate of the photon  j , V is the sodium volume of the sample part and ς the collimation hole surface. The second part of the simulation involved transferring the derived source terms A (E) emitted over the surface ς in specific directions and angles into a pulse height tally simulation (F8) at the HPGe sensor. Efficiency spectra R (E) resulting from simulation are then summed and weighted by A (E) to obtain the physical detector response y(E): y(E) =





[R (E)

A (E)dE] E

(10) Fig. 6. MCNP model of the experiment.

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Table 2 Simulation results (JEFF3.1.1). 24 −3

Core outlet activity (Bq cm Build-up activity (cps) Sample activity (Bq cm−3 ) Evaluated signal (cps)

)

23

Na

1.73 × 10 1.15 × 108 1.12 × 108 217 5

20

Ne

6.66 × 10 7.01 × 107 2.32 × 107 0

22

F

41

Na −1

1.38 × 10 1.38 × 108 5.03 × 106 1.03

7

4.82 × 10 4.87 × 105 4.77 × 105 0

8

Ar

1.75 × 10−2 1.42 1.38 0

limitations arising from the calculation times of the Monte-Carlo simulation and the presence of parasite sources near to the measurement. During the last part of the power increase (May 25th 2009), 8 accurate heat balance power measurements were carried out. Fig. 9 shows the power estimated using the heat balance measurement (error bars) (Brau, 2010, 2005), and the power measured using the ex-core boron-coated ionization chamber calibrated with the last heat power measurement (continuous curve). These reference measurements were used to study the 20 F signal’s behavior as a function of power. 3.2. Pre-validation of the delayed gamma power measurement

Fig. 7. Simulated gamma spectrum of the experiment (350 MWth).

from optimum, and the Monte-Carlo simulation will largely underestimate the magnitude of the scattered signal. The 22 Na, 41 Ar, and 23 Ne signals have no chance of being measured at the Phénix experiment. 3. Results 3.1. Observation of 20 F

The data obtained using ADONIS comprise, for each event k, an accurate value for the energy Ek , the arrival time Tk and the busy time Dk . The total input count rate T is accurately measured by the ADONIS system, as shown in Eq. (12) where Te is the sampling time and n is the total number of recorded events.

⎧ n = ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨

⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ = − T

max{k, Tk + Dk < n}

⎛

⎞

⎜ ⎜

ln ⎜ ⎜1 −

⎝

n n

Tk − Dk

⎟ ⎟ ⎟ ⎟ ⎠

(12)

i=k

Te

The system was installed in April 2009, in time for the start-up of the final tests program in May 2009. Thirty hours of data were recorded during reactor working operations. Fig. 8 shows a spectrum obtained at 302.5 MWth. As predicted by simulation, the 20 F signal at 302.5 MWth was measured with a count rate of 0.84 ± 0.11 cps, in the presence of a background noise of 1.75 cps. A strong scattering signal is observed, with lead X-ray peaks and a strong annihilation peak due to the lead shielding. The scattering signal was generally higher in the experiment than in the simulation, especially at low energies, due to particle tracking

Two factors f1 and f2 are determined, to maximize the number of recorded events corresponding to the row signal m = max{j, Tj + Dj < m & Ej ∈ [ε0 − f1  ; ε0 + f1 ]} and the background noise signal (assuming that the linear approximation of the Compton background shape to be respected) l = max{i, Ti + Di < l & Ei ∈ [ε0 − f1 f2  ; ε0 − f1 ] ∪ [ε0 + f1  ; ε0 + f1 f2 ]} where  is the energy resolution (first-order Gaussian shaped peak) and ε0 is the characteristic 20 F energy. Busy time sequences of the row signal Hj and the background noise signal Bi are then constructed, as

Fig. 8. Measured gamma spectrum at 302.5 MWth.

Fig. 9. Power increase on May 25th 2009.

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test, the power measurements were still far from the ultimately achievable performance of a 20 F power measurement. The 24 Na signal was determined with a random error of 2.5%, allowing us to study the influence of the reactor status on the activity of the activation products. Fig. 11 shows that: • The 24 Na signal is strongly affected by the build-up effect. An increase in signal strength is observed during the constant power sequences from 12:00 to 14:00 and from 15:00 to 16:30. After 16:30, although the power suddenly decreased to <50 MWth, a quasi-constant level of 24 Na activity was measured. • A significant decrease (−[3;10] %) in the 24 Na signal is observed at 15:00. This fall in activity is correlated to an increase in core temperature (+3.3%), which induces changes in the microscopic (spectrum effect) and macroscopic (density effect) cross sections. 20

Fig. 10. points.

F signal to released power ratio at the reference power measurement

shown in Eq. (13).



Hj =

{Dj , Ej ∈ [ε0 − f1 ; ε0 + f1 ]}

Bi = {Di , Ei ∈ [ε0 − f1 f2 ; ε0 − f1 ] ∪ [ε0 + f1 ; ε0 + f1 f2 ]}

(13)

The row signal rs and the noise signal n are then estimated by weighting each event by the non-pile-up probability. The row signal is also corrected by the f2 factor, in order to compensate for the asymmetry of the two energy windows. The filtered 20 F signal is finally obtained by subtracting n from rs , according to Eq. (14).

⎧ m

⎪ ⎪ ⎪ m eT Te (Hj +1/2) ⎪ ⎪ ⎪ ⎪ j=1 ⎪ ⎪ rs = T ⎪ ⎪ n ⎨ l

⎪ l eT Te (Bj +1/2) ⎪ ⎪ ⎪ ⎪ i=1 ⎪ ⎪ n = T ⎪ ⎪ (f2 − 1)n ⎪ ⎪ ⎩ 

(14)

= rs − n

In order to compare the measured 20 F and 24 Na signals with the heat reference power measurements, Figs. 10 and 11 show the ratio between thermal power and 20 F signal, and the ratio between thermal power and 24 Na signal, respectively, at each measurement point. The 20 F signal was estimated at the reference points, with a random error of 14%. Nevertheless, the 20 F signal exhibits a linear behavior as a function of thermal power, within this range of uncertainty. Due to non-optimal settings during the Phénix experimental

Fig. 11. points.

24

Na signal to released power ratio at the reference power measurement

Fig. 10 shows that the build-up effect is suppressed in the case of 20 F activity. The poor counting statistics of the measurement did not allow us to study the impact of the reactor parameters on the 20 F response. Theoretically, the 20 F and 23 Ne activities should be influenced, as should be that of 24 Na, by the sodium flow rate and changes in density as a function of temperature. 20 F and 23 Ne are affected to the same order of magnitude as the 24 Na, by variations in the sodium velocity, but the (n,˛) and (n,p) reaction thresholds correspond to a neutron energy greater than 1 MeV. The microscopic cross-section will not be affected by changes in temperature. Consequently, the biases induced by temperature variations (due to changes in target 23 Na nuclei concentration only) are not likely to be greater than 3%. These considerations show that the 20 F and 23 Ne power measurements will be limited in accuracy during sequences of increasing power, if real time corrections for the influence of flow rate are not applied. At nominal power, the sodium flow rate and temperature are quasi-constant, such that the burn-up and breeding phenomena are the only remaining parameters which could impact the system’s response. 3.3. Perspectives for delayed gamma power measurements An optimized system could be considered for power measurements, in which 20 F and 23 Ne are also used as power tagging agents on a primary coolant sample. 20 F and 23 Ne power measurement systems could be set-up (by adjusting the sodium transit time and the sample volume). The resulting high count rate, monitored by the adaptive ADONIS system, would allow high statistical accuracies to be achieved when monitoring nominal power. Fig. 12 shows the variations between the radioactivity and the cooling time (equivalent to transit time). In order to increase the 20 F signal, and reduce the 24 Na Compton background, the transit time from the reactor core to the measurement sample must be kept as short as technically possible. The ADONIS system allows metrological measurements to be made at rates of up to 1 Mcps (Coulon, 2009c). Its maximum throughput (output count rate vs. input count rate) occurs at 600 kcps, and its energy resolution is a function of the input count rate (thanks to the adaptive smoother). As an example, 20 F and 23 Ne power measurement systems were simulated under optimal conditions, in order to obtain an estimation of the potential performance of such a system, in terms of statistical accuracy and response time. The following characteristics were considered: • Direct sampling at the core outlet. • A transit time to the measurement sample equal to 5 s. • A mean cycle coolant time equal to 100 s.

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Fig. 14. Random error vs. integration time.

Fig. 12. Variations in radionuclide radioactivity as a function of transit time in a sodium sample.

Fig. 13 shows the simulated spectrum for this optimized configuration. Spectrum c is the simulated spectrum obtained using our methodology for the experimental case of the Phénix reactor. Spectrum a is the gamma spectrum measured during the Phénix experiment, illustrating the feasibility of measuring 20 F, and showing that good estimations of the direct signal can be derived from simulations, although with significantly underestimated values for the scattered signal. Spectrum d is thus the simulated signal in the optimized configuration. The sodium sample measurement is simulated by setting the throughput to its maximum value at nominal power, with degradations in the energy resolution and pulse pileup phenomena being taken into account. Finally, a scattered signal, estimated on the basis of the measurements made at the Phénix reactor, is added to the former, thus producing spectrum e. The magnitude of this noise could be reduced by installing the system far from any other gamma sources, and by designing a suitable collimator. This study shows that the suppression or reduction of shielding would allow the 23 Ne signal to be measured, and that the resulting decrease in transit time would strongly increase the 23 Ne and 20 F signals, in comparison to the 24 Na signal. It should be noted that no sum peaks could interfere with the 20 F photo-peak or the 23 Ne photo-peak. The computed 20 F signal has a count rate of 4500 cps,

whereas the 23 Ne signal has a count rate of 2700 cps. The measurement of high count rates will allow accurate measurements to be achieved. Fig. 14 shows the random errors calculated using Eq. (1) for 23 Ne and 20 F measurements, and Fig. 15 shows the achievable dynamic ranges. From the statistical point of view, high count rate measurements would allow a fast and accurate power measurement system to be developed. The dynamic range is limited to two or three decades. The system described in this paper could allow more stable measurements to be achieved than with conventional neutron measurements, thanks to the very good representativeness of the in-core fission rate, which allows the thermal efficiency to be monitored with greater accuracy. However, 24 Na measurements have shown that the activation phenomenon is affected by variations in sodium temperature and flow rate. Normally, the 23 Ne and 20 F radionuclides will also be affected by such variations. The accuracy of the measurement during a power increase will thus be limited by this phenomenon. At the nominal operating point, the temperature and flow rate are stabilized, such that burn-up and breeding are the only remaining parameters able to affect the measurement accuracy. The possibility of measuring two additional power tagging agents could limit these systematic errors. The irradiation factor of the neutron activation equation, (1 − e−(h/v) ) (where  is the decay constant, h is the fissile column height and v is the sodium velocity) does not have the same value for 23 Ne and 20 F. When a constant burn-up rate is considered, the ratio between the signals from these radionuclide gives an indication of the sodium velocity, as already noted in (Lennox, 1985), and this dependence provides an opportunity for the implementation of a corrective technique. Fig. 16 plots the 20 F/23 Ne ratio as a function of the sodium velocity.

Fig. 13. Measured and simulated spectra of a sodium coolant sample.

Fig. 15. Dynamic power range vs. integration time.

• A coaxial HPGe sensor with an active volume of 60 cm3 , an energy resolution of 2.0 keV at 1.634 MeV, and an energy resolution of 1.4 keV at 440 keV, at low count rates (the detector size could be also optimized).

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core could then be estimated from only one nuclear spectrometric measurement at all power levels, and during transient sequences, without the need for temperature corrections and frequent heat balance calibrations. 4. Conclusion

Fig. 16. Variation of the 20 F/23 Ne signal ratio as a function of sodium velocity.

Fig. 17. Reaction rate energy distribution in different enrichment configurations.

The increase in 239 Pu concentration leads to an increase in the number of neutrons produced by fission, and to neutron spectrum hardening. A recent study of PWRs shows that the 16 N power measurement is highly biased by the burn-up phenomenon (Lokhov, 2007). Fig. 17 shows the 20 F and 23 Ne reaction rate vs. energy distributions, for the cases of two different fuels: one entirely composed of 235 U, and one entirely composed of 239 Pu. The JEFF3.1.1 cross-section evaluation was applied, and combined with the corresponding Watt spectra. Table 3 gives the integrated values of reaction rate R, and the reaction rate ratios for different enrichment configurations. It can be seen that this ratio is independent of the power magnitude but dependent on fuel type, and despite its poor sensitivity (6.7 × 10−4 % Pu−1 ) could make use of the neutron spectrum hardening phenomenon as a burn-up indicator (with the sodium flow rate assumed to be constant). A correction technique, using the 20 F/23 Ne signal ratio to compensate for the impact of burn-up, could be investigated. If the a priori knowledge of the fuel’s isotopic composition is robust, the residual power could then be estimated by real-time simulations, on the basis of the corresponding transfer functions. The thermal power released by the reactor Table 3 Behavior of activation production rates as a function of the fuel’s isotopic composition.

5

100% U 100% 9 Pu 17% 9 Pu, 83% 5 U Bias for 1% changing in 9 Pu concentration

R20 F (U.A.)

R23 Ne (U.A.)

R20 F/R23 Ne

1.14 1.62 1.23 0.1%

3.03 4.06 3.21 0.39%

3.77 3.97 3.38 0.067%

New power measurement methods have been studied, to improve the power monitoring of a Sodium-cooled Fast Reactor. Delayed gamma power measurements have been proposed in this paper, in an effort to improve the safety and efficiency of such reactors. The use of neutron activation products to measure the released thermal power can be expected to guarantee reliable in-core fission rate representativeness. It could be used to monitor the reactor’s neutron flux under nominal conditions. Our study shows that the 20 F and 23 Ne produced by (n,˛) and (n,p) capture on 23 Na nuclei could be used as tagging agents. Their short decay period results in a low build-up phenomenon, thus allowing the measurement system to have a fast response time. Experimental tests at the Phénix reactor have shown that the 1.634 MeV photons of 20 F can be measured directly in the sodium coolant sample, by means of the high resolution, high count rate capabilities of the ADONIS gamma spectrometry system. A simulation study has shown that 23 Ne could also be measured in an optimized experimental configuration. The high count rate ability of the system allows a random error of 3% in the neutron power measurement to be obtained, with an integration time of 2 s. The maximal bias induced by the temperature effect is estimated at 3%, thanks to the high neutron capture reaction threshold of 20 F and 23 Ne. Corrective methods based on the dual measurement of 20 F and 23 Ne signals could also limit biases related to variations in flow rate at intermediate power levels, and could limit the method’s sensitivity to burn-up/breeding. The power monitoring method presented in this paper shows promising results for sodium-cooled fast reactors. The measurement of 20 F and 23 Ne by a high energy resolution, high count rate spectrometry system could be introduced as a complementary means of monitoring the thermal power released by the reactor core. The possibility of using the same system to detect cladding failures, with a low cooling time, is currently being studied. Further experimental tests and simulations are needed to provide full validation of the monitoring technique’s potential (design of the sampling method, impact of fertile blanket enrichment design of a germanium crystal volume to optimise the sensibility of the fission products detection). Acknowledgments The authors would like to thank the CEA-DRT and CEA-DAM for their financial support, and the Phénix staff for their collaboration. References Barat, E., Dautremer, T., Montagu, T., 2007. Nonparametric bayesian inference in nuclear spectrometry. In: Nucl. Sci. Sym. Conf. Rec. NSS07, pp. 880–887. Barat, E., Dautremer, T., Montagu, T., Normand, S., 2009. ADONIS: a new concept of X/gamma pulse analyzer. In: ANIMMA Conf. Rec. N210. Barat, E., Dautremer, T., Montagu, T., Trama, J.-C., 2006. A bimodal kalman smoother for nuclear spectrometry. Nucl. Instrum. Methods A567, 350–352. Bass, R., Haug, P., KrGger, K., Staginnus, B., 1966. Fast neutron excitation functions by activation techniques. EANDC(E) 66, 64. Brau, H.-P., 2005. Heat Balance: From Uncertainty to Corrective Action, CEA Phénix Tech. Rep. PA100XG93521. Brau, H.-P., 2010. BILTHER V2.0 Code for ADONIS Measurement, ICSM tech. rep. Costa, L., Devaux, J., 1974. Argon 41 Activity in Cover-gas Plenum of the Phénix Reactor, Impact of Argon Dilution into the Sodium. CEA Tech. Rep. DRNR/SEDC no. 75-547. Coulon, R., 2009a. Procedure of the Scientific Experiment No. 1103. Gamma Spectrometry. CEA Phénix Tech. Rep. PA103XE44103.

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