# Sodium fast reactors power monitoring using high resolution and high count rate gamma spectrometry.
## Simulation study

Romain Coulon, Stephane Normand, Loic Barbot, Thierry Domenech, Anne-Marie Frelin, Vladimir Kondrasovs, Eric Barat, Thierry Montagu, Thomas Dautremer, Jean Lefevre, et al.

► To cite this version:

Romain Coulon, Stephane Normand, Loic Barbot, Thierry Domenech, Anne-Marie Frelin, et al. Sodium fast reactors power monitoring using high resolution and high count rate gamma spectrometry. Simulation study. 2008 NSS/MIC - 2008 IEEE Nuclear Science Symposium and Medical Imaging conference, Oct 2008, Dresde, Germany. pp.973-977, 10.1109/NSSMIC.2008.4774558 . cea-05462312v2

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# Sodium Fast Reactors Power Monitoring Using High Resolution and High Count Rate Gamma Spectrometry. Simulation Study.

Romain Coulon, Stephane Normand, Loic Barbot, Thierry Domenech, Anne-Marie FreHn, Vladimir Kondrasovs, Eric Barat, Thierry Montagu, Thomas Dautremer, Jean Lefevre,

CEA, LIST, Laboratoire Capteurs et Architectures Electroniques, F-91191 Gif-sur-Yvette, France.

Vincent Dumarcher, Henri-Pierre Brau,

CEA, Marcoule, Groupe Essais Statistiques, F-30207 Bagnols sur Ceze, France.

and Gilles Ban,

ENSICAEN, F-14050 Caen, France.

**Abstract**-Sodium Fast Reactors (SFR) are studied in the international generation IV project to preserve uranium resources and transmute minor actinides. The french Phenix experimental reactor has already shown promising results. The reactor power is commonly calculated simultaneously by heat balance on water to vapour heat exchanger and by neutron flux measurements. Concentration of some gamma radionuclides in the primary coolant is also directly correlated with power. Therefore, we think that an on-line gamma measurement system could be settled as another help for generation IV SFR reactor exploitation. The 2°F is a particularly convenient tagging agent to design a fast time response system. This work shows that a gamma spectrometry system measuring the 2°F activity could be set as a power monitoring system for SFR reactor. This system wiD be tested at the Phenix reactor with the high count rate and high resolution Adonis spectrometer.

## I. INTRODUCTION

POWER monitoring using gamma measurement is already used in Pressurised Water Reactors (PWR) by using the I6N tagging agent. This study presents the use of gamma spectrometry to monitor the fourth generation SFR power. The main required characteristic of power monitoring systems is the ability to measure a large range of power with good accuracy and fast response. Then, gamma spectrometry systems should be able to measure gamma activity in a large count rate range, with high performance in resolution as well in high and in low count rates. This consideration limits the conventional spectrometry systems use but recent improvements may remove this difficulty. A gamma ray spectrometry processing called Adonis has been developed by the CEA-LIST for high resolution in high count rate and on-line applications [1].

This work deals with a complete simulation study to identify convenient gamma emitters contained in primary fluids and to link their activities to the reactor power. Gamma source term of the primary sodium was determined as a function of released thermal power and radionuclide transit at the measurement point. Phenix spectrum, partial cross-section evaluations and thermal hydraulic data were used for this calculation. Then, gamma spectra are simulated by Monte-Carlo transport code thanks to the obtained gamma source term.

## II. MATERIALS AND METHODS

We search the most convenient tagging agent for our application. For statistic consideration, it must have a high creation yield. It should also be a high energy gamma emitter. To obtain a short response time measurement this tagging agent must have a short decay period.
The first part will introduce the ADONIS system, then the gamma source term calculation in Phenix geometry will be presented to determine a convenient gamma emitter in our problematic.

## A. The ADONIS spectrometry system

Conventional spectrometry systems use matched filters as signal processing. Filter parameters are adjusted to prejudged pulses shape to optimized the spectral resolution. This is an important limitation to use conventional gamma spectrometry in power monitoring where the gamma signal flux can brutally changed.

Adonis uses a Hyper Pure Germanium diode cooled with liquid nitrogen and coupled with a reset transistor preamplifier. A nonlinear digital signal processing is then performed taking into account the stochastic nature of the pulses arrival. The Bimodal Kalman smoother algorithm gives an event stream composed, for each pulse of precise value of energy, duration, and separation with previous event. Ensuring event datation, this triplet allows analysis for time varying activities (cf. figure 1).

Therefore this system is able to provide on-line gamma spectra for count rates over 4 MSamples/s with still high metrology requierement. Moreover the spectral resolution obtained with Adonis is optimal whatever the count rate. ADONIS is particularly convenient to measure the large range of primary sodium gamma activity, achieving up 0.5 TBq.kg⁻¹ of ²⁴Na.

<figure><img src="image_2.png" /><figcaption>Fig. 1: Adonis electronic</figcaption></figure>

## B. SFR gamma source term calculation

The gamma source term is calculated as a function of the power and the flow rate in fuel assembly. Equations are an adaptation to SFR of PWR equations developed by B. Papin and P. Bernard [2]. The main trouble is to take into account the pool configuration of this kind of reactor.

Gamma source terms are calculated with neutron reactions introduced in table I. This calculation is made on Phenix reactor geometry with a measurement set on a hot pool sodium sampling system. One should notice that the calculation also took into account the dissolved argon (concentration of 0.019 ppm [3]) contained into primary sodium.

First, the reaction rate is calculated by discrete nuclear data values as shown in this equation :

$$R_r=N_x\sum_E \sigma(E)\Phi(E) \quad (1)$$

Where:

* R<sub>r</sub> is the reaction rate of the reaction r.

* N<sub>x</sub> is the atomic density of the target nucleus x in the homogenized core with non-irradiated fuel (data extracted from technical report [4]).

* σ(E) is the partial cross section of the reaction r' on the nucleus x. This nuclear data are available for different evaluations like JEFF3.1.1 or ENDF B-VII. To have a good precision
these data are discretized in logarithmic scale with 100 energy groups by decade (see the figure 2a).

• $\Phi(E)$ is the mean neutron Phenix reactor spectrum obtained in 33 energy groups.

Only in-core activation is considered for gamma source term calculation. Neutron transport simulations using MCNP5 have shown that ex-core activation by radiative capture could be neglected because of the high decreasing flux in the neutron core shielding (see the figure 2d).

The creation yield is then calculated as a function of the thermal power by this formula :

$$X_y = 0.9 * P \cdot \frac{R_{\text{act}}}{E_f \cdot R_{\text{fiss}} \cdot V_c} (2)$$

Where:

* $X_y$ is the creation yield producing the radionuclide y.

* P is the thermal power released by the core.

* $R_{\text{act}}$ is the reaction rate of the reaction creating y as activating isotope. We consider only the fissile zone of the core where 90 % of the thermal power is released, therefore a factor is added to compensate this approximation.

* $R_{\text{fiss}}$ is the fission reaction rate on $^{235}$U and $^{239}$Pu nucleus.

* $E_f$ is the mean energy released per fission.

* $V_c$ is sodium active volume.

The activating isotope concentration at the fuel assembly outlet is obtained by the following differential equation:

$$dN_y/dt = X_y - (\lambda_y + \alpha)N_y \quad (3)$$

Where:

* $N_y$ is the activating isotope y concentration at the fuel assembly outlet.

* $X_y$ is the creation yield of the activating isotope y.

* $\lambda_y$ is the decay constant of the activating isotope y.

* $\alpha$ is a hydraulic parameter which depends of the sodium velocity in fuel assembly. It is calculated as the ratio between sodium flow rate and the sodium volume of a fuel assembly.

During the sodium coolant cycle, radionuclides are diluted and could reenter an other times into the core if their decay period is long enough. This effect is neglected for short decay radionuclides as $^{20}$F and $^{23}$Ne but it is predominant for $^{24}$Na and $^{22}$Na. To take into account this cumulative effect, the activating isotope concentration is calculated by adding a cumulative term:

$$N'_y = N_y(1 + \exp(-\lambda_y \tau_a) / \lambda_y \tau_a) \quad (4)$$

<table><caption>TABLE I: Neutron reactions in primary sodium</caption><thead><tr><th>Nuclear reaction</th><th>Induced emitter</th><th>Decay period (s)</th><th>Photon energy (keV)</th><th>Branching ratio</th></tr></thead><tbody><tr><td><sup>23</sup>Na(n, 2n)</td><td><sup>22</sup>Na</td><td>8, 20.10<sup>7</sup></td><td>1274, 5</td><td>0,9994</td></tr><tr><td rowspan="4"><sup>23</sup>Na(n, γ)</td><td rowspan="4"><sup>24</sup>Na</td><td rowspan="4">5, 39.10<sup>4</sup></td><td>1368, 63</td><td>1</td></tr><tr><td>2754, 03</td><td>1</td></tr><tr><td>2870, 00</td><td>2.10<sup>-6</sup></td></tr><tr><td>3867, 20</td><td>5, 2.10<sup>-4</sup></td></tr><tr><td rowspan="2"><sup>24m</sup>Na</td><td rowspan="2"></td><td rowspan="2">2, 2.10<sup>-3</sup></td><td>4238, 00</td><td>7, 5.10<sup>-6</sup></td></tr><tr><td>472, 3</td><td>0,995</td></tr><tr><td rowspan="2"><sup>23</sup>Na(n, α)</td><td rowspan="2"><sup>20</sup>F</td><td rowspan="2">11, 03</td><td>1633, 70</td><td>1</td></tr><tr><td>3334, 4</td><td>1, 4.10<sup>4</sup></td></tr><tr><td rowspan="5"><sup>23</sup>Na(n, p)</td><td rowspan="5"><sup>23</sup>Ne</td><td rowspan="5">37, 2</td><td>439, 9</td><td>0,33</td></tr><tr><td>1636, 4</td><td>0,01</td></tr><tr><td>2076, 3</td><td>1.10<sup>-3</sup></td></tr><tr><td>2542, 3</td><td>2, 7.10<sup>-4</sup></td></tr><tr><td>2982, 2</td><td>3, 8.10<sup>-4</sup></td></tr><tr><td rowspan="2"><sup>40</sup>Ar(n, γ)</td><td rowspan="2"><sup>41</sup>Ar</td><td rowspan="2">6, 58.10<sup>3</sup></td><td>1293, 6</td><td>0,992</td></tr><tr><td>1677, 0</td><td>5, 2.10<sup>-4</sup></td></tr><tr><td rowspan="8"><sup>36</sup>Ar(n, 2n)</td><td rowspan="8"><sup>35</sup>Ar</td><td rowspan="8">1, 78</td><td>1219, 0</td><td>1, 35.10<sup>-2</sup></td></tr><tr><td>1763, 0</td><td>3, 12.10<sup>-3</sup></td></tr><tr><td>2155, 0</td><td>1, 49.10<sup>-5</sup></td></tr><tr><td>2694, 0</td><td>1, 48.10<sup>-3</sup></td></tr><tr><td>2748, 0</td><td>6, 48.10<sup>-5</sup></td></tr><tr><td>3003, 0</td><td>9, 77.10<sup>-4</sup></td></tr><tr><td>3918, 0</td><td>7, 02.10<sup>-5</sup></td></tr><tr><td>3967, 0</td><td>1, 49.10<sup>-5</sup></td></tr></tbody></table>
Where:

* N'γ is the cumulative concentration of the radionuclide γ at the outlet of fuel assembly.

<figure><img src="image_3.png" /><figcaption>Fig. 2: Nuclear data</figcaption></figure>

* τa is the mean transit time to perform a cycle.

This cumulative effect has an impact to correlate the gamma activity to the power. More the tagging agent has a long decay period, the response to obtain a power measurement is long.

Indeed a short decay period gamma emitter is better to delete this effect and to immediatly obtain the power measurement. The activating isotope concentration at the measurement point is then calculated by adding an other thermal hydraulic transfer function.

$$N''_{\gamma}=N'_{\gamma}\int_{0}^{\infty}\delta(\tau)\exp(-\lambda\gamma\tau)d\tau \quad (5)$$

Where:

* N''γ is the concentration of the radionuclide γ at the measurement point.

* δ(τ) is the hot pool dilution factor. δ(τ)=C'(τ)/C

Only global thermal hydraulic parameters τa, τb and δ, estimated by data obtained with a Phenix thermal hydraulic model called Colchix are used in this study [6].

$$N''_{\gamma}=N'_{\gamma}\delta \exp(-\lambda\gamma\tau b) \quad (6)$$

Where:

* δ is the global hot pool dilution factor.

* τb is the mean transit time at the measurement point.
In the hot pool, the sodium has a complex behaviour with the mixture of a jet effect, a diffusion effect and a dilution effect. A tridimensional thermal hydraulic simulation project using Trio code is considered in collaboration with the thermal hydraulic department of the CEAIDEN to improve the sodium flow distribution knowledge inside Phenix primary pool [5]. By convolving dilution distributions with a decay probability, a more precise thermal hydraulic transfer function will be determined for the cumulative effect and the hot pool transit.

To simulate the sensor response, MCNP5.4.1 is used with a pulse high tally in photon electron mode. In this simulation, a small coaxial hyper pure germanium sensor of 60 cm3 is considered and will be used for Phenix experimental setup. It has been chosen for pile-up limitation and for its high resolution ability.

### III. RESULTS

Spectra obtained by this methodology show possibility to measure the <sup>24</sup>Na, <sup>22</sup>Na, <sup>23</sup>Ne and <sup>20</sup>F tagging agents in sodium sample (cf. figure 3a). <sup>24</sup>Na and <sup>22</sup>Na are not very convenient for our application because of the cumulative effect due to their high decay period. Short decay period <sup>23</sup>Ne and <sup>20</sup>F tagging agent can give an immediate power measurement. Our study is focused on <sup>20</sup>F as tagging agent because <sup>23</sup>Ne exhibits too low photon energy of 440 keV and the sodium degas behaviour in the cover gas plenum must be known to correlate it to the heat power.

This calculation shows that a short time response power monitoring system using <sup>20</sup>F tagging agent is easily achievable if the sodium sampling volume and the transit time to measurement can be chosen. The transit time shortness (under 10 s) increase 20F signal in front of the 24Na Compton noise. The sampling volume setting permit to obtain the best input count rate (about 1 MSamples/s) on the detector in respect with a compromise between response velocity and high count rate limitation.

In this optimal configuration, a good precision of measurement with a short response time is available. At nominal power, the response is fast but the time response should increased when power decrease because of signal to noise ratio changing. The figure 3b shows the needed acquisition time to exceed the detection limits as a function of the power. Por this calculation, Adonis performances are extracted from experimental resolutions obtained for a 56 % efficiency HPGe. A 10 % efficiency HPGe and a new electronic will be used in the Phenix experimentation allowing better resolutions than previous ones. It's then possible to obtain a better power monitoring than estimated here.

This simulation study shows that the <sup>20</sup>F power measurement is achievable with a short response time on 4 decades of power range. Furthermore the on-line ability of Adonis permits to obtain a 6 times faster system than a conventional signal processing.

### IV. DISCUSSION

The experimental test will be set during the Phenix reactor "end life testing". The Delayed Neutron Detection (DND) room is the best available location on Phenix reactor but it is not optimal for short response time measurement. However, a potential correlation between the 20p activity and the reactor power could be proved. This system has been set for the clad failure detection by delayed neutron emitter measurement. This location is ideal for global power measurement because of short sodium transit time (about 30 s) and homogenized sampling done by 6 sampling points in hot pool.

The sensor is a reverse-electrode high purity germanium diode (10 % of efficiency). It is coupled with a transistor reset preamplifier and an electrical cryostat (Cryo-Cycle5) which is convenient for our deported measurement problematic (cf. figure 4).
Phenix DND room with the detector is modelized by MCNPS code. A lead shield covers the sodium volume to limit gamma noise on neutron chambers. This shielding of 22 cm thick limits the pile-up effect on the sensor but biased the measurement especially at low energy.

The other difficulty is to obtain a good statistic on experimental simulation with a Monte-Carlo code (cf. figure 3d). The ²⁰F signal is then calculated with the knowledge of Adonis experimental resolutions, simulated sensor responses at each gamma energy and mass attenuation coefficients in lead. Sodium thermal hydraulic behaviour is the most influent phenomena on the calculation. Source term calculations are also made for 2 extremes cases where the jet effect in the outlet of the assembly is maximal and where this effect is minimal. Tn the first case, the estimated 20p signal at 380 MW at the 1634 keY peak is 8.8 Samples/s for a total input count rate about 26.5 kSamples/s. In the second case, the ²⁰F signal is 6.5·10⁻² Samples/s for a total input count rate about 17.1 kSamples/s.

This simulation study shows the possibility of ²⁰F measurement but not supress statistical problem risks due to the pileup effect or the too low ²⁰F detection limit. Post-processing softwares are developed at the CEA-LIST to remove statistical problems in gamma spectrometry. So a new nonparametric Bayesian method will be used to extract the ²⁰F signal [7] and in the case of piled spectra, we will used an analytical pileup correction method using the duration variable given by Adonis [8].

<figure><img src="image_4.png" /><figcaption>Fig. 3: Simulation results</figcaption></figure>

V. CONCLUSION
This simulation study done by gamma term source calculations and Monte-Carlo simulations have shown the possibility to measure the 20p activity in the primary sodium for monitoring reactor-core power. These first detection limit estimations have shown that a power measurement method performed with Adonis spectrometry system could be settled as generation IV SPR power monitoring systems with matching by a large range of power in a short response time. An experiment in the french Phenix reactor is currently under preparation to validate the method and determine the experimental accuracy of this power measurement system.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Canberra Cryo-Cycle5 will be used for this experiment</figcaption></figure>

ACKNOWLEDGMENT

The authors would like to thank CEA-DRT and CEA-DAM for financial support.

REFERENCES

[1] E. Barat T Dautremer T. Montagu and J. C. Trama, A Bimodal Kalman Snwother for Nuclear Spectrometry, Nuclear Instruments and Methods in Physics Research A, A567 :350-352, 2006.

[2] B Papin and P. Bernard, Mesures de Puissance par Azote 16, CEA Technical Report, SEN nO 119, 1981.

[3] J. Devaux and L. Costa, Activite de /'Argon 41 dans le Ciel de Pile de Phenix, CEA Technical Report, SEDC n0547, 1974.

[4] J. B. Sicard, C. Carnoy and M. Robin, Donnees Necessaires au Calcul Neutronique Simplijie des 3 Premiers Cycles du Coeur Phenix, CEA Technical Report, LSRCY n02533, 1979.

[5] J. U. Bieder E. Graffard, Qualification of the CfV Code Trio_U for Full Scale Reactor Applications, Nuclear Engineering and Design, 238 :671-679, 2008.

[6] J. Feraud, J. Rion and J. P. Truong, DND Phenix. Experience Colchix 1. Analyse de Resultats, CEA Technical Report, LMTE n05015, 1989.

[7] E. Barat T. Dautremer and T. Montagu, Nonparametric Bayesian Inference in Nuclear Spectrometry, Nuclear Science Symposium Conference Record, NSS07:880-887, 2007.

[8] T. Trigano, Traitement Statistique du Signal Spectromhrique : Etude du Desempilement de Spectre en Energie pour la Spectromhrie Gamma, Ph.D. Thesis, ENST, 2005