S Di Genova

A Gallo

N Fedorczak

H Yang

G Ciraolo

J Romazanov

Y Marandet

H Bufferand

C Guillemaut

J P Gunn

C Gil

E Serre

S Brezinsek

Modelling of tungsten contamination and screening in WEST plasma discharges

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Tungsten (W) is one of the most suitable materials for the inner wall of magnetic confinment fusion devices due to its very high heat conductivity, high melting point, low fuel retention, and low sputtering yield. Nevertheless, even small quantities of partially ionised W ions entering in the confined plasma as impurities can trigger very high power losses through radiation and hence a reduction of central plasma temperature and, consequently, of the fusion reaction rate. For this reason, in view of future fusion reactors, we need to study W impurities source and transport starting from currently operating machines through both experiments and modeling. The ITER divertor will also be made of bulk W monoblocks [START_REF] Pitts | Physics conclusions in support of ITER W divertor monoblock shaping[END_REF]: these plasmafacing components (PFCs) are at present being tested in the W Environment Steady-state Tokamak (WEST) [START_REF] Bucalossi | The WEST project: Testing ITER divertor high heat flux component technology in a steady state tokamak environment[END_REF]. This machine is equipped with PFCs made of bulk W or W-coated CFC and presents strong core radiation losses most probably due to W contamination. At present, only the gross W erosion is experimentally estimated in WEST [START_REF] Meyer | Visible spectroscopy diagnostics for tungsten source assessment in the WEST tokamak: first measurements[END_REF][START_REF] Van Rooij | Tungsten divertor sources in WEST related to impurity inventory and local plasma conditions[END_REF] whereas no experimental estimate of the net W erosion is available. Therefore, modeling efforts are required to study W prompt redeposition and net erosion as well as to identify which PFCs are responsible for the highest contamination of the confined plasma. In this work we used numerical modelling to study W net sources and transport mechanisms in WEST L-mode discharges: starting from experimental data we modelled the background plasma with 2D transport simulations using the SolEdge-EIRENE package [START_REF] Bufferand | Numerical modelling for divertor design of the WEST device with a focus on plasma-wall interactions[END_REF] and we subsequently performed 3D Monte Carlo (MC) simulations to study W contamination with the ERO2.0 code [START_REF] Romazanov | Beryllium global erosion and deposition at JET-ILW simulated with ERO2.0[END_REF]. Similar approaches were adopted for several wall materials using different numerical models: OEDGE-ERO2.0 for berylium in ITER [START_REF] Romazanov | First monte-carlo modelling of global beryllium migration in ITER using ERO2.0[END_REF], EMC3-EIRENE for carbon in LHD [START_REF] Dai | EMC3-EIRENE modelling of edge impurity transport in the stochastic layer of the large helical device compared with extreme ultraviolet emission measurements[END_REF], and SOLPS-ITER-IMPGYRO for W in ITER [START_REF] Yamoto | Kinetic modeling of high-Z tungsten impurity transport in ITER plasmas using the IMPGYRO code in the trace impurity limit[END_REF]. H-mode discharges were not modelled in this work. Nevertheless, it has to be remarked that the presence of edge localised modes during H-mode can have a vital impact on machines equipped with W PFCs [START_REF] Brezinsek | Erosion, screening, and migration of tungsten in the JET divertor[END_REF]. The paper is organized as follows: in section 2 a representative WEST plasma discharge and the corresponding plasma simulations are presented; in section 3 the set-up of the MC simulations tracking W impurities is described; in section 4 the role of the different PFCs in WEST W contamination from the simulations is discussed followed by an analysis of the influence of light impurities on the capability of heavy wall impurities to reach the separatrix in section 5; in section 6 the role of self-sputtering in plasma contamination in different plasma conditions is discussed; finally, in section 7 a direct comparison with experimental data of the WI emission line from visible spectroscopy is carried out.

Modelling of the WEST background plasma

The numerical studies on W contamination performed in this work were based on the modelling of the WEST plasma discharge #55797 (figure 1). This is a typical WEST plasma discharge without external seeding of impurities. When the current flat-top phase is reached, the injected power is around 1 MW (3.4 s). Subsequently, external heating through LH antennae is injected amounting to about 5 MW in the flat-top phase (5.5 s) with the central line integrated density (CLID) achieving 4.5×10 19 m -2 . Modelling was performed on two different phases of the discharge: the first one is in the interval of time 3 -3.5 s, at the end of the Ohmic phase, and the second one in the interval of time 5 -5.5 s, during the end of the external heating ramp-up. In figure 1b the magnetic flux coordinate ψ N iso-surfaces of the magnetic reconstruction [START_REF] Faugeras | An overview of the numerical methods for tokamak plasma equilibrium computation implemented in the NICE code[END_REF] are shown. ψ N is defined as ψ N = (ψ -ψ ax )/(ψ sep -ψ ax ), where ψ is the magnetic flux, ψ ax is the magnetic flux at the magnetic axis, and ψ sep is the magnetic flux at the separatrix. Poloidal positions of WEST main PFCs are also shown in the figure .  The simulations of the plasma during the two phases were performed using the code package SolEdge-EIRENE. The package consists in a coupling between the multi-fluid code SolEdge [START_REF] Bufferand | Numerical modelling for divertor design of the WEST device with a focus on plasma-wall interactions[END_REF] and the MC neutral solver EIRENE [START_REF] Reiter | The EIRENE and B2-EIRENE codes[END_REF]. For this work we used the latest SolEdge version, named SolEdge3X [START_REF] Bufferand | Three-dimensional modelling of edge multicomponent plasma taking into account realistic wall geometry[END_REF][START_REF] Bufferand | Progress in edge plasma turbulence modelling hierarchy of models from 2D transport application to 3D fluid simulations in realistic tokamak geometry[END_REF][START_REF] Bufferand | Description of the model Application to 2D transport modelling Application to 3D turbulence modelling[END_REF]. At the time of writing, the modelling of complex nonaxisymmetric 3D limiters in SolEdge required further development. Hence, the SolEdge-EIRENE simulations presented in this work were performed in 2D mode assuming an axisymmetric wall. This idealisation strongly overestimates the antenna limiter surface wetted by the plasma in the machine. For this reason, the axisymmetric antenna in the simulation was positioned further away from the plasma compared to its actual position during the experiment, in order to lower the plasma flux at this component surface. Further considerations about the effects of an axisymmetric antenna on W The 2D simulations were performed assuming Deuterium (D) plasma since there was no seeding of external impurties in the discharge. The intrinsic content of light impurities in the tokamak was preferred to be added later in ERO2.0 simualtions as a free parameter to study its effect W sputtering and deposition (see sections from 4 to 7). The net power crossing the separatrix P SOL was considered to be lower than the actual one registered in the experiment to account for the radiation in the scrape-off layer (SOL) due to light impurities, so the adopted values were P SOL = 0.45 MW for the Ohmic phase and P SOL = 2.50 MW for the external heating phase, respectively. The gas puff was located at the outer midplane (OMP) and was adjusted to obtain a peak value of electron temperature T e comparable to the experimental one estimated by Langmuir probes embedded in the lower outer divertor target [START_REF] Gunn | Evidence for a poloidally localized enhancement of radial transport in the scrape-off layer of the Tore Supra tokamak[END_REF][START_REF] Dejarnac | Flush-mounted langmuir probes in the WEST tokamak divertor[END_REF]. The simulations were performed without self-consistent turbulence modelling, in the so-called transport mode. Hence, transport coefficients were adopted as a proxy for turbulent transport in the perpendicular direction. The transport coefficient for particles and momentum were cho-sen to be equal to the experimentally estimated average anomalous diffusion value in WEST L-mode discharges D = ν = 0.3 m 2 /s, while the energy ones for ions and electrons were set to the standard value χ i = χ e = 1 m 2 /s [START_REF] Ciraolo | Impact of divertor configuration on tokamak performances: focus on WEST experiments supported by SOLEDGE2D modeling[END_REF]. A uniform recycling coefficient R = 0.99 was adopted on the wall contour for modelling WEST W tiles, while the pump albedo coefficient was set to be R pump = 0.95 (typical assumption for WEST pumping system). Drifts were switched off. The plasma density during the two considered phases differ substantially in the SOL, with a factor of roughly 4 between them at the targets peak values, and also at the OMP separatrix so they will be referred to as "low" and "high" density plasma simulation in the following. The experimental data will be anyway shown with their acquisition time.

Comparison between SolEdge-EIRENE simulations and the lower divertor Langmuir probes are shown in figure 2, exhibiting a good match between probes and simulations at the divertor targets. It is possible to notice how, having adjusted the gas puff on the outer target peak T e , electron density n e values at the targets are also reasonably recovered. While simulations are converged with respect to outer divertor target T e , consistency of midplane profiles had to be verified. Edge density profile could be reconstructed from interferometry [START_REF] Gil | Renewal of the interfero-polarimeter diagnostic for WEST[END_REF] inversion and sweeping reflectometry [START_REF] Clairet | Fast sweeping reflectometry upgrade on Tore Supra[END_REF]. Note that interferometry inversion is subject to large uncertainties at the plasma edge due to weak constrains on the steep local gradients. Plots of n e at OMP and comparisons with experimental interferometry are presented in figure 3, showing a qualitative agreement. For the first time interval of 3-3.5 s also the reflectometry data are reported, it is possible to see how simulations are closer to them than to the interferometry data. It has to be remarked that in simulations the plasma particle flux at the upper divertor is not negligible with respect to the lower divertor, with just a factor of 7 between the peak values. This is not consistent with what is usually seen in WEST experiments in lower single null magnetic configurations, where there is usually a factor of 10-100 between the divertors particle flux peak values. It is in principle possible to improve the reconstruction by an ad-hoc modification using experimental data [START_REF] Gallo | Interpretative transport modeling of the WEST boundary plasma: main plasma and light impurities[END_REF] and this approach should be considered for future work, but this empirical correction is not always possible and was not repeated for this work. The fluid simulations were used as fixed steady state background for ERO2.0 simulations (see sections [START_REF] Meyer | Visible spectroscopy diagnostics for tungsten source assessment in the WEST tokamak: first measurements[END_REF][START_REF] Van Rooij | Tungsten divertor sources in WEST related to impurity inventory and local plasma conditions[END_REF][START_REF] Bufferand | Numerical modelling for divertor design of the WEST device with a focus on plasma-wall interactions[END_REF][START_REF] Romazanov | Beryllium global erosion and deposition at JET-ILW simulated with ERO2.0[END_REF][START_REF] Romazanov | First monte-carlo modelling of global beryllium migration in ITER using ERO2.0[END_REF]. For this reason the SolEdge-EIRENE simulations will be referred to as background plasmas in the following.

Wall impurities erosion and transport simulations set-up

To estimate W re-deposition a kinetic description is needed. Also, the high number of possible W ionisation states makes it very demanding to study W transport with a multi-fluid code. For these reasons, a MC impurity tracker was more suitable for this study. ERO2.0 was the code adopted for the numerical modelling of W erosion and 3D transport across plasma [START_REF] Romazanov | Beryllium global erosion and deposition at JET-ILW simulated with ERO2.0[END_REF][START_REF] Romazanov | First ERO2.0 modeling of be erosion and non-local transport in JET ITER-like wall[END_REF]. SolEdge-EIRENE simulations were used as input to obtain fluid background plasma for ERO2.0. The SolEdge EIRENE results data provided to ERO2.0 as input were spatial distributions of n e (considered to be equal to the ion density), T e , the main ion temperature T i , the main ion parallel velocity v , and the magnetic field B. Uniform values of concentration were used for each light impurity ionisation state. Even if ERO2.0 is a 3D code, the wall geometry is fixed here by the background plasma through an axial revolution of the 2D poloidal section used in SolEdge-EIRENE simulations and so the antenna-limiter is considered to be an axysimmetric object, rather than a set of discrete toroidal distributed antennae as in the experiment. This has some important implications, as will be discussed in section 4. Oxygen (O) was used as a proxy for the light impurities present in WEST (O, carbon, boron, nitrogen and others), and it was considered to be part of the background plasma inside the ERO2.0 simulations. Its global concentration was generally set to be 3% of the background plasma ions density (reasonable average value in WEST from experimental observations [START_REF] Van Rooij | Tungsten divertor sources in WEST related to impurity inventory and local plasma conditions[END_REF]), excluding special cases in which lower values were chosen to study the influence on the simulation of the parameter itself or in the case in which it was needed to compare results with experimental data, as it will specified in the text. It is worth it to remark that considering different light impurities as a proxy would not in general change the conclusions of this work. The presence of light impurities in the plasma influences both W erosion and transport in tokamaks. In ERO2.0 simulations W sputtering is influenced by the presence of light impurities in the background plasma through the energy of the projectile ions impacting the wall, considered to be equal to

E i = 2T i + 3ZT e ,
with temperature in eV (no convolutive effects of the Maxwellian energy distribution on the plasma interaction with a W wall are accounted by the code). This hypothesis may be not accurate if light impurities Mach number goes beyond unity under the effect of the friction with main ion plasma flowing at its own sound speed [START_REF] Tskhakaya | One-dimensional plasma sheath model in front of the divertor plates[END_REF]. However, this assumption remains a common standard in absence of a more precise modelling of light impurities behaviour in the sheath [START_REF] Stangeby | The Plasma Boundary of Magnetic Fusion Devices[END_REF], and the effect of light impurities impacting the wall at speeds similar to the main ion sound speed might be discussed elsewhere.

The sputtering threshold energy depends on the mass ratio between the projectile ion and the target wall atom [START_REF] Stangeby | The Plasma Boundary of Magnetic Fusion Devices[END_REF]. In WEST L-mode plasma discharge conditions described here, T e and T i are low enough to neglect W sputtering caused by D. On the other hand, the mass ratio between O (or carbon, or nitrogen) and W is high enough to make the light impurities sputtering completely dominate over the main ion sputtering. W transport processes in ERO2.0 are computed following the Fokker-Planck model. In this model, the two collisional operators (friction and diffusion in the velocity space) are both influenced by the light impurities presence. Under the hypothesis introduced by ERO2.0, light impurities influence the collisional operators quadratically with the background effective charge Z eff and through the background plasma effective mass m eff (key parameter for the background plasma Maxwellian distribution). High ionisation states of light impurities strongly influence the heavy impurities erosion. Moreover, they affect also their collisions across the plasma. However, if light impurities concentration is sufficiently low, the influence of light impurities on the collisional operators of the Fokker-Planck model is narrower than than the effect on the W sputtering yield. For example, passing from a background plasma with 1% of O 1+ to one with 3% of O 3+ , Z eff will pass from 1 to 1.1 , and m eff will pass from 2.10 amu to 2.42 amu. On the other hand, the O incident energy E i will pass from 2T i + 3T e to 2T i + 9T e . Considering T e = T i = 20 eV and an incidence angle with the wall equal to 60 • , the sputtering yield would pass from 1.2 × 10 -4 to 4.9 × 10 -3 . From the previous example it is possible to understand how W sputtering is very sensible to the light impurities content. Hence, the uniform concentration of O ionisation state was set in order to model better the SOL region where the plasma-wall interaction occurs than the confined region inside the separatrix. Previously published multi-ion runs of SolEdge-EIRENE [START_REF] Gallo | Interpretative transport modeling of the WEST boundary plasma: main plasma and light impurities[END_REF] suggest that not only the the lowest ionisation states are present in the SOL, but even a small amount of the highest ones. For simplicity, the only O ionisation states taken into account in the simulations are O + , O 2+ , and O 3+ , assuming a concentration ratio with the total O concentration (sum over all the ionisation states) of 75 : 100, 15 : 100, and 10 : 100 respectively (except the case in which it will be explicitly differently reported). These assumptions are based on the fact that, at the wall, light impurties lower ionisation states are expected to be found in higher content, since they are ejected by the wall as neutrals.

The sampling of the particles sputtering position, i.e. the probability of the particles to start their trajectory at a certain point of the wall, was cho-sen for this work to be equal to the normalized W gross erosion flux at the wall, while for the starting velocity distribution we adopted the Thompson distribution dY ∝ E(E + E b ) -α dE for the sputtering energy (where Y is the sputtering yield, E is the energy of the sputtered particle, E b is the bond energy of wall particles and α was set to be the standard value 3), while we adopted a simple cosine distribution for the polar angle, considering the direction normal to the wall surface coincident with the 0 angle direction. Finally, uniform distribution for the azimuthal angle was adopted in simulations. Actually, more accurate distributions for the polar angle [START_REF] Eksaeva | ERO modelling of tungsten erosion in the linear plasma device PSI-2[END_REF] and for the azimuthal one [START_REF] Eksaeva | Surface roughness effect on Mo physical sputtering and re-deposition in the linear plasma device PSI-2 predicted by ERO2.0[END_REF] are present in literature. However, common choices were prefered to make the simulations results interpretation simpler. For the sputtering yield, SDTrimSP5.0 simulations data were used [START_REF] Mutzke | Ion fluence dependence of the si sputtering yield by noble gas ion bombardment[END_REF]. No explicit terms for thermal forces were used in the Fokker-Planck model. Nevertheless, the collisional operators used in the simulations have a dependece on T i . Hence, temperature gradients had anyway an indirect effect on the particles transport. The line emissions are calculated after the transport computation as n im n e PEC λ (T e ), where n im is the density of the impurity in the ionisation state of emission of the considered line and PEC λ is the photon emission coefficient for the line λ [START_REF] Summers | The ADAS user manual[END_REF]. The perpendicular anomalous diffusion coefficient D an ⊥ was set, except where it will be explicitly differently reported, to be the value estimated for WEST in former works equal to 0.3 m 2 /s [START_REF] Ciraolo | Impact of divertor configuration on tokamak performances: focus on WEST experiments supported by SOLEDGE2D modeling[END_REF]. Outside the sheath, the electric field E was considered to be null.

Role of the different plasma-facing components in tungsten contamination

The heavy impurities contamination of the main plasma cannot be straightforwardly related to heavy impurity sources. In fact, even if the lower divertor is the PFC experiencing the highest incident particle and energy flux, the plasma particle flux itself screens wall impurities through friction. on the other hand, PFCs receiving a smaller incident particle flux could be the source for impurities that more likely end up crossing the separatrix and entering the confined plasma [START_REF] Sepetys | Tungsten sources in the divertor and the main chamber and contamination of the WEST tokamak plasmas[END_REF].

For this reason, it is important to test the contamination related to different PFCs, analyzing one component at a time in the simulations. This was done performing different ERO2.0 runs using only one PFC at a time as W source. This approach is reasonable only assuming that self-sputtering of a PFC caused by W originating from all other PFCs can be neglected. However, this working assumption was considered to be acceptable since, due to the W strong screening, W particles are likely to re-deposit on the same PFCs from which they are sputtered. The 6 PFCs for which this study was performed are antenna-limiter, inner wall, upper divertor, ceiling, baffle, and lower divertor. The latter was divided into its inner target and its outer target. Figure 4a shows the position in the poloidal section of these PFCs. Tables 1 and2 show the peak values of the plasma parameters at the different PFCs in the two background plasma. Figure 4b shows the total number of W particles found inside the separatrix in the simulations N in as a function of the W erosion rate φ W (expressed in s -1 ) for each considered PFC in both low and high density plasma cases using D an ⊥ = 1 m 2 /s. In the low density case, T i and T e at the antenna were too low for compute sputtering to occur, since the interpolated SDTrimSP5.0 results for O impacting W present a sputtering threshold at E i = 20 eV. Therefore, no results are given for that PFC. On the other hand, for the high density case it was possible to study all the PFCs. It is possible to see how, passing from low density to high density conditions, φ W increases but in most of the cases N in decreases, as simpler models would forecast [START_REF] Chankin | Monte carlo simulations of tungsten redeposition at the divertor target[END_REF], and also in accordance with former SolEdge-EIRENE + ERO2.0 modelling on WEST geometry [START_REF] Gallo | First efforts in numerical modeling of tungsten migration in WEST with SolEdge2D-EIRENE and ERO2.0[END_REF]. This is not true for the baffle, as discussed further below in this section. Figure 4 also shows how, despite having a weaker source, the main chamber PFCs do not have a negligible contribution to the confined plasma contamination. However, there is strong uncertainty about the W source of some of the main chamber PFCs: the plasma flux at the upper divertor, and so the W erosion at this component, could be affected by uncertainties on the position of the secondary X-point in the magnetic equilibrium reconstruction. On the other hand, it should be remarked that the axisymmetric antenna modelled in the simulations is not as close to the separatrix as the actual, toroidally discrete, WEST antennae were during the experiment (see 1b, grey line). Therefore, T i and T i at this PFC are underestimated, and so is the sputtering yield (which is a very strong non-linear function of the T i and T i ). The PFCs screening was assessed performing a study of the so-called W penetration factor τ W [START_REF] Fedorczak | Tungsten transport and sources control in JET ITER-like wall H-mode plasmas[END_REF][START_REF] Dux | Main chamber sources and edge transport of tungsten in H-mode plasmas at ASDEX upgrade[END_REF] defined in equation 1:

D an ⊥ = 1 m 2 /s. PFC peak value n e [m -3 ] T e [eV] T i [eV] v [ms -1 ] Inner target 2.3 ×
τ W = N in φ W (1)
τ W can be simply derived as follow: consider a single point model of the core W content. The balance of W particles inside it is given by equation 2:

dN in dt = - N in τ c W + αφ W (2)
Where N in is the number of W particles inside the core, τ c W is the confinment time of W particles and α is a screening factor that takes into account all the redeposition phenomena that could cause eroded W particles to impact the wall before entering the core. It is straightforward that, if the initial core W content is zero, in the final steady state the core W content is given by equation 3:

N in = αφ W τ c W = φ W τ W (3)
In which we find again the τ W defition presented in equation 1. It has to be remarked that, since α is tipically very small for W, τ W can be several order of magnitude smaller than the physical time scales describing W confinment inside the core. The meaning of τ W is related to the probability of a particle, starting from a certain PFC, to enter the confined plasma. This gives an estimation of how much a PFC is screened, despite the source strength or the related uncertainty in the model. Moreover, computing τ W for different values of D an ⊥ allows one to assess the importance between this free parameter of the model on W contamination.

D an ⊥ is the simulation input parameter most affected by uncertainty but also one of the most relevant for what concerns W transport, so it is essential to perform a scan. The considered values of D an ⊥ are 0.3 and 1 m 2 /s, values in the typical diffusion range in plasma SOL [START_REF] Stangeby | The Plasma Boundary of Magnetic Fusion Devices[END_REF], also found to be consistent with WEST experiments [START_REF] Ciraolo | Impact of divertor configuration on tokamak performances: focus on WEST experiments supported by SOLEDGE2D modeling[END_REF][START_REF] Gallo | Interpretative transport modeling of the WEST boundary plasma: main plasma and light impurities[END_REF][START_REF] Ciraolo | First modeling of strongly radiating WEST plasmas with SOLEDGE-EIRENE[END_REF], and the higher values 3 and 10 m 2 /s to model very high diffusion conditions. The results (tab. 3 and tab. 4) show that, despite a much stronger source, the divertor PFCs (namely lower divertor targets and baffle) present a smaller value of τ W compared to the main chamber PFCs one, even at the highest considered value of D an ⊥ . The small τ W values at the divertor can be explained both by its position and by the strong plasma flow that acts as a screen for impurities. On the other hand, the antenna and the inner wall have the highest τ W as their position causes particles to reach easily the separatrix. Moreover, at midplane the particle flux is 5 orders of magnitude lower than the one at the outer target. A non-axisymmetric antenna would have a different τ W that could be even higher, if positioned closer and the separatrix, while the forecast of the overall source of all the antennae combined would be complicated without a 3D numerical model (less eroded surface, but higher T i and T e , and higher plasma recycling that enhances n e ). Also the effects of a more complex transport model (including e.g. an explicit term for thermal forces, a not null electric field E outside the sheath, non-uniform D an ⊥ distribution) are interesting opportunities for future developments. In the high density case, τ W is noticeably smaller for most of the PFCs. This is explained by the enhancement of prompt redeposition with n e [START_REF] Kirschner | Modelling of plasma-wall interaction and impurity transport in fusion devices and prompt deposition of tungsten as application[END_REF]. Exceptions to this behavior are represented by the inner wall and the baffle. For the former τ W values are slightly lower in the high density case, but they remain on the same order of magnitude. For the latter, at low D an ⊥ values, τ W becomes higher when n e is higher. This is caused by the very small perpendicular distance of this PFC to the separatrix, combined to the fact that high density slightly enhances perpendicular transport (while the parallel transport is weakened). The upper divertor and the ceiling τ W are the ones that mostly decrease between the two cases. This is caused by the possible overestimation of plasma flux and screening at the top of the machine as described above (see section 2). In the simulations, at low D an ⊥ values the probability for W particles to reach the confined region is reduced by parallel transport and the friction with the plasma. These mechanisms flush W particles back towards the PFCs, causing them to redeposit before they can enter the confined plasma. In this regime, increasing D an ⊥ helps particles entering the core, so τ W increases with D an ⊥ . At high D an ⊥ values, diffusion is strong enough to make most particles enter the core. A further increase of D an ⊥ not only makes particles more easily enter the confined plasma, but also leave it. This is the reason why at high D an ⊥ values τ W reahces a plateau or even a small roll-over. Even if counterintuitive, the results obtained in the high diffusion cases are in qualitative agreement with analytical transport models for generical sputtered impurities described in litterature [START_REF] Stangeby | The Plasma Boundary of Magnetic Fusion Devices[END_REF].

log 10 (τ W [s]) D an ⊥ = 0.3 m 2 /s 1 m 2 /s 3 m 2 /

Role of light impurities content in tungsten contamination

If τ W was independent of the conditions of the background plasma at the wall, it would be possible to linearly scale N in with the erosion rate using equation 1. However, the properties of the incident plasma flux at the wall influence heavy impurities transport in several ways. Since in L-mode the sputtering of heavy impurities is mostly caused by light impurities, it is worth studing the effect of O content on τ W . Here we use the outer lower divertor target as a proxy for all the PFCs since in the former study it had very low τ W , so it is supposed to be very sensitive to changes of input parameters that could enhance contamination. In this exercise, 3 different configurations of O content in the plasma were considered: 1% and 3% of O (with the same ions mixture described above in section 3) and finally 3% of only O 3+ content. This analysis was performed on the low density plasma background. Results are shown in tab. the ones in the previous 2 cases. These τ W values get closer to the previous two cases as D an ⊥ increases. The reason is that E i depends on Z, therefore, higher charge of plasma components not only increases W erosion but also increases the initial energy that sputtered W atoms can reach. This, in turn, influences the impurities capability to avoid redeposition before crossing the separatrix (as it will be discussed in more detail in the next section). Similar considerations were pointed out in [START_REF] Marandet | Assessment of tungsten sources in the edge plasma of WEST[END_REF]. If D an ⊥ is high, the difference in light impurities charge is not particularly relevant. When D an ⊥ is equal or less than 1 m 2 /s this effect has instead a strong impact on a very screened component as the outer divertor target. In [START_REF] Chankin | Monte carlo simulations of tungsten redeposition at the divertor target[END_REF] it is also possible to see how the fraction of non-redeposited W particles can change significantly if the energy of the sputtered W atoms increases. It has to be pointed out that between the first 2 cases and the last one Z eff changes by the 15%. This also have effects on the results, but they were not further investigated here. In high diffusion conditions the initial energy of sputtered W neutrals becomes less relevant, but simulations with 3% O 3+ content show anyway τ W values 1.5-2 times higher than the the two other cases. This study shows how the charge of the light impurities influences W redeposition, moreover it is very well known how it also influences W erosion [START_REF] Stangeby | The Plasma Boundary of Magnetic Fusion Devices[END_REF]. The combined result of these two effects is shown in figure 5 (D an ⊥ = 3 m 2 /s in these simulations). The values of φ W , τ W , and N in for the two cases are shown in table 6.

Finally, it is interesting to study the prompt, the local, and the far redeposition in the two simulation shown in figure 5. These were evaluated calculating the distance from the W particles sputtering point and the point of their deposition at the wall d. Every particle deposited less than 1 cm away from the emission point was considered to be promptly redeposited. This threshold length was chosen since it should be equal to a few W 1+ Lar- [10 19 ] 3%O 0.86 2.9 2.5 3%O 3+

D an ⊥ = 3 m 2 /s φ W [10 19 s -1 ] τ W [10 -7 s] N in
3.03 5.2 15.9

Table 6: φ W , τ W , and N in using only the outer target as W source, D an ⊥ = 3 m 2 /s ,and a background plasma (low density one) with 3% O concentration, using different O charge mixture. mor radii that, at the background plasma condition at the outer target, shall corresponds to approximately 2 mm. Every particle deposited less than 1 m (but more than 1 cm) away from the target was considered to be locally redeposited, while for greater distances they were considered far redeposited. Results are presented in table 7.

The results show that increasing the background componets charge actually decreases the fraction of prompt redeposited particles. The ratio between local and far redeposition is similar in the two simulations, with a slightly more likely far redeposition when the background charge is higher. In the simulation with lower background charge, 12.5% of the non-promptly redeposited particles are far redeposited. With a higher background charge this fraction rises to 13%.

Deposition type Prompt

(d < 1 cm) Local (d 1 m) Far (d > 1 m) 3%O 92.0% 7.0% 1.0% 3%O 3+
88.5% 10.0% 1.5%

Table 7: Particles redeposition type fraction, based on the distance d between the particles sputtering point and the point of their deposition at the wall.

The simulations are the same described for figure 5.

Self-sputtering related contamination

Sputtering caused by W impurities impacting the wall is different from sputtering due to light species. First of all, a unitary mass ratio brings high energy transfer into a collision, and hence the sputtering yield increases rapidly with incident energy. Beyond a certain threshold (≈ 270 eV for an incidence angle of 60 • , according to the Eckstein fit formula [START_REF] Eckstein | Sputtering by Particle Bombardment[END_REF]) the cascade effect created by W impacting the wall is so strong that it's possible that even more than one W atom can be sputtered for each W ion impacting the wall, so the sputtering yield rises above 1. Also, incident energy of W impacting wall can be higher than the one carried by a light species: W ions can easily deposit with an ionisation state higher than 1 and this brings a high acceleration in the plasma sheath. Moreover, near the divertor targets, plasma friction can push W ions to a speed equal to a fraction of the plasma sound-speed (c s ), and since m W m D = 92 these ions have very large kinetic energy. Finally, during W self-sputtering, the cut-off of the initial W sputtered neutrals energy distribution has usually higher values than during sputtering by light impurities [START_REF] Kirschner | Erosion and Deposition mechanisms in Fusion Plasmas[END_REF]. In fact, considering e.g. a projectile incident energy of 200 eV the cut-off energy value for W sputtering by O is 33 eV, while for W selfsputtering is 130 eV. Similar considerations have been extensively discussed in literature [START_REF] Brooks | Modeling of sputtering erosion/redeposition status and implications for fusion design[END_REF][START_REF] Naujoks | Erosion and redeposition in the ASDEX upgrade divertor[END_REF]. In this work self-sputtering was examined over the two different backgrounds plasma, the simulations were iterated until reaching a convergence of the wall erosion rate, with each ERO2.0 iteration reading self-sputtering of W particles deposited in the previous step. O concentration was set according to the way described in section 3.

Background plasma sputtering and self-sputtering at the two divertors in the low density plasma background case are shown in figure 6a. The self-sputtering contribution is not pronunced at lower divertor targets (10-20% of intensification of the gross W flux), while a more significant erosion enhancement can be seen the at the upper divertor (60% of intensification of the gross W flux). However, there is only a factor of 1.3 between total wall erosion rate in the cases with and without self-sputtering. A significant difference in the sputtering energy of the particles (i.e. the initial energy of sputtered W a) is observed (6b): 31 eV is the maximum sputtering energy achieved in the simulation without self-sputtering. In the simulation with self-sputtering, 10% of the particles reach sputtering energies from 30 eV to beyond 100 eV. The higher sputtering energy is explained by the high deposition energy of projectile W particles impacting the wall. These heavy impurities can impact the wall at higher energy than the light ones present in the background plasma, as explained above at the beginning of the section. The effect of the high sputtering energy of part of the particles can be seen in figure 6c and6d. In this figure two different poloidal maps of n W are shown for the simulations corresponding to the cases without and with self-sputtering. Inside the inner boundary it is possible to read the average W density at the inner-boundary surface n Bound W . The average W density on the inner-boundary increases by a factor ≈ 4 -5 between the case with and without self-sputtering so, even if the wall erosion rate has only increased by a factor of 1.3, the density at the inner boundary noticeably increased.

This result can be explained as follows: taking as an example the lower divertor, the most important redeposition mechanism is the redeposition during the first Larmor gyration (prompt redeposition). However, this mechanism is not influenced at all by particles sputtering energy, as it depends on the ratio between W neutrals ionisation length and W 1+ Larmor radius, and so it is indipendent by W speed [START_REF] Chankin | Monte carlo simulations of tungsten redeposition at the divertor target[END_REF]. The rest of the main redeposition mechanisms are related to the electric field present in the plasma sheath E sheath and the friction with the plasma flowing to the target with a speed that, for the Bohm criterion, increases up to the sound speed at the sheath entrance. If W ions have high enough energy, they can exit the region of strong forces pushing them towards the targets. Otherwise, they will be decelerated until their trajectory is reversed and they will return to the targets (with energy being generally lower than the one they would have exiting the high redeposition region and then re-entering it). This explanation is similar to the one given in [START_REF] Chankin | Monte carlo simulations of tungsten redeposition at the divertor target[END_REF], in which only the effect of E sheath was considered, while the effects of the background plasma friction were only qualitatively discussed, but not included in the simulations. The results for the high density plasma background case are quite different: the total wall erosion rate increases between the cases without and with selfsputtering only by 1.5%. The difference of particles impact energy between the two different plasma background cases for the simulations without selfsputtering is shown in figure 7c: W particles in the low density case have higher average impact energy than in the high density case (112 eV the first, 32 eV the latter). The reason is the enhancement of promptly redeposition under high density conditions. Promptly redeposited W ions impact the wall with an energy similar to the one they had as atoms after being sputtered, while particles that are not promptly re-deposited can gain energy from the plasma with the mechanisms discribed above. Moreover, since the self-sputtering yield is a very non-linear function of the E i , the difference of impact energy is translated into a huge difference in self-sputtering yield between the low and high density case: on average it is equal to 5.55 × 10 -4 in high density case, and 1.85 × 10 -1 in low density case. This can be explained by the important role of n e in W redeposition: both ionisation rate and plasma friction scale linearly with density, and these phenomena strongly influence redeposition. The effect of the higher T e in the high density case is not straightforward: higher T e means higher sputtering energy (or self-sputtering energy, i.e. the sputtering energy of self-sputtered W particles), but also stronger sheath potential, ionisation rate, and friction force (through c s ). However, this study did not focus on such aspects and here we just state that in the high density case increasing T e did not correspond to a reduction of redeposition. Figure 7a and 7b show poloidal n W maps in the simulations without and with self-sputtering performed for the high density plasma case background, density at the separatrix is lower then in the previous case. Self-sputtering does not cause relevant changes on n Bound W . In this case, n Bound W goes from 0.9 × 10 13 m -3 without self-sputtering to 1.1 × 10 13 m -3 with self-sputtering. This is way less relevant then the effect of self-sputtering in the low density case, in which n Bound W goes from 0.4 × 10 14 m -3 without self sputtering to 1.7 × 10 14 m -3 with self-sputtering.

These considerations explain how self-sputtering can be both a very important mechanism of contamination and a very difficult phenomenon to forecast. However, simulations show that increasing density could be the way to control this contamination threat in L-mode discharges. These conclusion are similar to ones made in [START_REF] Chankin | Monte carlo simulations of tungsten redeposition at the divertor target[END_REF] about W self-sputtering in H-mode discharges. The complexity of the problem highlights the need of having some comparison with experiments. The lower divertor source is probably the more appropriate quantity to compare with experiments, since it is both the stronger one and the one that receives usually more attention by experimental measaurements. Indeed, also signals are higher and measurements easier to deal with.

Lower divertor tungsten source: model to experiment comparison

In order to compare the simulated lower divertor W source to the experimental one, synthetic diagnostics were used to reproduce visible spectroscopy. The synthetic diagnostics consist of post-processing the 2D emission map of a given visible wavelength of W calculated by ERO2.0 using SYNDI (a MC beam tracer) [START_REF] Gallo | Interpretative transport modeling of the WEST boundary plasma: main plasma and light impurities[END_REF], so that it is possible to obtain the line-integrated photon flux on the WEST visible spectroscopy system lines of sight. This allows for a direct one-to-one comparison between experiments and SolEdge-EIRENE + ERO2.0 simulations. Alternatively, an experimentally estimated inverse photon efficiency could have been used to estimate the W photon flux from the particle flux [START_REF] Brezinsek | Spectroscopic determination of inverse photon efficiencies of W atoms in the scrape-off layer of TEXTOR[END_REF]. Figure 8 shows the lines of sight considered by simulations and the ones available in the experiment. Yellow lines were only modelled in simulations, while green ones were both reproduced in simulations and available in the experiment.

The wavelength for which the visible spectroscopy data were analysed is the standard WI line 400.9 nm. The two targets were simulated separately since this allows to assume different O concentration for each target, so the small effect of photons emitted from the other target was neglected. The self-sputtering was also neglected as it does not influence much erosion, as previously discussed. Since erosion depends on O content, the experimental O visible signal OII 435.1 nm at the targets (figure 9) was used to make an educated guess on the O concentration ratio to set in the simulations. During the first time interval (3-3.5 s) the OII signal is strongly unbalanced between the targets, with a difference of about one order of magnitude. Then, in the second time interval (5-.5 s), the signal peaks at the targets become very similar. It is not clear how much the unbalanced configuration depends on n e and T e difference between the targets and how much it depends on an actual O concentration difference. However, light impurities self-consistent numerical modelling in former works have shown that it is possible to have O concentration unbalances between the WEST divertor targets with a slightly higher O content at the inner target [START_REF] Gallo | Interpretative transport modeling of the WEST boundary plasma: main plasma and light impurities[END_REF].

An O concentration scan was performed in ERO2.0 for each target in each plasma density case. In the low density case the O concentration values set for the simulations were 1%, 2%, and 3% for the inner target , 0.1%, 0.2%, and 0.3% for the outer target, while in the high density plasma the values 0.1%, 0.2%, and 0.3% were used for both the targets. Results are shown in figure 10: in the low density case the WI photon flux profile was very well reproduced at the outer target for O concentration equal 0.2% , while for the inner target a value of 3% was needed. This difference in the W visible signal between the targets is qualitatively similar to the one seen in the experiment for the OII line during the interval 3 -3.5 s. During the interval 5 -5.5 s, the WI 400.9 nm signal recovers some symmetry. In high density plasma simulations a good agreement at the outer target is found for O concentration equal to 0.1% with the shape again well reproduced, while for the inner target the shape is not recovered even when the magnitude of the peak is similar, with the peak itself being also shifted in position.

Very good agreement was obtained for the time interval t = 3 -3.5 s on both targets, and for the the time interval t = 5-5.5 s on the outer target. On the inner target during the time interval t = 5-5.5 s, the observed mismatch in the profile could be improved in future efforts by implementing spatially resolved light impurity profiles in the code. Nevertheless, it is possible to obtain comparable results tuning O concentration on physically acceptable values, this can be useful to reduce the uncertainty related to the lower divertor source and move the analyses to the study of other PFCs.

Conclusions

W contamination in WEST was studied through ERO2.0 numerical modelling starting from SolEdge-EIRENE simulations of the background plasma of two different phases of the WEST discharge #55797. The contamination contribution from different PFCs was investigated, suggesting that PFCs experiencing a smaller incident particle flux can can have an important role in contamination. In accordance with former publications [START_REF] Chankin | Monte carlo simulations of tungsten redeposition at the divertor target[END_REF][START_REF] Gallo | First efforts in numerical modeling of tungsten migration in WEST with SolEdge2D-EIRENE and ERO2.0[END_REF], simulations showed that passing from a low to a high density background plasma, W sources increases but the confined plasma contamination weakens for most of the PFCs.

To overcome the model uncertainties concerning W sources, the penetration factor τ W was computed for each PFC for both background plasma density case assuming different anomalous diffusion coneffiecients. This study showed that the lower divertor is the best screened PFC in most conditions, while the main chamber PFCs are usually very weakly screened. Besides this, the upper divertor and the antenna-limiter need a closer investigation since they are suspected to have an important role in WEST W contamination but also to be subject to strong uncertainties in the model, while the baffle screening is the most sensitive to the plasma and diffusion conditions. The influence of light impurities plasma content in W contamination was studied through τ W using different O concentrations and charge mixtures in the simulations, which showed that not only W sources are influenced by light impurities charge, but also the probability of sputtered W particles to enter into the confined plasma avoiding redeposition mechanisms. Self-sputtering was also modelled. Results were very different in the two plasma density cases: in the low density case W impurities impacting the wall cause a slight erosion enhancement due to self-sputtering. Nevertheless, their impact speed was high enough to allow self-sputtered impurities to have sufficient energy to escape redeposition mechanisms and heavily increase confined plasma contamination. In the high density case the high prompt redeposition does not allow W impurities to gain much energy from the plasma, so their impact speed is not high enough to influence either erosion or confined plasma contamination through self-sputtering. Finally, a direct comparison with the WI 400.9 nm visible signal measured at the divertor targets was performed using a synthetic diagnostic. The OII 435.1 nm line signal trend in the discharge was used as an indication for the simulations O concentration ratio between the targets in the two modelled plasma discharge phases. The results showed a good agreement with the experimental data for values of O concentration between 0.1% and 3%, and the capability of the model to reproduce a realistic W visible signal shape at the outer target.

In the future the model could be improved by different aspects: with the future development of 3D plasma transport code working in realistic geometry, the passage to 3D background plasma with a complex wall and magnetic ripples could be an important step ahead for the modelling of W sources from toroidally discrete objects like WEST antennas and limiters.. A selfconsistency in light impurities sputtering could improve the source and sputtering energy estimation. Finally, comparison with main chamber sources would help the accuracy of the source estimation for weakly screened PFCs.

Figure 1

 1 Figure 1: a) Time trace of input and radiated power, central line integrated density (CLID), and plasma current in WEST discharge #55797. b) Magnetic flux coordinate ψ N following the magnetic reconstruction of the discharge (produced with NICE [11]), central line of sight used for measure CLID (green line), and wall adopted in the SolEdge-EIRENE simulations (red dashed line), purple line indicates the separatrix.

Figure 2 :

 2 Figure 2: Comparison between simulations and Langmuir probes during t = 3 -3.5 s (a and b), and during t = 5 -5.5 s (c and d).

Figure 3 :

 3 Figure 3: Comparison between simulations and interferometry during t = 3 -3.5 s (a), and during t = 5 -5.5 s (b).

Figure 4 :

 4 Figure 4: a) WEST PFCs modelled in ERO2.0 as W source. Black crosses indicate the strike points. b) Core contamination N in as a function of W erosion rate φ W for each PFC in low and high density plasma case, with D an ⊥ = 1 m 2 /s.

Figure 5 :

 5 Figure 5: W density poloidal map using only the outer target as W source and a background plasma (low density one) with 3% O concentration, in a) a mixture of the first 3 O ionisation states are used (see section 3), in b) only O 3+ is present in the background. D an ⊥ = 3 m 2 /s in the simulations.

Figure 6 :

 6 Figure 6: a) Plasma background sputtering and W self-sputtering at the two divertors in low density plasma background case. b) Test particles sputtering energy probability density in low density plasma background in steady-state without and with self-sputtering. c) Poloidal W density map without selfsputtering, and d) with self-sputtering. O concentration was set according to the description of section 3.

Figure 7 :

 7 Figure 7: Poloidal W density map in high density plasma case a) without selfsputtering, and b) with self-sputtering. c) W wall impact energy in low and high density plasma case (self-sputtered impurities not included). Dashed lines show the average impact energy for the low density plasma (LDP) case and high density plasma (HDP) case. O concentration was set according to the description of section 3.

Figure 8 :

 8 Figure 8: Visible spectroscopy lines of sight pointing at the lower divertor.Yellow lines were only modelled in simulations, while green ones were both reproduced in simulations and available in the experiment.

Figure 9 :

 9 Photon flux [10 17 m -2 s -1 sr -1 ] OII 435.1 nm visible spectroscopy 55797 t = 3-3.5 s 55797 t = 5-5.5 s

Figure 10 :

 10 Photon flux [10 16 m -2 s -1 sr -1 ]

2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 Major radius [m] 0 2 4 6 Electron density [10 19 m -3 ] Lower divertor SolEdge-EIRENE 0.45 MW 55797 Langmuir probes 3-3.5 s (a) 2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 Major radius [m] 0 10 20 30 40 50 Electron Temperature [eV] Lower divertor SolEdge-EIRENE 0.45 MW 55797 Langmuir probes 3-3.5 s (b) 2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 Major radius [m] 0 5 10 15 20 Electron density [10 19 m -3 ] Lower divertor SolEdge-EIRENE 2.5 MW 55797 Langmuir probes 5-5.5 s (c) 2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 Major radius [m] 0 20 40 60 Electron Temperature [eV] Lower divertor SolEdge-EIRENE 2.5 MW 55797 Langmuir probes 5-5.5 s

	(d)

Table 1 :

 1 Low density background plasma properties peak values at the different PFCs. PFC peak value n e [m -3 ] T e [eV] T i [eV] v [ms -1 ]

		10 19	16.2	16.6	3.5 × 10 4
	Outer target	8.4 × 10 18	26.9	19.9	4 × 10 4
	Upper divertor 5.2 × 10 18	19.2	20.2	3.2 × 10 4
	Inner wall	1.2 × 10 15	0.9	6.7	1.2 × 10 4
	Ceiling	2.2 × 10 17	6.0	10.0	2.1 × 10 4
	Antenna	2.0 × 10 15	1.0	3.9	1.0 × 10 4
	Baffle	2.5 × 10 18	11.5	15.0	1.2 × 10 4

Table 2 :

 2 High density background plasma properties peak values at the different PFCs.

Table 3 :

 3

	s 10 m 2 /s

log 10 (τ W [s]) in low density plasma case. Simulations were not statistically capable to detect very low values, these are expected to be < -12. log 10 (τ W [s]) D an ⊥ = 0.3 m 2 /s 1 m 2 /s 3 m 2 /s 10 m 2 /s

Table 4 :

 4 log 10 (τ W [s]) in high density plasma case. Simulations were not statistically capable to detect very slow values, these are expected to be < -12.

Table 5 :

 5 5: 1% O and 3% O concentration cases lead to equivalent τ W (despite small fluctuations for low D an ⊥ explicable by the effect of MC noise on very small τ W values). The cases with 3% O 3+ show values of τ W up to 100 times higher then O.T. log 10 (τ W [s]) D an ⊥ = 0.3 m 2 /s 1 m 2 /s 3 m 2 /s 10 m 2 /s Outer target log 10 (τ W [s]) in low density plasma case under different plasma O contents. In the first two cases the mixture of O charge states described formerly in the paper was used (section 3), in the last one only O 3+ was considered.

	1%O	-9.97	-8.50 -6.43	-5.58
	3%O	-10.12	-8.15 -6.54	-5.63
	3%O 3+	-8.05	-7.00 -6.28	-5.42

Acknowledgement

This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.


Thomas Treal

Philip L Jackson

Aurore Meugnot
email: aurore.meugnot@universite-paris-saclay.fr

Natural postural oscillations during facial expression of pain in virtual characters modulate early and late ERP components of empathy

Keywords: Empathy, Virtual character, EEG, Idle motion, Biological motion, Behavioral realism 1

Empathy research can benefit from advances in virtual reality to create more ecological paradigms involving realistic digital characters. However, the genuineness of the characters needs to be developed further in order to trigger a spontaneous affective reaction in users and favor a natural interaction. In this perspective, a recent study has shown that adding humancaptured postural oscillations (biological idle motion) to a virtual character increased the participants' self-reported empathic response to the character's facial expression of pain. The present study aimed to examine more specifically which processes of empathy is affected by the presence of idle motion using electroencephalography (EEG). Twenty healthy young adults were presented with video clips of a virtual character displaying a facial expression of pain while its body was either still or animated with pre-recorded natural human postural oscillations. The EEG response of participants was recorded during the video clips. After the video clips, participants had to rate the intensity of the pain expression. The results showed that participants attributed more pain to characters that displayed idle motion, and that idle motion increased both early (affective resonance) and late (perspective-taking) event-related potentials (ERPs) associated with empathy for pain. The effect of idle motion on participants' pain rating and on late ERP associated with perspective-taking were positively correlated.

These results confirm the potential of idle motion to increase participants' empathic response to the character's pain expression, and suggest that this might be mediated thought its perspective-taking component.

Introduction

Empathy, which is defined as the ability to share and understand the mental states of others [START_REF] Decety | The Functional Architecture of Human Empathy[END_REF], has been widely studied in affective and social neurosciences [START_REF] Bernhardt | The neural basis of empathy[END_REF][START_REF] Decety | The Functional Architecture of Human Empathy[END_REF]Jauniaux et al., 2019;[START_REF] Lamm | Meta-analytic evidence for common and distinct neural networks associated with directly experienced pain and empathy for pain[END_REF][START_REF] Zaki | The neuroscience of empathy : Progress, pitfalls and promise[END_REF]. Although there are different theoretical models describing the processes of empathy, scholars in neuroscience agree that it is underpinned by at least two core processes: 1) an automatic and vicarious activation of the mental state of the other called affective sharing/resonance and 2) a more controlled and cognitive process of making inferences about the other's mental state called perspective-taking [START_REF] Bird | The self to other model of empathy : Providing a new framework for understanding empathy impairments in psychopathy, autism, and alexithymia[END_REF][START_REF] Coll | Are we really measuring empathy? Proposal for a new measurement framework[END_REF][START_REF] Cuff | Empathy : A Review of the Concept[END_REF][START_REF] Decety | The Functional Architecture of Human Empathy[END_REF][START_REF] Zaki | The neuroscience of empathy : Progress, pitfalls and promise[END_REF]. The underlying cerebral organization of these processes were highlighted by fMRI studies showing a common circuit of neural activation (anterior cingulate cortex (ACC), anterior insula (AI)) during the perception of pain in others and during self-pain experience (affective resonance) [START_REF] Jackson | How do we perceive the pain of others? A window into the neural processes involved in empathy[END_REF][START_REF] Singer | Empathy for pain involves the affective but not sensory components of pain[END_REF] as well as an activation of brain areas associated with perspective-taking (precuneus, right temporo-parietal junction (rTPJ), temporal pole, ventromedial prefrontal cortex) [START_REF] Healey | Cognitive and Affective Perspective-Taking : Evidence for Shared and Dissociable Anatomical Substrates[END_REF][START_REF] Jackson | Empathy examined through the neural mechanisms involved in imagining how I feel versus how you feel pain[END_REF][START_REF] Lamm | Meta-analytic evidence for common and distinct neural networks associated with directly experienced pain and empathy for pain[END_REF] when observing pain in others. Other studies have used the temporal resolution of EEG to emphasize that the process of affective resonance occurs early and the process of perspective-taking occurs later [START_REF] Fan | Temporal dynamic of neural mechanisms involved in empathy for pain : An event-related brain potential study[END_REF][START_REF] Sessa | Double dissociation of neural responses supporting perceptual and cognitive components of social cognition : Evidence from processing of others' pain[END_REF]. Indeed, [START_REF] Fan | Temporal dynamic of neural mechanisms involved in empathy for pain : An event-related brain potential study[END_REF], showed that observing pictures of hands in painful situation elicits a positive shift in early event-related potentials (ERPs) (before 360 ms) compared to observing these same stimuli in neutral situation, and that this difference is insensitive to the task (i.e., judging the presence of pain vs counting the number of hands on the picture). By contrast, for later evoked potentials (occurring between 360 and 800 ms), a positive shift was observed for the painful stimuli only when participants were judging the level of pain but not when they were counting the hands. In the same vein, Sessa and colleagues, (2014) showed that observing a facial expression of pain also provokes a positive shift in the early ERPs (between 110 et 360ms) compared to a neutral facial expression. In contrast, presenting a painful context (presentation of a sentence before the presentation of a neutral facial expression) elicits a positive shift only in the later ERPs (between 400 and 800ms) but not in the early ERPs compared to a neutral context. The majority of these neuroscience studies on human empathy have been conducted using stimuli composed of pictures of injured limbs (e.g., [START_REF] Coll | The effect of tDCS over the right temporoparietal junction on pain empathy[END_REF][START_REF] Fan | Temporal dynamic of neural mechanisms involved in empathy for pain : An event-related brain potential study[END_REF][START_REF] Jackson | How do we perceive the pain of others? A window into the neural processes involved in empathy[END_REF][START_REF] Jackson | Empathy examined through the neural mechanisms involved in imagining how I feel versus how you feel pain[END_REF] or pictures of facial expression of pain (e.g., [START_REF] Coll | The effect of tDCS over the right temporoparietal junction on pain empathy[END_REF][START_REF] Huang | Shared beliefs enhance shared feelings : Religious/irreligious identifications modulate empathic neural responses[END_REF][START_REF] Li | Behavioral and electctrophysiological evidence for enhanced sensitivity to subtle variations of pain expressions of same-race than other-race faces[END_REF][START_REF] Sessa | Double dissociation of neural responses supporting perceptual and cognitive components of social cognition : Evidence from processing of others' pain[END_REF][START_REF] Sheng | Manipulations of cognitive strategies and intergroup relationships reduce the racial bias in empathic neural responses[END_REF] which respond to the technical constraints of method used to measure the brain response (in this case IRMf and EEG). Although these stimuli have led to great advances in the understanding of human empathy, the need has come for more ecological paradigms to be able to extrapolate laboratory results to everyday life [START_REF] Jackson | EEVEE : The Empathy-Enhancing Virtual Evolving Environment[END_REF][START_REF] Zaki | The Need for a Cognitive Neuroscience of Naturalistic Social Cognition[END_REF], 2012). Particularly, one of the future challenges of empathy research is to determine precisely what an empathic behavior is and how it is linked to the processes of empathy [START_REF] Jackson | EEVEE : The Empathy-Enhancing Virtual Evolving Environment[END_REF][START_REF] Lamm | Imaging empathy and prosocial emotions[END_REF][START_REF] Zaki | Integrating Empathy and Interpersonal Emotion Regulation[END_REF][START_REF] Zaki | The neuroscience of empathy : Progress, pitfalls and promise[END_REF]. Currently, the stimuli used are not able to elicit the interactive dimension of the empathic process. Yet, this interactive dimension is at the core of complex phenomena, such as empathic behaviors, which occur only in social context [START_REF] Schilbach | Toward a second-person neuroscience[END_REF][START_REF] Zaki | Integrating Empathy and Interpersonal Emotion Regulation[END_REF][START_REF] Zaki | The neuroscience of empathy : Progress, pitfalls and promise[END_REF].

To address this need of more ecological paradigms, empathy research can benefit from virtual reality, which allows to keep the rigorous control and constraints imposed by social cognitive and affective neuroscience methods and experiments while simulating a natural interaction [START_REF] Bombari | Studying social interactions through immersive virtual environment technology : Virtues, pitfalls, and future challenges[END_REF][START_REF] De Gelder | Virtual reality and the new psychophysics[END_REF][START_REF] Jackson | EEVEE : The Empathy-Enhancing Virtual Evolving Environment[END_REF][START_REF] Pan | Why and how to use virtual reality to study human social interaction : The challenges of exploring a new research landscape[END_REF][START_REF] Wykowska | Embodied artificial agents for understanding human social cognition[END_REF]. However, some advances in virtual reality are needed to be able to reproduce a natural interaction with participants. Indeed, although observing virtual characters' facial expressions elicit in part the same cerebral responses as pictures of human facial expressions, differences remain [START_REF] Kätsyri | Amygdala responds to direct gaze in real but not in computer-generated faces[END_REF][START_REF] Kegel | Dynamic human and avatar facial expressions elicit differential brain responses[END_REF][START_REF] Moser | Amygdala activation at 3T in response to human and avatar facial expressions of emotions[END_REF]. Particularly, the study of Kergel and collaborators (2020) showed that observing a dynamic facial expression of fear coming from a video of a human being elicits a stronger activation of the brain areas associated with the affective resonance network (ACC, AI) compared to observing the same dynamic facial expression of fear coming from a virtual character. This decrease in the affective resonance might result from the perception of the virtual characters as artificial or non-human entities and thus as less important partners for human interaction [START_REF] Kegel | Dynamic human and avatar facial expressions elicit differential brain responses[END_REF]. It therefore seems that the perception of a lesser humaneness in stimuli leads to a decrease of the affective resonance. In another fMRI study, the same decrease to less human stimuli has been observed for the perspective-taking network [START_REF] Krach | Can Machines Think? Interaction and Perspective Taking with Robots Investigated via fMRI[END_REF]. In this study, participants played a game with different partners (computer, functional robot, anthropomorphic robot and human), and the activation in the participants' rTPJ (a brain area known to be involved in perspective taking [START_REF] Decety | The role of the right temporoparietal junction in social interaction : How low-level computational processes contribute to meta-cognition[END_REF][START_REF] Jackson | Empathy examined through the neural mechanisms involved in imagining how I feel versus how you feel pain[END_REF])) increased linearly with the humaneness of the partners. These results are corroborated by an EEG study [START_REF] Vaes | Minimal humanity cues induce neural empathic reactions towards non-human entities[END_REF] which showed that observing vegetables with attributed human names (adding humaneness) elicited a stronger responses of late ERPs associated with perspective-taking (between 360 and 540ms) at right centralparietal electrodes which are aligned with the rTPJ [START_REF] Coll | The effect of tDCS over the right temporoparietal junction on pain empathy[END_REF][START_REF] Mai | Using tDCS to Explore the Role of the Right Temporo-Parietal Junction in Theory of Mind and Cognitive Empathy[END_REF]. Taken together, these results highlight the progress that still needs to be made regarding the realism of virtual characters and, particularly, the importance to improve their perceived humaneness by the human brain to get even closer to the cerebral response elicited by human stimuli.

One way to achieve this goal is to improve the behavioral realism of virtual characters. Indeed, the majority of studies focus only on the facial expression without including body movements in the characters. Yet, a fundamental characteristic of human beings is to always be moving, even so slightly (Hunter & Kearney, 1981). Motionlessness is very rare. Thus, a way to enhance the humaneness of virtual characters via their behavioral realism is to infuse them with idle motion. These motions refer to all movements that are permanently present in humans, such as postural oscillations, breathing or eye blinking. [START_REF] Egges | Personalised real-time idle motion synthesis[END_REF]. Recent studies by our group have recently shown that implementing idle motion in a virtual character expressing pain enhances the perceived intensity and believability of its pain expression [START_REF] Treal | Combining trunk movement and facial expression enhances the perceived intensity and believability of an avatar's pain expression[END_REF] as well as self-reported empathic response of participants towards its pain expression [START_REF] Treal | Natural human postural oscillations enhance the empathic response to a facial pain expression in a virtual character[END_REF]. In this latter study, Treal and colleagues (2021) implemented natural human postural oscillations from motion capture data in a virtual character expressing pain. They showed that participants judge the pain expression as more intense and reported feeling more touched by the pain expression when the character was animated with slightly perceptible biological idle motion. We postulated that implemented in the form of biological motion, idle motion could lead to an early categorization of the virtual character as a human being resulting in a higher empathic response to the character's pain expression. This hypothesis is consistent with the fact that biological motion would be perceived early at a preattentive stage [START_REF] Hirai | The two-process theory of biological motion processing[END_REF] and that it could serve as a perceptual "life detector" [START_REF] Johnson | Biological motion : A perceptual life detector?[END_REF][START_REF] Troje | The inversion effect in biological motion perception : Evidence for a « life detector[END_REF].

The present study aimed to extend these previous findings by investigating with EEG which processes of empathy (i.e., affective resonance and perspective taking) is specifically affected by the presence of idle motion. Virtual characters expressing pain with a dynamic facial expression, which was either animated with idle body motion (Idle condition) or presented with a fixed body (Still condition), were presented to the participants. It was hypothesized that the presence of idle motion would influence the early ERPs associated with affective resonance (P2 and N2-N3 fronto-central) [START_REF] Coll | Meta-analysis of ERP investigations of pain empathy underlines methodological issues in ERP research[END_REF][START_REF] Fan | Temporal dynamic of neural mechanisms involved in empathy for pain : An event-related brain potential study[END_REF][START_REF] Sessa | Double dissociation of neural responses supporting perceptual and cognitive components of social cognition : Evidence from processing of others' pain[END_REF] as well as the later component associated perspective-taking (LPP central-parietal [START_REF] Coll | Meta-analysis of ERP investigations of pain empathy underlines methodological issues in ERP research[END_REF][START_REF] Fan | Temporal dynamic of neural mechanisms involved in empathy for pain : An event-related brain potential study[END_REF][START_REF] Sessa | Double dissociation of neural responses supporting perceptual and cognitive components of social cognition : Evidence from processing of others' pain[END_REF] and right central-parietal [START_REF] Vaes | Minimal humanity cues induce neural empathic reactions towards non-human entities[END_REF]). Particularly, a change of the early ERPs associated with affective resonance would confirm the hypothesis of an early encoding of idle motion by the human brain.

Method

Participants. A power analysis, based on previous studies analyzing ERPs for pain [START_REF] Coll | The effect of tDCS over the right temporoparietal junction on pain empathy[END_REF][START_REF] Sessa | Double dissociation of neural responses supporting perceptual and cognitive components of social cognition : Evidence from processing of others' pain[END_REF], conducted with G*power (α = .05, 1 -β = .95) revealed the requirement of at least 19 participants. Twenty healthy young adults without neurological or psychiatric disorder took part in the experiment (7 women, mean age = 23.1 ± 3.8 years, range = 18-29 years). Each participant had normal or corrected-to-normal vision.

The study was approved by the Ethics Committee of Paris-Saclay University (#CER-Paris-Saclay-2020-147) and conducted in accordance with the Declaration of Helsinki. The participants gave written informed consent to take part in this study.

EEG recording

EEG activity was continuously recorded from 64 active electrodes (actiCAP slim, Brain Products GmbH, Gilching, Germany) at a frequency of 5000 Hz with acquisition reference at FCz. Electrodes impedance were kept under 50kΩ. Eye blinks were detected using an electrooculogram (EOG) (two electrodes placed above and under the left eye) and Fp1 and Fp2 electrodes.

Stimuli. The stimuli consisted in two video clips (duration = 1 second) showing the upper body of a male virtual character (Figure 1, Supplementary Material section) from the Empathy-Enhancing Virtual Evolving Environment (EEVEE) [START_REF] Jackson | EEVEE : The Empathy-Enhancing Virtual Evolving Environment[END_REF]. The video clips were created using Blender® (Blender Foundation, Amsterdam, Netherlands).

The virtual character was animated with a dynamic facial expression of pain from 40% to 60% of the maximal intensity, either with body animation (Idle condition, see the Body Animation section below for a detailed description of the method) or without body animation (Still condition).

Facial expression of pain animation. The character's facial expression of pain was created using Action Units (AUs) according to the Facial Action Coding System (FACS) [START_REF] Ekman | Manual for the facial action coding system[END_REF]. The characteristic AUs from the facial expression of pain [AU4 (brow lowerer), AU6 (cheek raiser), AU7 (lid tightener), AU9 (nose wrinkler), AU10 (upper lip raiser) and AU43 (eyes closed)); and five occasional AUs (AU12 (lip corner puller), AU20 (lip stretcher), AU25 (lips part), AU26 (jaw drop) and AU27 (mouth stretch)] [START_REF] Prkachin | The consistency of facial expressions of pain : A comparison across modalities[END_REF] were manipulated using Blender to create the dynamic facial expression of pain. Each video began with the character showing a pain expression at 40% of the maximal intensity.

The level of the AUs were increased linearly to reach 60% of the maximal intensity over 400 milliseconds (ms). The pain expression was then maintained for 600 ms until the end of the clip (see Figure 1).

Task and Procedure

Once the participants had given their written informed consent, the EEG net was installed, and the impedance gel was applied to the electrodes. They then received instructions for the task. The task was programmed using Psychopy [START_REF] Peirce | PsychoPy2 : Experiments in behavior made easy[END_REF] and displayed on a computer screen (20-inch monitor, 60Hz refresh state, resolution = 1680 x 1050 pixels) at a viewing distance of 70 cm from the participants. Each trial began with the presentation of a black screen (duration = 1000 ms), followed by a white fixation cross (duration =1000-1800 ms) and by a video clip (duration = 1000 ms). Participants were instructed to look at the fixation cross until the start of the video clip, and, not blink from the beginning of the fixation cross to the end of the video clip. After the video clip, participants had to judge the intensity of the character's pain expression by moving a cursor on a visual analog scale (VAS) (Left extremity "Mild pain", Right extremity "Very intense pain" [In French "Douleur peu intense" and "Douleur très intense"]). The cursor initially appeared at the middle of the VAS. Each stimulus was displayed 100 times for a total of 200 trials for the task (100 trials * two body conditions). The order of the stimuli was randomized across the task. After every 20 trials, a pause screen was displayed, participants clicked on a rectangle in the center of the screen when they were ready to resume the task. Before the experimental phase, participants performed a familiarization phase composed of 20 trials (10 trials of each condition displayed randomly). The duration of the task was approximately 30 minutes.

Behavioral data analysis

Pain intensity rating. The position of the cursor along the scale was converted to numerical values between 0 ("Mild pain") and 100 ("Very intense pain"). The average pain rating was calculated for each condition of body animation (Idle and Still). A two-tailed paired t-test was then performed on the pain rating between the Idle and Still conditions.

ERP preprocessing and analysis

All EEG analyses were performed using MNE-Python0.21 [START_REF] Gramfort | MEG and EEG data analysis with MNE-Python[END_REF]. Data were resampled offline at a frequency of 500Hz, band pass filtered (0.1 and 40Hz) and an additional 50-Hz notch filter was used to reduce electrical noise. Bad channels were detected based on visual inspection and interpolated. The signal was then re-referenced using the average of all electrodes. The epochs were then created using a 100 milliseconds pre-stimulus baseline. Epochs containing eye blinks or values exceeding ±150 µV were excluded from the analysis. All data sets contained at least 50 epochs per condition without artefacts (min = 58, mean = 88.03 ± 11.67). Time windows were based on previous studies [START_REF] Coll | The effect of tDCS over the right temporoparietal junction on pain empathy[END_REF][START_REF] Sessa | Double dissociation of neural responses supporting perceptual and cognitive components of social cognition : Evidence from processing of others' pain[END_REF][START_REF] Vaes | Minimal humanity cues induce neural empathic reactions towards non-human entities[END_REF] and were adjusted using the aggregate grand average from trials of our data [START_REF] Brooks | Data-driven region-of-interest selection without inflating Type I error rate : Safe data-driven ROI selection[END_REF]. The mean amplitudes of the P2 (185-245ms) and the N2-N3 (250-400ms) components were calculated at fronto-central electrodes (FCz, Cz, FC1, FC2, C1, C2), the LPP (600-1000ms) component at centro-parietal electrodes (cLPP) (Cz, CPz, C1, CP1, C2, CP2) [START_REF] Coll | Meta-analysis of ERP investigations of pain empathy underlines methodological issues in ERP research[END_REF] and right centro-parietal (rLPP) (C4, C6, CP4, CP6) [START_REF] Vaes | Minimal humanity cues induce neural empathic reactions towards non-human entities[END_REF]. Two-tailed paired t-tests were then performed on each ERP between the Idle and Still conditions. In case of significant difference between potentials, a Pearson correlation was performed between the difference of the significant ERP amplitude in each condition (ERP Idle -ERP Still) and the difference in the pain judgment in each condition (Pain judgment Idle -Pain judgment Still).

Results

Pain intensity rating. Paired t-test revealed that participants judged the pain expression as significantly more intense in the Idle condition (mean = 40.35,95% CI [32.32,48.38]) than in the Still condition (mean = 38.38,95% CI [30.11,46.65

Discussion

The present study tested with EEG whether the neural response underlying empathy for a virtual character's facial expression of pain was influenced by the presence of idle motion. The results showed that that adding idle motion in a virtual character expressing pain significantly increased the participants' pain rating, as well as the early affective N2-N3 and the later cognitive rLPP cerebral responses. No difference between the still and idle conditions was found on the P2 and cLPP components.

The influence of idle motion on the early N2-N3 ERP corroborated the hypothesis of an early influence of these movements. Previous studies have associated this ERP with affective resonance [START_REF] Fan | Temporal dynamic of neural mechanisms involved in empathy for pain : An event-related brain potential study[END_REF][START_REF] Sessa | Double dissociation of neural responses supporting perceptual and cognitive components of social cognition : Evidence from processing of others' pain[END_REF]. Observing painful stimuli elicits a positive shift in this ERP relative to non-painful stimuli and this effect is not task [START_REF] Fan | Temporal dynamic of neural mechanisms involved in empathy for pain : An event-related brain potential study[END_REF] or context [START_REF] Sessa | Double dissociation of neural responses supporting perceptual and cognitive components of social cognition : Evidence from processing of others' pain[END_REF] dependent. In contrast to previous literature, the present study did not compare a painful situation to a neutral one, but two painful stimuli.

Interestingly, the present results could be interpreted in line with those obtained from studies of racial ingroup bias in empathy (RIBE) which also compared two painful conditions [START_REF] Sheng | Manipulations of cognitive strategies and intergroup relationships reduce the racial bias in empathic neural responses[END_REF]. Indeed, it has been shown that observing same-race faces (Asian participants observing Asian faces) elicited a significantly more negative N2 response compared to the observation of other-race faces (Asian participants observing Caucasian faces) regardless of the context (painful or neutral) [START_REF] Sheng | Manipulations of cognitive strategies and intergroup relationships reduce the racial bias in empathic neural responses[END_REF]. This racial ingroup bias in empathy was associated with a higher affective resonance toward same-race stimuli [START_REF] Azevedo | Their pain is not our pain : Brain and autonomic correlates of empathic resonance with the pain of same and different race individuals[END_REF][START_REF] Contreras-Huerta | Racial Bias in Neural Empathic Responses to Pain[END_REF][START_REF] Xu | Do You Feel My Pain? Racial Group Membership Modulates Empathic Neural Responses[END_REF], see Han, 2018, for a review). Therefore, idle motion could have influenced the early response associated with affective resonance in the same way as racial ingroup bias in empathy inducing a higher affective resonance in participants. Interestingly, this race-effect with a more negative N2 response has been largely observed in numerous studies [START_REF] Dickter | Racial ingroup and outgroup attention biases revealed by event-related brain potentials[END_REF][START_REF] Ito | Race and gender on the brain : Electrocortical measures of attention to the race and gender of multiply categorizable individuals[END_REF], 2005;[START_REF] Kubota | Multiple Cues in Social Perception : The Time Course of Processing Race and Facial Expression[END_REF], see Ito & Bartholow, 2009, for a review). Ito & Bartholow, 2009, interpreted this result as the reflection of "automatic encoding of, and orienting toward, racial category information". In the present context, the more negative N2-N3 in the idle condition could also reflect an automatic encoding of human characteristics, i.e., the presence of idle movements.

This would be in accordance with the hypothesis that idle motion provokes an early categorization of the character as a human being [START_REF] Treal | Natural human postural oscillations enhance the empathic response to a facial pain expression in a virtual character[END_REF] rather than an object.

Particularly, the biological dimension of the present movement could be primordial for this human categorization. This interpretation is supported by recent empirical studies showing that in virtual characters, biological motion enhances their acceptability [START_REF] Piwek | Empirical evaluation of the uncanny valley hypothesis fails to confirm the predicted effect of motion[END_REF] as well as visual attention of participants [START_REF] Williams | Human body motion captures visual attention and elicits pupillary dilation[END_REF] compared to mechanical motion. The human brain would be automatically orienting toward biological motion, which is concordant with the idea that its perception is pre-attentive [START_REF] Hirai | The two-process theory of biological motion processing[END_REF].

However, further studies comparing biological and mechanical idle motion are required to examine whether the biological dimension of idle motion could be responsible for the influence on the early cerebral processes associated with affective resonance.

The LPP has been associated with perspective taking in previous study [START_REF] Fan | Temporal dynamic of neural mechanisms involved in empathy for pain : An event-related brain potential study[END_REF][START_REF] Sessa | Double dissociation of neural responses supporting perceptual and cognitive components of social cognition : Evidence from processing of others' pain[END_REF][START_REF] Vaes | Minimal humanity cues induce neural empathic reactions towards non-human entities[END_REF]. [START_REF] Fan | Temporal dynamic of neural mechanisms involved in empathy for pain : An event-related brain potential study[END_REF], showed that this component was sensitive to painful vs. neutral stimuli only when participants were asked to judge the pain (vs. counting the number of hands in the picture). In the same vein, Sessa and colleagues (2014) showed that this component was larger for the presentation of a painful context (presentation of a sentence) compared to a neutral context and was not sensitive to a facial expression of pain compared to a neutral expression. Interestingly, Vaes and collaborators (2016) showed that increasing the humaneness of non-human entities (by describing vegetables with human names rather than adjectives) enhanced late ERP at right centroparietal sites. The authors interpreted this result as related to mind attribution during the humanization process of non-human entities. Hence, the larger rLPP in the present study might suggest that idle motion would enhance mind attribution in characters by increasing their humanness in the participants' eyes. Interestingly, the positive correlation between the effect of idle motion on participants' pain rating and its effect on the rLPP would suggest that the more idle motion contributed to strengthen mind attribution to the virtual character, the more the participants judged its pain as intense compared with the still condition. Although this hypothesis needs to be confirmed by future studies, the biological dimension of movement may be paramount in this process of mind attribution. As suggested by Vaes and collaborators (2016) the late ERP at right centro-parietal sites may be related to the activation of the rTPJ as this brain area was already associated with the degree of humanness of a stimuli [START_REF] Krach | Can Machines Think? Interaction and Perspective Taking with Robots Investigated via fMRI[END_REF]. Moreover, a tDCS study targeting the rTPJ showed that a cathodal stimulation (a stimulation that decrease the neuronal excitability) at CP6 site led to a decrease in the participants' pain judgment of a facial expression of pain [START_REF] Coll | The effect of tDCS over the right temporoparietal junction on pain empathy[END_REF]. This decrease in the participants' pain judgment could be due to a decrease of their ability to overcome their egocentric bias [START_REF] Coll | The effect of tDCS over the right temporoparietal junction on pain empathy[END_REF] as the rTPJ is known to be involved in the self-other distinction [START_REF] Lamm | Imaging empathy and prosocial emotions[END_REF][START_REF] Preckel | On the interaction of social affect and cognition : Empathy, compassion and theory of mind[END_REF].

Particularly, the right supramarginal gyrus seems crucial to avoid an egocentric bias during the judgment of others state [START_REF] Silani | Right Supramarginal Gyrus Is Crucial to Overcome Emotional Egocentricity Bias in Social Judgments[END_REF]. Thus, by giving participants the illusion of being in presence of an agent imbued with intention, idle motion may have helped participants to overcome an egocentric bias. Participants would then be more focused on the behavioral cues of the virtual character to judge its pain, resulting in an increased perceived intensity. However, due to the poor spatial resolution of EEG, other studies with fMRI for instance could help to test this hypothesis on the role of the rTPJ in the interpretation of idle motion in the context of interaction with a virtual character.

Conclusion

Taken together, the present results showed that idle motion increased both the early negative affective response (N2-N3) and the late positive response (rLPP) associated with perspective taking, demonstrating its usefulness to create a more ecological empathic reaction to the character's expression of pain. Idle motion could have the potential to reduce or suppress the remaining differences in brain response between the observation of virtual

  Body Animation. For the Idle condition, the character's body was animated with pre-recorded human postural oscillations, i.e., movements resulting from dynamic human equilibrium and breathing. For the Still condition, the character's body was fixed at the initial posture of the person in the pre-recorded motion capture sequence (see the method section of Treal et al., 2021 for details).

Figure 1 -

 1 Figure 1 -Left side: virtual character's facial expression of pain at the beginning of the clip (AUs at 40% of the maximum contraction). Right side: virtual character's facial expression of pain from 400ms to 1000ms (AUs at 60% of the maximum contraction).

  ]) [t(19) = 3.23, p = .004, d = .74]. ERPs. P2: Paired t-test did not reveal a significant difference on the P2 component between the Idle (mean = -0.77 µV, 95% CI [-1.6, 0.06]) and Still conditions (mean = -0.71 µV, 95% CI [-1.47, 0.05]) [t(19) = -0.40, p = .697, d = -.09] (Figure 2). N2-N3: Paired t-test revealed that the N2-N3 component was significantly more negative in the Idle condition (mean = -1.54 µV, 95% CI [-2.29, -0.79]) than in the Still condition (mean = -1.25 µV, 95% CI [-2.00, -0.49]) [t(19) = -2.24, p = .037, d = -.51] (Figure 2).

Figure 2 -

 2 Figure 2 -Average time-course for event-related potentials in the Idle and Still conditions recorded at frontocentral electrodes (C1, C2, Cz, FC1, FC2, FCz). (* p < .05)

Figure 3 -

 3 Figure 3 -Average time-course for event-related potentials in the Idle and Still conditions recorded at centroparietal electrodes (C1, C2, Cz, CP1, CP2, CPz)

Figure 4 -

 4 Figure 4 -Average time-course for event-related potentials in the Idle and Still conditions recorded at right centro-parietal electrodes (C4, C6, CP4, CP6). (* p < .05)

Figure 5 -

 5 Figure 5 -Correlation between the difference of the right late positive potential (rLPP) between the Idle and Still conditions and the difference in the pain judgment between the Idle and Still conditions.