C Cifuentes Quintal

M Reymond

F Fiorito

F Martin

M Pontillon

J C Richaud

T Doualle

Y Pontillon
email: yves.pontillon@cea.fr

L Gallais

A laser-based system to heat nuclear fuel pellets at high temperature

Annealing tests are of utmost importance in nuclear fuel research particularly to study thermophysical properties of the material, microstructure evolution or the released gas as a function of temperature. As an alternative to conventional furnace or induction annealing, we report on a laser-heating experiment allowing one to heat a nuclear fuel pellet made of uranium dioxide, UO2, or potentially other nuclear fuel pellet in an isothermal and controlled manner. For that purpose, we propose to use an indirect heating method based on a two compartment tungsten crucible, one containing the sample and the other one acting as a laser susceptor for efficient and homogeneous heating of the assembly. With this concept we demonstrate the heating of UO2 samples up to 1500°C at a maximum heating rate of 30°C/s with the use of two 500 W lasers. The system is however scalable to higher heating rates or higher temperatures by increasing the laser power up to few kW. The experiment has been designed to heat a Pressurized Water Reactor fuel pellet, but the concept could be easily applied to other sample geometries or materials.

I.

Introduction

Experimental data allowing for an accurate qualification of nuclear fuel together with quantification of its behavior under both nominal or hypothetical accidental conditions is of crucial importance in the nuclear industry. For instance, predicting accurately the Fission Gas Release (FGR) from high burn up UO2 and/or MOX (Mixed Oxide) fuels at off-normal conditions is a significant and important challenge. Usual studies in this field require dedicated annealing tests in order to monitor both the absolute level and the time dependence of the released gas. In this context an annealing device, referred as MERARG (French acronym for Means of Study for Annealing and Gaseous Release Analysis) [START_REF] Menegon | Evidence of two gas release kinetics during the oxidation of an irradiated PWR UO2 fuel[END_REF][START_REF] Pontillon | ADAGIO technique: from UO2 fuels to MOX fuels[END_REF][START_REF] Noirot | Fission gas release behaviour of a 103 gwd/t(hm) fuel disc during a 1200 degrees c annealing test[END_REF], has been developed to study the behavior of nuclear fuel under thermal transient representative of Loss of Coolant Accident (LOCA). It allows annealing at high temperature, usually between 1200 °C and 1600 °C but can reach peak of 2800 °C, on irradiated nuclear fuel pellets with slow (between 0.05 and 0.5 °C/s) and moderate (maximum 20-30 °C/s) temperature ramps thanks to an induction furnace. This device is coupled both with dedicated analysis loops -that are designed to identify and quantify the gaseous fission products released during the annealing sequence-, and extensive ex-situ microstructure characterization technics (i.e. SEM, TEM, EPMA, SIMS) of the annealed fuel sample. Recently we have upgraded MERARG with an imaging system for the real time monitoring of the sample surface to provide additional information on the microstructure evolution and possible fragmentation during the annealing tests. This optical system is also coupled with non-contact temperature measurements by thermal radiation analysis to monitor and control the fuel temperature (Vidal et al, 2020).

To study other types of hypothetical accidentals sequences such as Reactivity Initiated Accident (RIA), a laser-based platform is currently being developed at CEA to perform specific annealing tests on nuclear fuels (Vidal et al, 2020 ;[START_REF] Reymond | Thermo-mechanical simulations of laser heating experiments on UO2[END_REF]. In this context it is interesting to build on MERARG's concept by proposing an analogous experiment using lasers to reach similar performances and possibly to surpass current limitations. The perspective of our work is to propose a single laser platform able to investigate nuclear fuel behavior under various conditions, by using the flexibility of the laser heating technique. Indeed, the management of out-of-pile experiments on irradiated fuels in a "hot-laboratory" environment is often challenging and developing a unique and flexible platform is important both from a scientific and from an operating point of view.

The main advantage of the laser-heating technique is the ability to deliver large amounts of energy at high rates, thus allowing one to reach high heating rates. It is also a contactless technique providing and facilitating the implementation of the surrounding instrumentation. Moreover, the beam characteristics (wavelength, beam size, temporal and spatial shape, exposure time, power) are highly configurable and, as a consequence, can be finely adjusted for a specific target process. Because of these advantages, laser techniques have been successfully applied for heating in different studies related to nuclear fuels studies: direct laser surface heating for melting point measurement [START_REF] Manara | New techniques for high-temperature melting measurements in volatile refractory materials via laser surface heating[END_REF], laser heated furnace for Knudsen cell mass spectrometry [START_REF] Colle | Very high temperature laser heated furnace for Knudsen cell mass spectrometry[END_REF], laser heating and melting in aerodynamic levitation [START_REF] Weber | Aerodynamic levitator for in situ x-ray structure measurements on high temperature and molten nuclear fuel materials[END_REF] or laser-induced thermos-desorption [START_REF] Horlait | A new thermo-desorption laser-heating setup for studying noble gas diffusion and release from materials at high temperatures[END_REF] to give some examples.

In this paper, we report on a laser-heating experiment allowing one to heat a PWR (pressurized water reactor) nuclear fuel pellet in an isothermal and controlled manner. Various concepts and configurations have first been taken into account and the retained one, on the basis of thermal and optical simulations, is detailed in the first part of the paper. The approach is quite similar to the one presented in [START_REF] Colle | Very high temperature laser heated furnace for Knudsen cell mass spectrometry[END_REF], but with specificities based on MERARG's concept, and the objective to be used to heat fuel pellets. Moreover, our system is compatible with specific instruments that were specifically designed for MERARG (Vidal et al, 2020). We will present the experimental developments that have been conducted on the CHAUCOLASE (French acronym for Controlled Laser based heating) platform, a high power laser facility to conduct annealing tests at high temperature, previously presented in [START_REF] Minissale | A high power laser facility to conduct annealing tests at high temperature[END_REF]. Finally, as a proof of concept, we conducted a heating experiment with depleted UO2 fuel pellets that we submitted to a typical thermal sequence of interest.

II. Concept and General Design

The objective of the laser heating device is to heat a nuclear ceramic cylinder made of uranium dioxide, UO2, or potentially other nuclear fuels (Mixed OXide (MOX) for instance), of around 8 mm of diameter and 13.5 mm high. The heating should be as homogenous as possible within the sample, minimizing thermal gradients in order to avoid thermal stresses inside that can cause for example fractures in the fuel. In addition, from a general point of view, the temperature ramps applied thanks to MERARG cover a range from 0.05°C/s to 30-40°C/s for target temperatures between 800°C and 1500°C. These parameters make it possible to cover the majority of thermal sequences representative of the incident situations studied with this device. However, most of the studies (i.e. for the study of LOCAs) focus on the couple 20°C/s -1200°C Two alternative configurations have been considered before choosing the retained one (figure 1): a) Illuminating directly the pellet on its whole circumference, UO2 being a strongly absorbing material at the used wavelength ; b) Illuminating directly a crucible containing the pellet. Despite their simplicity, the weaknesses of these direct approaches are limiting their applicability.

Illuminating the pellet on its whole circumference in a homogeneous way is tedious and would require the use of four or more beamlets, more beams meaning a better homogeneity of the induced thermal loading but more experimental complexity. Alternatively, diverging beams covering the pellet diameter could be used, but still with experimental complexity. Moreover, the integrity of the pellet in these thermal sequences is not assured as cracking and fragmentation is expected. As such, illuminating directly the pellet cannot be considered. Illuminating directly a crucible would ensure a more homogeneous heating of the pellet by radiative and conductive heat exchanges from the crucible to the sample. The issue of homogeneity remains however the same as the crucible must be heated in the most homogenous way possible if one wants to heat the sample inside homogeneously as well, leading to the use of four or more beams. Moreover, the crucibles typically used are made either of tungsten, platinum or molybdenum which are metals and are as such have highly reflective surfaces. This would lead to important loss of laser power as it will be showed later, an important amount of it being simply reflected instead of being absorbed.

For all these reasons, the third envisioned configuration consists in c) confining the laser beam between a metallic crucible and a second metallic wall that we will hereinafter call hood (Figure 1.c).

The beam is injected in this system through a small opening cut in this second wall. The beam is thus confined and absorbed through multiple reflections between the internal crucible and the hood, ensuring that almost all of the laser intensity is absorbed by the system, a small fraction being obviously lost by reflection through the opening in the hood. This configuration is interesting because the power absorbed by the hood would then contribute to the heating of the sample by radiative heating of the crucible and as such it limits power loses due to optical reflections. However a part of the power is lost by thermal radiation from the external surfaces of the hood. To ensure homogeneous heating of this system, the laser beam must be roughly the same height as the crucible and in order to minimize the losses through the openings, it must be as thin as possible. Therefore, our laser beam must have the shape of a thin laser line. This configuration is further explored in the simulations in the next section.

Let's note also that an alternative solution would have been a crucible, as in b), with holes for injection of the laser inside the crucible, it was however not retained because of possible uncontrolled heating of some parts of the sample that could lead to vaporization.

III. Simulations

III.a. Thermal simulations

We have conducted series of thermal simulations to ensure the validity of our approach and to have a first evaluation of the laser power needed. To do so, the pellet-crucible system has firstly been modeled in a Finite Element simulation software (COMSOL Multiphysics) in a 2D axisymmetric geometry (see Figure 2). The crucible material is Tungsten, and we have used the thermal properties recommended in [START_REF] Davis | ITER material properties handbook[END_REF] for the simulations. The crucible geometry and dimensions corresponds to the one currently in used on the MERARG facility. The thermal properties of UO2 were taken from [START_REF] Fink | Thermophysical properties of uranium dioxide[END_REF]. We have considered heat conduction inside the crucible and the pellet, with perfect heat contact between the two materials. Radiative heat exchange inside the crucible is considered, as radiative heat losses towards ambient from the external wall of the crucible. Convection is however not taken into account in the simulations because the experiments have been conducted in vacuum. At this point the laser deposited power is considered as a homogeneous incoming heat flux on the external cylindrical surface of the crucible. The optical aspects will be considered in the next section. We have taken into account a ratio of absorbed power to incident power of 0.3, which is the order of magnitude at 1 µm wavelength [START_REF] Minissale | The temperature dependence of optical properties of tungsten in the visible and near-infrared domains: an experimental and theoretical study[END_REF], as such for a considered laser flux of 1000 W, only 300 W of heat flux is applied on the crucible (we will refer to 'laser flux' and 'heat flux" in the following). For a first estimation of the required laser power and thermal gradients in the pellet, we have conducted simulations with the experimental configuration displayed in Figure 2.a corresponding to direct illumination of the crucible. On Figure 3 we report on the pellet core temperature in case of a laser heat flux ranging from 100 to 1000 W, for an exposure time up to 10 minutes. As showed on this figure, with a laser flux of 1000 W, corresponding to a heat flux of 300 W, we reach a temperature plateau close to 1400 °C with approximately a 12°C/s ramping speed. As shown also on Figure 3, there is a temperature gradient in the pellet, which corresponds to +/-50°C from the center temperature.

These simulations showed that it should be possible in this simple configuration to reach the required temperature range of interest with a reasonable laser power considering the state-of-the-art of industrial lasers. This comes at the cost of losing 70% of the incident power, that would represent a safety hazard in addition to not being efficient. To speed-up the temperature increase, a higher laser power would be required, with more lost power to manage. These simulations confirmed the need of a second metallic wall to confine laser power both from a practical and safety point of view. We now consider the complete system, as showed in Figure 2.b. In this 2D axisymmetric simulation, the openings in the hood are not considered. The simulation conditions are the same as previously described, with the exception that the heat source is now located on the external surface of the crucible and internal surface of the hood, as described in Figure 2.b, and that it is fully absorbed in the cavity. As such for a laser flux of 1000 W, a heat flux of 500 W is applied on both each of the two walls. This choice is arbitrary at this point but based on the fact that there are multiple reflection and scattering of the beams inside the cavity. The optical simulations described below will refine this assumption.

The simulation results are presented in Figure 4. More than 1600°C can be reached with 1000 W of total power and 1400°C for 500 W, which is half the power required without the hood. 1400°C can also be reached with a heating rate of 20°C/s from our simulations. This confirms that the approach allows us to reach temperature and ramping speed of interest while keeping the used laser power as low as possible, and ensuring the safety of experimental conditions.

III.b. Optical simulations

Having discussed the configuration and studied the required laser power, we now proceed to define the optical configuration. For that purpose, we have used an optical ray tracing approach, under the COMSOL software, that is coupled to heat transfer simulations, the rays being used to defined the heat sources on the incident surfaces and the amount of transported power. We have considered as the starting point, the characteristics of available laser sources: Gaussian distribution of intensity, with radial symmetry and a beam diameter of 6.5mm (defined at 1/e²). To shape the beam into a line adapted to its insertion in the hood, we have used a combination of a plano-convex cylindrical divergent lens in one plane and one plano-convave cylindrical convergent lens in another plane. The first lens is used to focus the beam in the thin slit aperture of the hood, while the second lens enlarges the beam to cover the height of the crucible (see figure 5). Their focal lengths have been chosen as 200 mm and -50 mm respectively, based on geometrical optics consideration and standard lenses available. As a compromise between heating homogeneity and simplicity we have chosen a hood with two slit openings. The laser beam is injected as described in figure 5 so that it is incident at a glazing angle on the crucible to avoid back reflection through the slits. By considering the reflectance of the crucible and of the hood and its nature (diffuse or specular), we can calculate the resulting intensity distribution in the crucible-hood interstice induced by the numerous reflection and absorption between the two walls. This intensity distribution across the mesh can then be used as a heat source for thermal simulations. Different parametric studies have been conducted on the effect of hood diameter and thickness, position and width of the slits, surface quality (polished with specular reflection or rough finish with diffuse reflection) to quantify the impact of such parameters on the thermal response and the sensitivity associated with each of these parameters. This has led to experimental configuration that is described in the next section.

IV. Experiments

IV.a. Crucible assembly

The hood and crucible parts previously described have been produced in Tungsten (Figure 6). The slits have 3 mm width and 40 mm height. The surface has a rough finish with a surface roughness measured in the range 300-400 nm (root mean square height). Consequently, there is no specular reflection in the visible and near infrared. We have measured a diffuse reflectivity of 64% at 1 µm wavelength, using a home-made system based on a supercontinuum laser source, an integrating sphere and an array spectrometer. This value is in line with reported values of Tungsten in the literature [START_REF] Minissale | The temperature dependence of optical properties of tungsten in the visible and near-infrared domains: an experimental and theoretical study[END_REF]. The high temperature interaction between the tungsten crucible and the UO2 can possibly hinder the quality of the current heat treatments. The non-oxidation of the metal crucible during the experiments is systematically checked thanks to the surface condition of the latter, which retains its original shape and surface aspect. It does not show, moreover, any trace of upper oxide of W of blue or orange color. This point is also confirmed by the feedback from more than 25 years of use of the MERARG furnace in a high activity cell [START_REF] Ravel | Pagas inventories: results obtained using the ADAGIO facility[END_REF].

IV.b. Experimental configuration

Experiments have been conducted on the CHAUCOLASE facility, a modular platform develop and shared between CEA and Institut Fresnel which is dedicated to develop and qualify laser heating techniques to study materials at high temperature [START_REF] Minissale | A high power laser facility to conduct annealing tests at high temperature[END_REF]Vidal et al, 2020 ;Gallais et al, 2021). For the experiments described in this paper we have used a high power CW ytterbium fiber laser (SPI laser Qube 1500), which can deliver 1500 W of maximum power with a monomode laser beam and with a typical rising time of few microseconds. The main beam is splitted into two beamlets with a 50/50 beamsplitter and directed with high reflective mirrors. After passing through the lenses that have been described previously, the beams are sent through laser windows in a vacuum chamber with a base pressure of 2×10 -2 mbar. The crucible and hood assembly is placed at the center of the experimental chamber, mounted on a ceramic sample holder. The schematic of the experiment is described on Figure 7. The chamber is equipped with lateral viewports that have been used for observation or temperature monitoring through different lines of sight that are numbered from 1 to 3 on Figure 7. Line 1 was equipped with a CMOS camera for the adjustment of the laser beam line with respect to the slit. This alignment is done at low power before the heating experiments. Another line on the opposite side was also equipped with a similar camera for alignment. Line 2 was equipped with a monochromatic pyrometer operating at 1.27 μm, this wavelength corresponds to the X-point region of W where emissivity does not vary as a function of temperature [START_REF] Cagran | Spectral emissivities and emissivity xpoints of pure molybdenum and tungsten[END_REF]. It has been used to measure the surface temperature of the hood during the experiments. On line 3 a thermal camera has been used to observe the thermal gradients on the hood surface.

An upper viewport gives access to the crucible cover and the sample through the opening (line 4).

During the experiments this line has been equipped with either a pyrometer pointing on the cover for temperature measurements, a thermal camera to observe the thermal gradients on the surface, or a camera to observe the sample through the opening.

IV.c. Temperature measurements

The evaluation of the sample temperature is a critical point in the experiment. Optical pyrometry could be used to measure the temperature of the sample through the opening but this option was not selected because of the final application on irradiated fuels and experience on the current MERARG system: gas release, fragmentation of the sample or unknown emissivity implies too much uncertainty on the temperature. Alternatively, the crucible was equipped with a thermocouple type C inserted in the internal chamber described in Figure 2. For the hot cell application, the temperature measured by the thermocouple will be used for the laser power regulation thought a feedback loop, as it is the case on the current MERARG system for adjustment of the power of the HF generator [START_REF] Pontillon | ADAGIO technique: from UO2 fuels to MOX fuels[END_REF]. It The experimental results obtained have been compared to simulations performed with the finite element model based on coupled optical/thermal simulations described previously. The model was used to obtain the temperature distribution in the hood/crucible assembly and at the positions of the measurements. This approach is intended to give the correlation factor between the available measurements during an experiment, and the real temperature of the sample that cannot be directly monitored. Figure 10 reports on an example of such a temperature distribution, calculated for experimental conditions, with the location of the 3 measurements (pyrometers and thermocouple) indicated, and the simulated / experimental temperature reported at these 3 locations. The calculated values are consistent with the experiment, with however some deviations. These deviations however lie below the 5% range in the reported example on Figure 10, and in the other investigated case with Silver as fused material. On this basis, we can then relate the temperature distribution in the assembly and sample to the thermocouple measurement through the simulation.

The TC measurement is chosen as the reference since it is used in the feedback control loop of the laser power for reasons exposed previously and it cannot be affected by changes of emissivity or optical attenuation due to window contamination as the pyrometer could be in future hot cell experiments. If we know look at the relation between the TC temperature and the sample temperature, which is the one of interest, the calibration experiments on fuse materials have led to a temperature ratio of 1.1: fuse of silver (melting point of 961°C) is observed for TC temperature of 1052°C and fuse of copper (1085°C) is observed for TC temperature of 1194°C. Obtaining this temperature ratio concludes the thermal qualification phase of the system. One can notice that a more complete approach consists of using a second thermocouple inserted in the core of a pellet instead of a fuse material. Both approaches are used as standard procedures on the MERARG system [Vidal et al, 2020].

V.b. Laser controlled heating of UO2 target From the previously described calibration measurements, it was possible to obtain a correlation coefficient between the sample temperature and the TC temperature. The objective of experiments is then to obtain smooth and well controlled heating ramps, as well as stable temperature plateau. The qualification of the temperature regulation system was done with dedicated experiment with a UO2 pellet in the crucible and with one of the pyrometer pointing at the surface of the UO2 pellet through the opening in the crucible to monitor its temperature. An example of a regulated temperature sequence is given in Figure 11. This particular sequence corresponds for the UO2 sample to a targeted ramp of 5°C/s from ambient to 1300°C, followed by a temperature plateau for few minutes. As shown on this figure the heating rate corresponds to the setting rate and the temperature plateau is stable within +/-1°C with a minimal overshot of less than 10°C, which corresponds to less than 1% of the setting point. At this point, maximum temperature ramps up to 30°C/s have been achieved (Figure 12). Higher heating rates can be theoretically achieved, the limitation at this point being the available laser power on the experimental set-up (1 kW). Finally, these experiments have been conducted under vacuum as the goal was to validate the concept of these experiments. If these experiments were to be conducted on irradiated fuel, a sweeping gas would be used to carry out the released gaseous fission products towards the online measurement loop. The presence of this sweeping gas would induce heat losses through convective heat exchange and should be taken into account in the simulations if one wants to accurately predicts the thermal response of the experiment for a given laser power.

Conclusion

Annealing tests are of utmost importance in nuclear fuel research particularly to study thermophysical properties of the material, micro structure evolution or the released gas as a function of temperature.

As an alternative to conventional furnace or induction annealing, we have introduced and demonstrated in this work a laser-heating device that can drive nuclear fuel pellets at high temperature in well-controlled conditions. The current system can be used to heat nuclear fuel pellets up to 1500°C at a maximum heating rate of 30°C/s with the use of two 500 W lasers. The system is however scalable to higher heating rates or higher temperatures since few kW laser systems are now easily available. The perspective of our work is now to integrate this technique on the MERARG platform in order to be able to investigate nuclear fuel behavior under various conditions, by using the flexibility of the laser heating technique.

Figure 1 :

 1 Figure 1: Top view of two of the three considered configurations. The number of laser beamlets is not restricted to 4. a) Illuminating directly the pellet. b) Illuminating directly a crucible containing the pellet. c) Confining the laser beam between two metallic walls. A part of the laser power is absorbed at each reflection on the metallic surfaces.

Figure 2 :

 2 Figure 2: Schematic and meshing of the crucible assembly and UO2 pellet. a) Configuration with direct heating of the crucible only. b) Configuration with the crucible / hood assembly and internal heating due to laser confinment. The pellet is placed inside by removing the cover part.

Figure 3 :

 3 Figure 3: (a) Temperature evolution at the center of the pellet as a function of time for various laser power ; (b) Temperature distribution in the pellet/crucible assembly after reaching the steady state regime for 1000 W.

Figure 4 :

 4 Figure 4: (a) Temperature evolution at the center of the pellet as a function of time for various laser power ; (b) Temperature distribution in the pellet/crucible/hood assembly after reaching the steady state regime for 500 W of laser power.

Figure 5 :

 5 Figure 5: Ray tracing simulation of the laser heating system. (a) two optical systems based on cylindrical lenses are used to shape the gaussian beam in a thin line at the entrance of the hood/crucible assembly. (b), (c), (d), (e) top view of hood/crucible assembly. After passing through the opening, the rays are absorbed and scattered on the tungsten surfaces.

Figure 6 :

 6 Figure 6: The hood/crucible tungsten assembly. (a) the main crucible is on the left with the crucible cover. On the right is the hood with one slit opening visible. (b) The assembly on its ceramic post.

Figure 7 :

 7 Figure 7: Schematic of the experimental set-up. (a) Top view of the experimental chamber equipped with viewports. (b) sideview of the chamber. The hood/crucible assembly is placed at the center of the chamber. The laser beam path is shown in red. 1, 2, 3 and 4 are different lines of sight for the optical instrumentation, that are refered to in the manuscript. TC corresponds to the thermocouple used for temperature monitoring of the crucible.

Figure 9 :

 9 Figure 9: Results of a calibration experiment conducted with thermal fuses. (a) The temperature measured by the different instruments, at positions given on Figure 8. At time 485 s after the start of the laser heating sequence, melting of the copper fuse is observed with the in situ observation system. (b) in situ observation of melting of the copper fuse. (c) The sample after removal from the crucible: the fused copper is visible at the top of the alumina holder.

Figure 10 :

 10 Figure 10: (a) Simulation of the temperature distribution in the crucible/hood assembly for an input power of 230 W after reaching the stating state regime. The calculated temperatures are reported on the 3 measurement locations in the experiment: crucible cover, external hood, and internal chamber at the location of the thermocouple. (b) Temperature distribution in the core of pellet sample.

Figure 11 :

 11 Figure 11: Laser heating sequence with active regulation. Reported is the temperature measured at the surface of the UO2 sample in the crucible. This measurement is done with a pyrometer through the opening in the crucible.

Figure 12 :

 12 Figure 12: Different obtained heating ramps with described system. The measurements are done with a pyrometer through the opening in the crucible.

Acknowledgments

This work was conducted in the framework of the MATLASE chair, a joint research and teaching program between Ecole Centrale Méditerranée et CEA Cadarache.

The authors wish to thank EDF and Framatome for supporting this work in the frame of Tripartite Institute (CEA/EDF/FRA).

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

is then necessary to have a good knowledge of the relation between this measured temperature and the sample temperature, which is not directly accessible. For that we rely on the numerical simulations and the different temperature measurements available that we summarize on Figure 8. The investigation of the correlation between these different measurements and the sample temperature is carried out in the next section. Uncertainty analysis of the temperature measurements with the used instruments (pyrometers and thermocouple) applied to Tungsten can be found in reference [START_REF] Minissale | A high power laser facility to conduct annealing tests at high temperature[END_REF]. The maximum uncertainty is related to pyrometric measurements and is related on the one hand on the sensor (given as ±2% of the temperature reading by the manufacturer) and on the other hand on the uncertainty on emissivity of Tungsten material used in these experiments. With a conservative value of 10% uncertainty on the emissivity the related uncertainty on the temperature is 10-3T, with T the temperature in Kelvin. For instance, at 2000 K it corresponds to 2%. The total uncertainty in this case can then be estimated to 4%.

V. Results and Discussion

V.a. Temperature calibration

We report firstly on the methodology that has been developed and the calibration experiments that have been conducted in order to link the sample temperature to the 3 external temperature measurements (the 2 pyrometers and the thermocouple described in Figure 8). For calibration purpose we have used the thermal fuse method: a material with a well-known melting point is heated in the crucible with in situ observation so that when fusion occurs the temperature is known. We have worked with Copper, with a melting point of 961°C, and silver, with a melting point of 1085°C.

Filaments of these materials were inserted in a sample mock-up made of alumina, that was observed through the crucible opening during the heating experiments. The laser power was then slowly increased, to obtain heating ramps of typically 1°C/s, up to observation of melting of the fuse material.

An example of such a heating sequence and temperature measurements is described in Figure 9.

Supplementary Material

The details of the COMSOL simulations are provided as a supplementary material document.

Author's contributions


Corentin Reiss
email: corentin.reiss@cea.fr

Antoine Gerschenfeld

Catherine Colin
email: catherine.colin@toulouse-inp.fr

CFD simulations of boiling flows in nuclear reactor conditions

Keywords:

come

Numerical Toolkit

TrioCFD open-source CFD code developed at CEA [START_REF] Angeli | [END_REF].

Euler-Euler approach [START_REF] Ishii | Thermo-fluid dynamics of two-phase flow[END_REF]:

∂(α k ρ k ) ∂t + ∇ • (α k ρ k ⃗ u k ) = Γ k ∂(α k ρ k ⃗ u k ) ∂t + ∇ • (α k ρ k ⃗ u k ⊗ ⃗ u k ) = -α k ∇P + ∇ • [α k µ k ∇ ⃗ u k -α k ρ k u ′ i u ′ j ] + ⃗ F ki + α k ρ k ⃗ g ∂(α k ρ k e k ) ∂t + ∇ • (α k ρ k e k ⃗ u k ) = -P (∂ t α k + ∇ • (α k ⃗ u k )) +∇ • [α k λ k ∇T k -α k ρ k u ′ i e ′ k ] + q ki + q kw k -ω turbulence model [6]
Tomiyama drag force [START_REF] Tomiyama | [END_REF], Burns turbulent dispersion [8], Sugrue lift force [9], Lubchenko wall lubrication [10].

Zeitoun condensation [START_REF] Zeitoun | Transactions of the ASME[END_REF], Kurul-Podowski boiling [START_REF] Kurul | International Heat Transfer Conference[END_REF].

Air-water adiabatic validation

Upwards, downwards and micro-gravity flow experiments in pipes at atmospheric pressure [START_REF][END_REF]14]. Steady-state radially-dependent experimental diameter is enforced in the simulations.

F. Colin microgravity

M 1, J l = 0.27, J g = 0.03 M 3, J l = 0.77, J g = 0.044 M 4, J l = 1.0, J g = 0.028

Debora: a reactor-similarity experiment

The Debora loop is a vertical heated Freon-12 pipe that fills similarity criteria with nuclear reactor conditions [START_REF] Garnier | Multiphase Science and Technology[END_REF]. Density ratio, Weber number and Boiling number are respected.

Liquid temperatures, void fractions, gas velocities and Sauter mean diameters are measured at different altitudes and radial positions.

Conclusions and perspectives

• Interfacial forces for isolated bubbles must be modified to simulate high void fraction, high pressure reactor flows

• Next step: build a unique set of closures for all runs

D 2 ,

 2 J l = .491 (ms -1 ) J g = 0.0275 J g = 0.0556 J g = 0.129 J g = 0.190 J l = .986 (ms -1 ) J g = 0.0473 J g = 0.113 J g = 0.242 J g = 0.321 J l = 0.5, J g = 0.033 D 2a, J l = 0.5, J g = 0.018 D 4, J l = 1.0, J g = 0.0238 J l = 5. (ms -1 ) J l = .986 (ms -1 )J g = 0.0473 J g = 0.113 J g = 0.242 J g = 0.321

1 .

 1 Build an Interfacial Area Equation or population balance model to determine bubble diameter 2. Validate model on adiabatic flows using force closure terms 3. Add condensation and boiling terms to simulate complete system

	Our approach:
	1. Select heat transfer and force terms
	2. Enforce 3D experimental diameter measurements in the flow
	3. Validate models on reactor similarity experiment

4. Future work: model bubble diameter in reactor conditions


M Nesser

O Maloberti

C Pineau

J Dupuy

J-P Birat

J Fortin

GOES's Domain Structure in the Vicinity and On the Lines Post-Laser Treatment

Keywords: Domain structure, Electrical steels, Pulsed laser, Surface treatment, Power loss, MFM, MOIF

Pulsed laser processing for domain's refinement is a recent technology implemented on an industrial scale. The present study focuses on the impact of different laser pulse durations on the magnetic properties such as total losses and domain structure of 0.28 mm thick grainoriented electrical steel (GOES). Three pulse durations are considered Long Pulse (LP), Short-Pulse (SP) and Ultra-Short Pulse (USP). The latter has not been yet applied for domain refinement treatments, hence the interest of this research. Iron loss measurements made with the single sheet tester (SST) demonstrated a maximum loss reduction of 18% at induction of 0.5T and a frequency of 50Hz following USP laser treatment. At a high induction of 1.7T and a frequency of 50Hz, both LP and USP pulse lengths achieved a reduction in total losses of 16%. Moreover, the behaviour of the magnetic structure under laser treatment was detailed. The magnetic images were visualized by magneto-optical indicator film (MOIF). A reduction from 308 µm to 217 µm in the average domain size was observed post laser treatment with USP duration. Furthermore, the domain structure in the vicinity and on the laser line was visualized on a nanoscale using a magnetic force microscope (MFM). All these results confirmed the dependence of the laser-matter interaction on the laser pulse duration.

Introduction

Magnetic domain refinement is a technique widely used by manufacturers of grain-oriented silicon steels to reduce iron losses [START_REF]Laser processing for reducing core loss of grain oriented silicon steel[END_REF]. The impact of domain refinement using advanced pulsed lasers on the power loss of grain-oriented FeSi steels has been investigated (2) (3), with apparently some specificities depending on the pulse duration. Puchy et al. studied surface treatment using a pulsed fibre laser with a wavelength of 1064 nm and pulse duration between 50 µs and 500 µs on Fe-3.2Si electrical GOES(M165-35S). They proved a decrease in magnetic domain width for high laser pulses number with an optimum of 10 pulses for single pulse energy of 0.6 mJ [START_REF] Puchy | The Influence of Fiber Laser Pulse Processing on Coercivity and Nanohardness of Fe-3.2Si Grain-Oriented Electrical Steel in relation with its Surface Changes and Magnetic Domains Modifications[END_REF]. The physical origins of the changes in domain's structure due to laser treatment are not fully detailed yet. Thus, these origins may help to better explain the impact of laser processing on the macro-scale magnetic properties. Surface treatment with an ultra-short pulse laser (USP) remains unfamiliar for the refining of electrical steels, although it presents a great potential, mainly as a reproducible and high temperature resistant process. In this work, we studied the behaviour of iron loss and domain structure of grain oriented electrical steel (GOES) submitted to laser treatment with different pulse widths, with emphasis on the effect of ultra-short pulses.

We distinguished three types of laser effects depending on the pulse duration (thermal effect, groove effect or both). The laser treatment with LP duration had mainly a thermal effect while the short pulse duration presented a thermal effect that led to slight grooves on the material's surface. Lastly, the ultra-short pulse duration showed clean grooves of some micrometres in depth [START_REF] Nesser | Impact of Ultra-Short Pulsed Laser (USPL) Ablation Process on Separated Loss Coefficients of Grain Oriented Electrical Steels[END_REF]. Regarding the experimental measurements, power losses were identified with single sheet tester equipment (SST -BROCKHAUS Measurements) ensuring an accuracy of 0.5% at high induction and 3% at low induction. The magnetic domain width was visualized with a magneto-optical indicator film (MOIF). Finally, a complete understanding of the magnetic domain structure on laser spot and in the vicinity of the laser line was detailed using a Magnetic Force Microscope (MFM).

Experimental Procedures

Material and laser treatment

The considered material is a commercial grain-oriented Fe-(3wt%)Si [R120-27] with a thickness of 0.28 mm. A pulsed Ytterbium fiber laser with a wavelength of 1.064 μm and pulse duration between 4 ns and 200 ns was used to perform treatments with short and long pulse durations. Whereas, an Amplitude laser performing a wavelength of 1.030 μm and a pulse width between a few hundred of fs and 10 ps (see Table 1) was adapted for ultra-short pulse duration treatments. Sheet dimensions were chosen according to the dedicated experimental equipment: 150 mm squared sheets were selected for SST measurements, 60 mm squared sheets for MOIF and 10 mm squared sheets for MFM.

Laser Pulse Duration

Laser Fluence ((J The optical image and profile analysis corresponding to laser effect on the sample surface were presented in a previous article (3): the laser effect was mainly a thermal heating of the surface in the case of LP, without removal of the coating nor significant modification of the surface. For SP laser, the laser line mark sinks a few micrometers into the surface of the sample with formation of relief edges, the coating could be locally damaged by this process. In the case of USP, this pulse duration permits engraving by sublimation with a laser line mark, the coating and a few µm of metal are thus removed. Therefore, no sheet bending was detected with the optimized laser configurations listed in Table 1.

Experimental measurements

We visualized the magnetic domain structure of the samples with two different yet complementary magnetic imaging techniques: the magneto-optical indicator film MOIF presented is formed with a thin film of soft magnetic material possessing strong magneto-optical properties (Garnet Film with strong Verdet constant). The imaging concept is as follows: a light beam passes through a polarized layer, and then enters the indicator film placed under the sample. Its polarization will change due to the magneto-optical Faraday Effect between the film's magnetic domains and the magnetic domains of the sample. Thus, the reflected beam's polarization follows the sample's magnetic structure. The magneto-optical image is then recorded by the high-resolution digital camera. The speed and simplicity of visualizing magnetic image are the main advantages of this technique (magnetic image in 1s). However, its resolution is limited to 25 µm. The second imaging technique applied is magnetic force microscopy (MFM). It is an imaging mode of atomic force microscopy (AFM) dedicated to visualize the surface distribution of magnetic domains and walls of the sample. This mode requires a specific probe with a thin layer of magnetic material on the tip. The magnetic images presented in this work were performed with a hard magnetic coating with low magnetic moment on the tip. This imaging mode is based on a two-pass data collection during a scan. In the first pass, the tip scans the surface topography. Then, in the second pass, the tipsample distance is incremented and held constant based on the topographic line data obtained in the first pass. Thus, the influence of Van Der Waals forces becomes negligible, as the tip is mainly affected by the magnetic force. Thus, the resulting image holds predominantly the magnetic information of the specimen surface. The MOIF imaging tool captures an 18.5x12.4 mm image and the samples involved were squares of 60 mm side while smaller samples (10 mm square) were used for MFM where the image size is 120×120 µm 2 . For MFM imaging, chemical and mechanical polishing were performed prior to laser processing on the specimen since high quality MFM imaging requires a smooth surface finish. The polishing procedure started by etching the specimen in a hydrogen chloride solution to remove the insulating coating. Then, the sample was ground with silicon carbide papers of different (successively decreasing) grain sizes. The final polishing step was realized with a colloidal suspension of amorphous silica in order to achieve minimal surface roughness. Regarding the macroscopic measurements, we measured the total power loss of each sample before and after laser treatment with the SST to ensure an accurate comparison.

Experimental results

Power losses variation

Various laser configurations were tested to finally select the optimal ones resulting in maximum loss reduction. This optimization was performed for each pulse duration (LP, SP and USP) (3) (5). Laser treatments with LP, SP or USP duration were done on three samples. Magnetic measurement was performed for each sample before and after laser treatment by the SST equipment at medium (0.5T and 1T) and high (1.5T and 1.7T) inductions for a frequency of 50 Hz. In Figure 1, we presented the variation of the total power loss for each sample after treatment measured for the 4 induction levels: 0.5T, 1T, 1.5T and 1.7T at a frequency of 50Hz. The sample exposed to laser treatment at USP duration showed a maximum loss reduction of 18% at an induction level of 0.5T. However, for the induction level of 1.7T, both LP and USP pulse lengths provided 16% reduction in total loss.

Figure 1 The Percentage of Total Power Losses Variation under Laser Treatment with Different Pulse Durations: Long Pulse (LP), Short Pulse (SP), Ultra-Short Pulse (USP) (sample thickness 0.28mm) (sample thickness 0.28mm) (Measurement accuracy ± 1%).

Domains Structures at the Vicinity of Laser Lines (MOIF images)

In parallel, the impact of the laser treatment on the structure of the magnetic domains of the sheet has been investigated. We visualized the change of the magnetic domain structure with MOIF resulting from the laser treatment. Magnetic images were taken in the same area prior and post laser treatment. Figure 2 illustrates the magnetic domains prior to and post treatment with the LP duration laser. The number of magnetic domains increased across the majority of the sample area.

Domains Structures on the Laser Lines (MFM images)

An observation of the magnetic domain structure on the laser lines at a minor scale was performed using MFM (resolution down to a few nanometers). In these images (Figure 5-Figure 7), the dark and light contrasts are representative of the repulsive and attractive interactions between the magnetic layer on the probe and the magnetic domains on the sample surface. These visualizations were performed on 0.23 mm thick Fe-(3wt%)Si, a material of the same grade with lower thickness investigated in our previous publication. This thickness was covered in a previously published paper in which we demonstrated a similar impact of the three laser configurations on the iron loss reduction, even more significant (3) (5). Since these MFM visualizations reveal an interesting magnetic domain behavior according to each pulse duration. We were persuaded of the value to illustrate these results. In Figure 5, laser treatment with LP duration performed a multiplication of relatively small spike-like domains in the vicinity of laser line. According to Néel (6), spike-shaped domains are attached to inclusions and grain boundaries in magnetic materials. These domains tend to facilitate the reversal magnetization mechanisms near the coercive point and the remanence (7) (8). Spike-like domains are relatively thin compared to the main 180° domains observed in MOIF images. The magnetic structure involving these spikelike domains was highly disturbed at a distance from the laser line which refers to the heat affected zone. This zone exhibits significant thermal stress due to the rapid heating and cooling during the laser processing. This probably leads to a residual axial or out-of-plane 1D tensile stress and hence compression in the sample thickness. Lancet closure domains are noticeably clear on the laser path. Laser treatment with SP duration resulted in a similar structure further to the laser path. Relatively small spike-like domains are present near the laser point (Figure 6). This multiplicity of welloriented closure domains (minimizing magnetic poles and demagnetizing field) improves the magnetization reversal mechanisms under quasi-static working conditions. On the other hand, the magnetic structure involving these spike-like domains remains strongly disturbed even at a certain distance from the laser path (corresponding to the thermally affected area). This area may act as a transition zone between the laser lines with refined closure domains' structure and the nominal 180° main magnetic domains of classical GOES. However, in the case of laser treatment with USP duration, the spike-like domains near the laser line are 180° oriented domains with an average width of 20 µm which is the largest among the other treatments (Figure 7). Although this result is not in favor of the magnetization reversal mechanisms, the laser treatment with USP duration has contributed to an advantageous refinement of the global domain structure. Both effects are thus compromised, resulting finally in a reduction of the total losses. When compared to the impacts of LP and SP duration laser treatments, the transient magnetic structure involving the spikelike domains is barely disturbed near the laser path. This could be attributed to laser-matter interaction under the USP laser, which has practically no heat-affected areas. Meanwhile, on the laser path, the plasma formed during the ablation process at extremely high temperature T e for electrons [START_REF] Leitza | Metal Ablation with Short and Ultrashort Laser Pulses[END_REF], could generate a surface shock wave at extremely high peak pressure P r in the axial direction (i.e., perpendicular to the plane of the sheet). The resulting residual stress obtained post treatment contributed to the appearance of domains in different shapes and orientation inside the grooves. Yet, we were not able to capture an image on the laser path as the groove was quit deep to be reached by the tip (groove depth of a few µm). An alternative solution remains to be found to overcome this difficulty and complete the perspective analysis.

Conclusions

Each type of laser treatment demonstrated different impact on the power losses and the domain structure. The comparison was noticeable both close to and on the laser path: The long-pulse (LP) and short-pulse (SP) lasers generated thin spike-like domains close to laser path and closure domains (lancet-like domains and 90° plane closure domains) slightly further from these paths. However, the laser with ultra-short pulse (USP) duration generated wider spike-like domains close to the laser path while efficiently minimizing main 180° domains size. It resulted also in less disruption and disorientation in the transition region of the magnetic structure. The distinct impact of each treatment refers to the dissimilar laser-material interactions that took place depending on certain laser parameters, notably the pulse duration. Laser treatment with USP duration laser was proved to be advantageous in reducing the total loss of the 0.28 mm thick FeSi sheets and ensuring a maximum domain refinement.

Figure 2

 2 Figure 2 MOIF images of GO Sample (60×60mm 2 ) Before and After Long Pulse (LP) Laser Treatment (image size 12.4×18.5mm 2 ) (sample thickness 0.28mm).

Figure 3

 3 Figure 3 MOIF images of GO SamplesBefore and After Short Pulse (SP) Laser Treatment (sample thickness 0.28mm).

Figure 4

 4 Figure 4 MOIF images of GO Samples (60×60mm 2 ) Before and After Ultra-Short Pulse (USP) Laser Treatment (sample thickness 0.28mm).

Figure 5

 5 Figure 5 Magnetic Image of GO Sample under a Long Pulse (LP) Laser Treatment Collected with MFM Showing the Magnetic Domain Structure on the Laser Line (sample thickness 0.23mm).

Figure 6

 6 Figure 6 Magnetic Image of GO Sample under a Short Pulse (SP) Laser Treatment Collected with MFM Showing the Magnetic Domain Structure on the Laser Line (sample thickness 0.23mm).

Figure 7

 7 Figure 7 Magnetic Image of GO Sample under a Ultra-Short Pulse (USP) Laser Treatment Collected with MFM Showing the Magnetic Domain Structure on the Laser Line (sample thickness 0.23mm).

Table 2 The

 2

	The

Average Width of the Magnetic Domain Before and After the Laser Treatment with Different Pulse Durations.

Acknowledgements

This research has received funding from the European Research Council under the H2020-IND-CE-2016-17/H2020-FOF-2017 Program (Grant No. 766437).


Razakatiana Martial
email: rzkmartial@gmail.com

Limad-Edmi

Christophe Kolski
email: christophe.kolski@uphf.fr

Thomas Mahatody
email: tsmahatody@gmail.com

René Mandiau
email: rene.mandiau@uphf.fr

Human-agent Interaction based on Game Theory: Case of a road traffic supervision task

Keywords: intelligent agent, multiagent system, game theory, road traffic supervision, simulation

This work contributes to the field of human-system interaction modeling through an artificial intelligence approach. It focuses on the cooperative realization of a complex task. For this purpose, we propose a human-agent interaction model based on game theory to describe the decision making between the human operator and the assistant agent. The proposed model is based on searching Nash equilibria for a repeated two-player game in which each player has a choice between two actions. In particular, the assistant agent knows how to calculate the equilibrium that depends on information coming from the context (human operator and work environment). This approach allows us to consider a context aware human-machine system. Then, the assistant agent knows how to optimize its intervention with regard to the human operator assisted by this agent during a complex task. For the validation of our model, we highlight the efficiency of the assistant agent using this principle by considering a road traffic simulator using Netlogo. An analysis of the simulation results is provided to illustrate the effectiveness of our approach.

I. INTRODUCTION

Human-computer interaction (HCI) is becoming increasingly important in the design and implementation of new industrial interactive devices and assistance systems [START_REF] Jacko | Human computer interaction handbook: Fundamentals, evolving technologies, and emerging applications[END_REF]. Since the emergence of Artificial Intelligence (AI) at the end of the seventies in the world of interactive systems (cf. for example [START_REF] Edmonds | Adaptative Man-Computer Interfaces[END_REF]), the need for efficiency and user-friendliness with interactive systems has been increasing. This crossfertilization between HCI and AI leads to co-called intelligent, personalized or context-aware interactive systems. The new user interfaces constitute devices, aiming at the user being able to interact with the system with ease, assisted by an agent [START_REF] Mandiau | A new approach for the cooperation between human(s) and assistance system(s): a system based on intentional states[END_REF], which is intelligent in the sense of AI. Thus, beyond the visual aspects, human-user interaction models are implemented. This implies an important dimension of research on human-machine interaction: the underlying software mechanisms and the principle of adaptation to ensure intelligent interaction. Several software mechanisms based on AI models have been used through more and more case studies in intelligent interactions [START_REF] Kolski | Cross-fertilisation between human-computer interaction and artificial intelligence[END_REF]: inference engine, fuzzy systems, Markov models, and so on, whether in a centralized or distributed framework (in particular, multi-agent systems (MAS) approaches). Intelligent agents already have their place in several application domains: e-commerce, Intelligent Transport Systems (ITS), simulation, and so on [START_REF] Grislin-Le Strugeon | Agents intelligents en interaction homme-machine dans les systèmes d'information[END_REF]. If we focus on road traffic simulation, several studies are based on MAS approaches. For instance, in [START_REF] Kponyo | Real time statut collection and dynamic vehicular traffic control using ant colony optimization[END_REF] the authors proposed a multi-agent approach using the ant colony principle to manage the traffic flow. In addition, several approaches use intelligent agents on traffic signal controls and commands at each intersection as in [START_REF] Roozemon | Agent controlled traffic lights[END_REF], [START_REF] Liu | Intelligent Traffic Light Control Using Distributed Multi-agent Q Learning[END_REF] and [START_REF] Hirankitti | A Multi-Agent Approach for Intelligent Traffic-Light Control[END_REF]. However, none of such approaches takes explicitly into account information from human operator in charge of traffic control in a specific sector; that can lead to poorly coordinated activities between human beings and intelligent agents. In this research, we are interested in distributed interaction models for the implementation of human-agent interaction systems. In particular, we focus on the intelligent agent behavior towards a human being, in the context of a complex task with critical situation. After this introduction, section II provides a state of art on intelligent agents in road traffic simulation. Section III proposes the principle of interaction between humans and intelligent agents, using game theory. Section IV presents the framework of the simulation involving a human being and an intelligent agent in traffic supervision. The results obtained are described in Section V. Finally, the last section provides a conclusion and research perspectives.

II. STATE OF ART ON INTELLIGENT AGENT IN ROAD TRAFFIC SIMULATION

Several definitions about agents are available in the literature [10] [11] [12] [START_REF] Alvarodo | Construction of a basic intelligent agent[END_REF]. An agent is generally defined as an entity capable of reacting in a given environment using its sensors [START_REF] Oskpouei | Intelligent agent: a comprehensive survey[END_REF]. By extension, an intelligent agent is a particular agent that can act without human intervention [START_REF] Müller | Architecture and application of intelligent agent: a survey[END_REF]. This work focuses on their use in the case of road traffic simulation.

Congestion is a difficult problem to solve in the case of urban road traffic supervision. Several studies have focused on the use of intelligent agents to solve traffic problems. Traffic light management was the main topic on the use of intelligent agents [START_REF] Roozemon | Agent controlled traffic lights[END_REF], while using a technique to predict future traffic conditions and vehicle movements [START_REF] Liu | Intelligent Traffic Light Control Using Distributed Multi-agent Q Learning[END_REF] [START_REF] Zhang | Intelligent traffic signal control using reinforcement leaning with partial detection[END_REF]. To reduce the extent of congestion at road intersections, Yeo et al. [START_REF] Yeo | Impact of vehicle detection accuracy to the performance of intelligent traffic control[END_REF] propose an improvement in traffic by trying to capture traffic information around the intersection. In addition, a multi-agent approach has been proposed to solve these traffic problems, as in [START_REF] Hirankitti | A Multi-Agent Approach for Intelligent Traffic-Light Control[END_REF], [START_REF] Doniec | A behavioral multi-agent model for road traffic simulation[END_REF] and [START_REF] Champion | Simulation comportementale du trafic routier en intersection : Un mécanisme de résolution de conflit[END_REF]. In [START_REF] Camurri | Environments for Multi-Agent Systems III[END_REF], the authors propose Co-Fields, a coordination model for multiagent systems; it is used to guide the cars toward their destinations avoiding the most crowded areas.

Other solutions based on intelligent agents can be mentioned, for example: the use of Internet of Things (IoTs) for Intelligent Transport Systems (ITS) [START_REF] Al-Sakran | Intelligent Traffic Information System Based on Integration of Internet of Things and Agent Technology[END_REF], the use of virtual agents able to interact with tangible objects in traffic simulation on RFID (Radio Frequency IDentification) tabletops [START_REF] Lebrun | A model for managing interactions between tangible and virtual agents on an RFID interactive tabletop: Case study in traffic simulation[END_REF]. In [START_REF] Zhang | Intelligent traffic signal control using reinforcement leaning with partial detection[END_REF], intelligent agents, each dedicated to traffic lights, have a reinforcement learning mechanism. In addition, a solution to the problem of intersection management is proposed by [START_REF] Doniec | A behavioral multi-agent model for road traffic simulation[END_REF] and [START_REF] Mandiau | Behaviour based on decision matrices for a coordination between agents in a urban traffic simulation[END_REF]; these authors use a payoff matrix that allows each vehicle to decide whether to stop or continue (go, stop). In order to improve the road traffic situation, Wang et al. propose a virtual vehicle coordination approach based on the theory of group consensus to sense environment information efficiently [START_REF] Wang | Virtual Vehicle Coordination for Vehicles as Ambient Sensing Platforms[END_REF]. In [START_REF] Perronnet | Deadlock Prevention of Self-Driving Vehicles in a Network of Intersections[END_REF], a model of a network of intersections is proposed in order to obtain deadlock-free traffic with a specified route. Finally, a recent study reviews the state-of-the-art around the application of bioinspired methods in the field of ITS [START_REF] Del Ser | Bioinspired Computational Intelligence and Transportation Systems: A Long Road Ahead[END_REF]. However, none of the above-mentioned approaches explicitly takes into account the human operator to accomplish the traffic road supervision. On this subject, a human operator can be characterized by several aspects or attributes depending on the context modeling [START_REF] Dey | Understanding and using context[END_REF]. For example, in the user profile, one can consider the level of knowledge in relation to the functioning of the system with which the user interacts [START_REF] Hall-Ellis | The Dreyfus Model of Skill Acquisition: A Career Development Framework for Succession Planning and Management in Academic Libraries[END_REF]. The level of instantaneous workload can also be taken into account, for example according to five levels as in [START_REF] Kirwan | Human factor in ATM system design life cycle[END_REF]. It is also possible to take into account user preferences, goal(s), level of expertise, etc. The following proposal aims to take into account explicitly the human operator's actions in the context of human-agent interaction.

III. PROPOSAL OF A MODEL BASED ON GAME THEORY

In this section, a multiagent interaction model, in which several human beings and software agents may be located, is proposed. However, in this paper, we focus the study on a system composed of one human being and one software agent. After a brief introduction on game theory, a formalization of the system is presented.

A. Definition of a two-player game

A two-player game is defined as a situation in which two participants can each make their own decision; one's payoff depends not only on his or her action; it also depends on the other's action. A game is characterized by the following elements:

1) The players: These are the participants.

2) Actions for each player: These are the choices available for each player at each move of the game.

3) The rules of the game: they determine how the game is played and the rules to be respected: each player may play simultaneously or successively.

4) The type of game: cooperative or non-cooperative. It is said to be cooperative in the case where participants can communicate with each other in order to be able to decide together on the strategies to adopt in order to win; it is non-cooperative in the opposite case.

B. Interaction model based on game theory

Game-based coordination allows each participant to choose the appropriate actions in response to the actions of other players (in our case, only one other player). In this type of game, we assume that the agent is rational. The equilibrium of the game is a set of optimal strategies for each player. The search for this equilibrium thus allows each agent to decide on the optimal action to perform using the game matrix. The most commonly used is Nash equilibria [START_REF] Szilagyi | Investigation of N-Person Games by Agent-Based Modeling[END_REF], [START_REF] Nash | Equilibrium points in n-person games[END_REF]. In this case, Nash equilibria refers to the strategy in which neither player has an interest in unilaterally changing his or her strategy.

C. Presentation of a game

A game can be represented as a payoff matrix whose elements are the players' payoffs (Table 1). In Table 1, the participants of the game are called Player 1 and Player 2. Then, act11 and act12 are the possible actions for Player 1; act21 and act22 are the possible actions for Player 2 [START_REF] Mandiau | Behaviour based on decision matrices for a coordination between agents in a urban traffic simulation[END_REF] [START_REF] Szilagyi | Investigation of N-Person Games by Agent-Based Modeling[END_REF]. Thus, the payoffs (defined by utilities) of each player are expressed as follows: i  {1,2}:

 Ui(act11, act21) refers to the payoff of player i when Player 1 plays act11 and the other player plays act21

 Ui(act11, act22) refers to the payoff of player i when Player 1 plays act11 and the other player plays act22

 Ui(act12, act21) refers to the payoff of player i when Player 1 plays act12 and the other player plays act21

 Ui(act12, act22) refers to the payoff of player i when Player 1 plays act12 and the other player plays act22. Given a system modeled by a game, the participants should find the best possible result by trying to maximize theirs payoffs. One method for optimizing the solution of a game is to look for Nash equilibria [START_REF] Nash | Equilibrium points in n-person games[END_REF], for the benefits of all participants. To determine an equilibrium, we choose the algorithm described in [START_REF] Hamila | Strategic dominance and dynamic programming for multiagent plannning, application to the multi-robot box-pushing problem[END_REF] [31] (its explanation will not be detailed here).

IV. TWO-PLAYER GAME FORMALIZATION

In this section, we propose a model of intelligent interaction between an agent and a human user. The proposed interaction model is based on the principle of game theory in the case of multi-agent resolution of a given problem. The players are: a human being and an intelligent agent assisting him or her in the completion of the task. For both players, several possible actions can be considered as part of the interaction. However, to simplify the game, we will summarize it in only two actions: the cooperation that we later note by (C) and the noncooperation noted by (D). Our system will therefore be modeled by a game with two players and two possible actions for each player [START_REF] Shoham | Multiagent Systems: Algorithmic, Game Theoretic and Logicial Foundations[END_REF].

a) Description of the players' actions

For the human being, (C) means a request for help or an expectation of advice or relevant information that may influence his or her decision. (D) means that he or she is autonomous: in this case, the human being simply acts without asking for the help of the assistant (software agent).

For the software agent: (C) means that it acts directly or makes a proposal to the human being about what he or she can do. (D) means that the agent does nothing (it does not respond) by leaving the human being to fend for himself or herself, without assistance (in consequence the human being can learn or continue to learn by doing, which is similar to the concept of learning by doing [START_REF] Dufour | Learning by Doing: A Handbook for Professional Learning Communities at Work[END_REF]).

b) Construction of the payoff matrix in two-action game

For the calculation of the matrix, we propose the following formulas, in which:

 wl refers to the user's workload level (Five levels, according with [START_REF] Kirwan | Human factor in ATM system design life cycle[END_REF]: No activity (level 1), Relaxed (level 2), Comfortable (level 3), High (level 4), Excessive (level 5));

 crt refers to the criticality level of the situation (Five levels, according with [START_REF] Purucker | Comparing the Perception of Critical Longitudinal Distances between Dynamic Driving Simulation, Test Track and Vehicle in the Loop[END_REF]: Insensible (level 1), Harmless (level 2), Unpleasant (level 3), Dangerous (level 4), Uncontrollable (level 5));

 usl refers to the user's experience level (Five levels, according with [START_REF] Hall-Ellis | The Dreyfus Model of Skill Acquisition: A Career Development Framework for Succession Planning and Management in Academic Libraries[END_REF]: Novice (level 1), Advanced Beginner (level 2), Competent (level 3), Proficient (level 4), Expert (level 5)).

In our two-game based model, we have chosen the human payoff values according to the following adaptation principles:  If the user does not have enough experience on the task (low experience level: less than level 3), it is preferable for the software agent to act, especially if the workload level and the criticality level are high.

 If the user has a high level of experience in the field: (values between 3 and 5) in which he or she is involved, he or she does not need assistance, especially if his or her workload level and the criticality level are low.

 The human being's payoff that requires cooperation is proportional to the level of his or her workload and to the criticality level.

 If the user is autonomous (work without assistance by the agent), he or she reduces his or her payoff according to the criticality level of the situation, especially if the user does not have enough experience, he or she takes risks not to ask the agent for help (i.e. for assistance).

For the human being, we therefore propose the human utility function noted UH(xh,xa), with xa the response of the software agent to the human user's action xh.

 UH (C, C) = wl + 2 × crt -2 × usl  UH ( D, C) = usl -(wl + crt)  UH ( C, D) = usl -(1 + crt)  UH ( D, D) = usl -crt
For the software agent, the utility function is noted UA(xh,xa), with xh the user's action and xa the software agent's response:

1) If the user requests help, the assistant's payoff, if any, is proportional to the workload and criticality level.

2) If the user has a high level of experience, it can be considered that he or she does not need assistance, especially if the workload and criticality levels are low. This allows the assistant not to waste time (and to let the human learn by doing, in the sense of [START_REF] Dufour | Learning by Doing: A Handbook for Professional Learning Communities at Work[END_REF]).

3) If the human being requests cooperation and the assistant does not respond, the assistant may consider that the human being does not need help, except in the case of high workload and criticality levels.

4) If the user is autonomous, he/she reduces his or her payoff according to the criticality level of the situation,

UA(C, C) = wl + crtusl UA(D, C) = uslwl UA(C, D) =wl UA (D, D) = uslcrt

Thus, the cooperative game involving the human operator and the assistant agent is modeled by a repeated game of N moves, where N is the number of iterations considered in the case study. The average payoff of human operator depends on the decision history of both players:

GH = 1 𝑁 ∑ 𝑈 𝐻 (𝑥 𝑖 , 𝑥 𝑖 ̅̅̅) 𝑁 𝑖=1
where: 𝑥 𝑖 the action chosen in the i-th move by the human being and 𝑥 𝑖 ̅̅̅ denote the choice of assistant agent.

For the assistant agent, the average payoff is given by the following formula: GA= where: 𝑥 𝑖 designates the action chosen in the i -th round by the assistant and 𝑥 𝑖 ̅̅̅ for the human operator. UH and UA are the two utility functions proposed above.

In the following section, we consider a system composed of a software agent and a human operator in the context of traffic supervision simulation.

V. CASE STUDY USING NETLOGO

A. Presentation of Netlogo platform

Netlogo is a multi-agent programmable modeling environment. The choice of this platform in our work is justified given its simplicity in terms of agent creation and implementation. In addition, it supports multi-agent collaborative interaction via its client-server architecture across the network. The simulation is based on the work of Wilensky and Stroup [START_REF] Wilensky | NetLogo HubNet Gridlock AlternateHubNet[END_REF] according to the concept of participatory simulation. Human beings take on the role of clients that can connect via a hubnet server. Software agents can take the initiative to act at a traffic junction or send messages to human operators.

B. Description of the traffic simulator a) The server

The main simulator provides an overview and control of the road traffic. According to the simulator user interface (server), it is possible to create software agents for road traffic management. To do this, we use the create-new-assistant button: a wizard is created randomly at any intersection position. To be able to choose the intersection for the new assistant, we can use the "choose-inter-ass" button: this allows choosing the intersection of the newly created assistant agent with the mouse (the assistant is created).

The "suppr-ass" button allows you to delete an assistant from all assistants. On the server (Fig. 1), it is possible to visualize the values of the traffic information: The average speed of vehicles, the number of intersections, the number of human beings involved in traffic management, the number of software agents involved, the number of accidents (vehicles in collision), the average level of human workloads, the controls allowing to modify some parameters (speed limiter, acceleration...). On the right-hand side of the server user interface (Fig. 1), one can also see the evolution of the Nash equilibria, which changes dynamically according to the game payoff matrix. This matrix will reflect the evolution of parameters such as the user's workload and experience levels (which will have consequences on the values in the matrix). On the far right of interface, one can see in real time the evolution of the maximum number of stopped vehicles waiting for the entry of an intersection. The "go" button is used to launch the simulation of the traffic.

Thus, the criticality level is calculated from a set of information from the traffic simulator: for example, the density of vehicles, the number of stopped vehicles. This level can take one of ten possible values, divided into five levels as expressed above: Insensible, Harmless, Unpleasant, Dangerous, Uncontrollable.

b) The client. Several clients (i.e. user interfaces) can be connected at the same time for traffic management. The client allows the human being to intervene on the simulator. So, the client can modify the speed limit via a slider, choose an intersection and change the colors of the latter's lights (Fig. 2). The client also allows modifying the workload level of the human being, as well as the level of his or her profile.

c) Software agent

The software agent is an assistant agent created to help the human being in the context of traffic supervision. This agent intervenes following the human decision, by exchanging the colors of the lights at one or more intersections. For this purpose, the following algorithm is implemented in the simulator:

1) Update of the game payoff matrix according to the proposed and/or estimated information. 2) Finding an equilibrium.

3) Based on this equilibrium, the agent chooses an action adapted to the current application (for example, it evaluates the traffic flow, and changes the colour of the lights for a given intersection).

4) Repeat the analysis after a certain number of cycles.

C. Results of the simulation and interpretation

The system consists of an intelligent agent and a human being connected as a hubnet client, with a number of vehicles equal to 84. This number (84) was chosen for the following reason: in the simulator, as many vehicles as desired can be created, but it is important not to exceed the available spaces (roads). In addition, to have a criticality level threshold, the number of vehicles must be large. In our simulation, we assume an environment with four intersections (it is possible to have many more; but we think that this choice is sufficient to validate idea). That leads to generate about 84 vehicles while keeping an environment that can easily evolve (if the number of vehicles is too large, it would be necessary to define a space occupation management and an anticipation mechanism for agents that would exceed the problem of this paper, see for example [START_REF] Doniec | Controlling no-normative behaviors by anticipation for autonomous agents[END_REF]).

Then, traffic behavior does not depend on the number of iterations. It only depends on the actions of the human being and whether or not the assistant agent intervenes, according to the Nash equilibria; the assistant agent calculates these equilibria at each iteration. Of course, the human being does not calculate this equilibrium. The assistant agent calculates the Nash equilibria and then makes the decision to intervene or not. If the agent judges that the intervention is not necessary, it may take care of other tasks, which conditions the result during a current iteration. We believe that the choice of 50 for the number of iterations is sufficient to be able to vary the parameters of the matrix, and show the interest of the approach. However, we can of course go beyond 50 depending on the duration of observation. Thus, the average payoff of the assistant and that of the human being depend on the number of iterations.

The results provided below are obtained without any human intervention. Fig. 3 thus shows the evolution of the number of interventions of the agent in relation to the evolution of the state of the human being during iterations:

 work_load_level: refers to the level of human workload (this level can be modified on the client interface).

 user_experience_level: level of experience of the human being.

 Number_of_coop: number of interventions of the software agent.

Thus, the curve visible in Fig. 4 shows the evolution of the number of vehicles stopped according to the instantaneous equilibriums conditioned by the context information considered for 50 iterations. As explained above, the number of iterations is sufficient in this context. The evolution of the number of interventions of the agent depends on the workload level and the user's experience level:  Between iterations 11 and 21, Fig. 3 shows that the software agent does not intervene: this is justified because during this period, the level of experience is high while the workload level is low.

 There are not many more interventions between iterations 21 to 30 (for the same reasons).

 From 31 st iteration, the number of interventions increases. This is due to an increase in the level of human workload compared to the user's level of experience. Thus, the curve in Fig. 5 shows the evolution of the average vehicle speed for the 50 iterations of observations.

D. Results concerning the Nash equilibrium

During the 50 cycles, we can see (Fig. 3) the variation of Nash equilibria according to the evolution of the context information that determines the payoff matrix the game: the level of experience of the human being and his or her workload level. For the number of iterations, we can have any number of iterations; but for the sake of clarity of the evolution of the number of interventions, the average speed, the average waiting time of the vehicles, we have considered on Figures 3 to 6 about fifty iterations. [CC]: means that the human being is waiting for help and that the software agent is acting at one or more traffic junctions.

[CC] and [CD]: mean that the human being may or may not be autonomous; but the assistant always acts as long as there is cooperation in the Nash equilibrium calculated at each iteration.

[DD]: means that the human being is autonomous and that the assistant does nothing. In this case, the human being must act because the assistant will not do anything (for example, the agent can solve other traffic problems).

E. Interpretation

At any time, the software agent calculates the game payoff matrix. Then it determines the equilibrium and from it, the agent can examine the action of the human being and then it reacts to this action in relation to the Nash equilibria obtained. Fig. 4 shows that the increase in the number of assistant interventions leads to a decrease in the number of stopped vehicles during the simulation. This result explains the fact that if the human being needs the intervention of the assistant, the latter intervenes by considering the Nash equilibria. If the human being should be autonomous, for example when the criticality level and workload level are low and the level of experience is high, the agent does not intervene in view of the equilibrium result. In this case, if the human being does not intervene, there will be an overall slowdown of the crossroads. Thus, the evolution of the average speed curve (Fig. 5) and the average waiting time at lights (Fig. 6) illustrate the result of the work carried out by the software agent when necessary in terms of traffic flow. Despite the decrease in the average traffic speed for example (in cases where the human being has a high level of expertise and a minimal workload), the assistant agent who does not intervene has the possibility to take special care of other complex tasks. So, in the sense of the payoff of the assistant, we can say that even if it does not intervene, its payoff can be translated by its availability to other tasks. These results are promising, despite the relatively simple behavior of the software agent in view of the complexity of the application in which it is involved. Indeed, these results show the effectiveness of the intervention (or non-intervention) of the software agent while considering the information related to the context.

VI. CONCLUSION

This work has presented an interaction model, considering a software agent, based on game theory. The case study on road traffic supervision shows the interest and simplicity of implementing the software agent using the game matrix. The agent calculates the equilibrium at any time and decides the appropriate action based on Nash equilibria. The results thus show the effectiveness of the software agent in traffic management even in the absence of human intervention. The motivation for the use of game theory is to be able to consider an agent that can help the operator by taking care of other complex tasks at the same time. The agent must not waste unnecessary time in its interventions: this is the basic principle used for the proposal of utility functions. The game considered here is a repeated and cooperative two-player game between the human operator and the assistant agent. Our research perspectives focus on the generalization of the approach, by implementing several intelligent agents as assistants to several human beings for the supervision of road traffic. Another perspective will be to embed each assistant agent with learning capabilities, in relation to the history of interactions.

Fig. 1 .

 1 Fig. 1. User interface of the simulator (hubnet server)

Fig. 2 .

 2 Fig. 2. User interface of the simulator (hubnet client)

Fig. 3 .

 3 Fig. 3. Workload level, User experience level and Numbers of interventions of the software agent.

Fig. 4 .

 4 Fig. 4. Number of stopped vehicles

Fig. 5 .

 5 Fig. 5. Average speed of the vehicles

Fig. 6 .

 6 Fig. 6. Average waiting time of vehicles As visible in Fig. 3, the evolution of the Nash equilibrium is translated by the evolution of the number of interventions of the assistant. This number increases in the case of intervention (CC) for the current iteration. Otherwise, the number of interventions does not change; but in the case (DD), the assistant leaves the human operator to deal with other activities. Scoring in the simulation results: Nash equilibria in the case of two players are given in the form of [CC], [CD], [DD], [DC]. For each observation cycle, the task of the software agent is to identify first the crossroads that have the maximum number of vehicles waiting for the entrance. Then the agent changes the lights: the green lights turn red and vice versa:

TABLE 1 .

 1 PAYOFF MATRIX

		Player 2
		act21	act22
		U1(act11,
	act11	act21) U2(act11,	U1(act11, act22) U2(act11, act22)
	Player 1	act21) U1(act12,act21
	act12	) U2(act12,	U1(act12, act22) U2(act12, act22)
		ct21)