J Gaspar

Y Corre

F Rigollet

M-H Aumeunier

E Bernard

S Brezinsek

X Courtois

R Dejarnac

M Diez

L Dubus

N Ehret

N Fedorczak

M Firdaouss

M Houry

M Le Bohec

T Loarer

C Martin

V Moncada

P Moreau

C Pocheau

P Reilhac

E Tsitrone

Overview of the emissivity measurements performed in WEST: in-situ and post-mortem observations

This paper summarizes the emissivity measurements performed on the plasma facing units (PFU) of the WEST lower divertor during the first phase of WEST running with a mix of actively cooled ITER-like PFUs made of bulk tungsten and inertially cooled PFUs made of graphite with a coating of tungsten. In-situ assessment of the emissivity and laboratory measurements after removing the W-coated graphite and ITER-grade PFUs from the WEST device are shown. The measurements exhibit a complex pattern with strong emissivity variation as function of space and time mainly explained with the variation of magnetic equilibrium (strike point location) as well as the plasma performances during the experimental campaigns. The exposed ITER-grade PFU exhibits sharp spatial variation of the emissivity from 0.05 to 0.85 at a monoblock scale (12mm) at the transition of the erosion (strike point location) and deposition (next to the strike point location) areas on the high field side. In the low field side, the emissivity varies from 0.12, at the strike point location, to 0.2 few cm away in the low field side direction. This emissivity range after exposure is much higher than the emissivity variation of unexposed PFU with emissivity from 0.09 to 0.15. In-situ observation performed on the W-coated graphite PFU shows a rapid evolution, typically few pulses, of the emissivity in the inner and outer strike point location. The whole spatial distribution is discussed as well as his variation due to the plasma operation from the start-up of WEST to the removal of the tungsten (W) coated graphite components.

Introduction

Infrared (IR) thermography is widely used in fusion research to study the heat load distribution on the plasma facing units (PFU) [START_REF] Houry | The very high spatial resolution infrared thermography on ITER-like tungsten monoblocks in WEST Tokamak[END_REF][START_REF] Sieglin | Power load studies in JET and ASDEX-Upgrade with full-W divertors[END_REF][START_REF] Sieglin | Real-Time Infrared Thermography at ASDEX Upgrade[END_REF] as well as ensuring their protections [START_REF] Courtois | Full coverage infrared thermography diagnostic for WEST machine protection[END_REF][START_REF] Balboa | Upgrade of the infrared camera diagnostics for the JET ITER-like wall divertor[END_REF][START_REF] Arnoux | A protection system for the JET ITER-like wall based on imaging diagnostics[END_REF][START_REF] Jakubowski | Infrared imaging systems for wall protection in the W7-X stellarator[END_REF]. To these ends, assessing the emissivity of tungsten (W) components, as used for the ITER divertor [START_REF] Hirai | Use of tungsten material for the ITER divertor[END_REF][START_REF] Pitts | Physics conclusions in support of ITER W divertor monoblock shaping[END_REF], is necessary to derive accurate surface temperature from radiation measured by infrared systems. The W emissivity is low and dependent on various parameters as wavelength, temperature, and surface state such as its composition (oxidation, impurities) and its structure (roughness, cracks, deposited layers). During plasma operation, the PFU surface state is expected to evolve as function of time because of the plasma wall interaction processes which are likely different from pulse to pulse. Consequently, this is strongly affecting the emissivity value and distribution [START_REF] Terry | Divertor IR thermography on Alcator C-Mod[END_REF][START_REF] Fedorczak | Infra-red thermography estimate of deposited heat load dynamics on the lower tungsten divertor of WEST[END_REF][START_REF] Vondracek | Divertor infrared thermography on COMPASS[END_REF][START_REF] Doerner | Investigation of He-W interactions using DiMES on DIII-D[END_REF]. As a first step, a dedicated setup has been developed to measure the emissivity of W samples representative of the WEST lower divertor, including samples with different damage levels generated by electron gun (micro-cracks and crack network) [START_REF] Gaspar | Emissivity measurement of tungsten plasma facing components of the WEST tokamak[END_REF]. The experimental results show, as expected, the dependencies with wavelength, temperature and surface state (roughness, cracks, pollution by impurities). For the same wavelength and temperature, the surface state shows a strong influence with a large increase of the emissivity with the micro crack and cracks network, by a factor up to 4. However, the samples used in this study did not see plasma operation that could have modified the surface state through plasma surface interaction (erosion, deposition and possible damages) [START_REF] Gray | Dependence of divertor heat flux widths on heating power, flux expansion, and plasma current in the NSTX[END_REF][START_REF] Diez | In situ observation of tungsten plasma-facing components after the first phase of operation of the WEST tokamak[END_REF][START_REF] Sitjes | Wendelstein 7-X Near Real-Time Image Diagnostic System for Plasma-Facing Components Protection[END_REF]. As a second step, an in-situ method has been developed to assess the emissivity evolution of the WEST divertor PFUs [START_REF] Gaspar | In-situ assessment of the emissivity of tungsten plasma facing components of the WEST tokamak[END_REF]. The method is based on the measured infrared (IR) radiance, coming from isothermal PFUs at several temperature levels, to be compared with embedded thermal sensors before each pulse with the consideration of multiple reflection through photonic modelling. The third step relies on post-mortem measurements to carefully evaluate the emissivity in laboratory. This paper presents an overview of the emissivity measurements performed on the WEST divertor PFUs of the first phase of WEST where the divertor is composed with a mixt of W-coated graphite and ITER-grade PFUs. The paper is divided in two parts, the first part shows the in-situ assessment of the W-coated graphite PFUs. The method developed in [START_REF] Gaspar | In-situ assessment of the emissivity of tungsten plasma facing components of the WEST tokamak[END_REF] has been applied over two experimental campaigns showing significant progress regarding the plasma performances (time duration and injected power). The emissivity distribution and its evolution with the plasma conditions: strike point location, cumulated time and energy, wall conditioning and fueling (H/D/He) are discussed. The entire W-coated graphite components have recently been removed to equip the lower divertor with actively cooled components (WEST phase 2) allowing post-mortem studies. The second part of the paper summarizes the post-mortem emissivity measurements performed in laboratory. The emissivities of W-coated and ITER-grade PFUs have been measured for a large number of PFUs allowing the observation of the emissivity distribution over a ripple modulation (toroidal section of 20° of the machine) but also within a millimeter scale.

Emissivity evolution during WEST operation

Thermal measurements and emissivity calculation

The phase 1 of operation of WEST extending from 2017 to 2020 is composed by five experimental campaigns named from C1 to C5 [START_REF] Bucalossi | Operating a full tungsten actively cooled tokamak: overview of WEST first phase of operation[END_REF]. During this period, 3889 plasmas have been performed for a total plasma duration of about 7h15 and 21.2 GJ of cumulated injected energy, mainly electron heating using lower hybrid launchers (LHCD heating), in various divertor configurations: lower single null (LSN), upper single null (USN) and double null (DN). In LSN configuration the inner strike point (ISP) and outer strike point (OSP) are located on the lower divertor which is composed by 12 independent toroidal sectors of 30°. Each sector is equipped by 38 plasma facing units (PFUs), thus a total of 456 PFUs is required to cover the full divertor ring (see figure 1 a). During the phase 1, the lower divertor was composed of a mix of actively cooled ITER-like and inertially cooled W-coated graphite PFUs. A set of ITER-grade PFUs based on the W monoblock concept with 35 flat monoblocks (MB) of individual size ~28 mm × 12 mm × 26 mm (width × depth × height) assembled with a gap of 0.5 mm on a CuCrZr heat sink tube [START_REF] Missirlian | The WEST project: Current status of the ITER-like tungsten divertor[END_REF] have been tested before the full completion of the divertor foreseen in phase 2. The number of ITER-grade PFU increased over the campaigns with 6 PFUs during C1 and C2, 12 PFUs during C3 and 14 PFUs during C4. The lower divertor was completed with inertially cooled graphite PFUs with a W-coating (~15 µm) and 1° toroidal bevel geometry, each unit is composed by one component for the ISP (high field side) and one for the OSP (low field side [START_REF] Firdaouss | Heat flux depositions on the WEST divertor and first wall components[END_REF] (see figure 1b)). The temperature of the WEST lower divertor is monitored during and in-between pulses by a set of complementary thermal diagnostics: 20 thermocouples (TCs) sensors embedded in the component at 7.5mm below the surface [START_REF] Gaspar | First heat flux estimation in the lower divertor of WEST with embedded thermal measurements[END_REF], 4 Fiber Bragg Grating (FBG) probes including 11 sensors each [START_REF] Corre | Integration of fiber Bragg grating temperature sensors in plasma facing components of the WEST tokamak[END_REF] embedded at 3.5 and 7mm below the surface and standard IR thermography systems [START_REF] Courtois | Full coverage infrared thermography diagnostic for WEST machine protection[END_REF]. The standard IR system used in this analysis consists of actively cooled endoscope located at the top of the chamber monitoring the lower divertor. The IR cameras are equipped with a narrow filter at the wavelength 3.9 ± 0.1μm with a frame size of 640x512 pixels. The IR system is calibrated and translate the collected radiance into blackbody surface temperature (emissivity equal to 1). The projected pixel size is about 2.5 mm/pixel for the reported PFU studied in this paper. One IR camera is monitoring a sector (Q6A) equipped with onboard diagnostics 16 TCs including broader PFUs with 4 TCs (x2 inner and outer) and flush-mounted LPs [START_REF] Dejarnac | Flush-mounted Langmuir probes in the WEST tokamak divertor[END_REF] as illustrated in fig 1 c). These PFUs are located at the maximal heat load location due to the ripple magnetic field modulation (PFU#21 for the outer and PFU#31 for the inner side respectively). The following analysis is based on this two PFUs for the in-situ measurements. The last 4 TCs are installed in another sector not studied here.

The temperature of the inertial W-coated graphite PFUs increases over the day due to the repetition of energetic pulses while the rest of the vacuum vessel is maintained at 70°C thanks to the water cooling loops. During the C4 campaign from July to November 2019, 1442 discharges have been performed, in which 1112 and 330 are fueled with deuterium and helium respectively, corresponding to a cumulated plasma duration of 9678 s and 2991 s. The total injected energy (radio frequency and inductive heating) is about 15.96 GJ with almost 6.31 GJ conducted to the divertor for a duration of 10112 s in LSN configuration. For the C4 campaign, about 20 days exhibit divertor temperature increase sufficiently high to estimate the emissivity. Figure 2 a) shows the evolution of the initial temperature (as recorded before the pulses with the TC system) over the last 4 days of the campaign (helium campaign) with an initial temperature increase from 70°C up to 345°C and 246°C for OSP (red) and ISP (blue) PFUs, respectively. The rest of the device is mainly kept to 70°C the temperature of the water-cooling loop. The figure 2 b) shows the toroidal distribution of the initial temperature for the 10 instrumented PFUs that follows the ripple modulation. In [START_REF] Gaspar | In-situ assessment of the emissivity of tungsten plasma facing components of the WEST tokamak[END_REF] a method was developed to estimate in-situ the emissivity of the W-coated graphite divertor tiles in the WEST tokamak. The method is based on the simultaneous recording of the IR radiance and TC coming from isothermal PFU at several temperature levels before each pulse. The collected radiance is composed of two terms. The first one is the emitted radiance depending on PFUs temperature and its emissivity, the second one is the reflected radiance coming from the surrounding and self-reflection of the divertor on itself due to multiple reflection in the metallic high reflective environment. The radiance is measured twice, when the PFU is at the two different temperatures 𝑇 1 and 𝑇 2 . The measured radiances by the IR system can be written as follows:

𝐿 𝑚1 = 𝜀𝐿 𝐵𝐵1 + 𝐿 𝑟1 (1)
𝐿 𝑚2 = 𝜀𝐿 𝐵𝐵2 + 𝐿 𝑟2 ( 2
)
where 𝜀 is the emissivity (supposed unchanged or low variation at the two temperatures), 𝐿 𝑚1 and 𝐿 𝑚2 are the measured radiances at the PFU temperatures 𝑇 1 and 𝑇 2 , 𝐿 𝐵𝐵1 and 𝐿 𝐵𝐵2 are the blackbody radiances computed with the temperatures 𝑇 1 and 𝑇 2 given by the TCs, 𝐿 𝑟1 and 𝐿 𝑟2 are the reflected radiances when the PFU temperatures are at 𝑇 1 and 𝑇 2 . Usually, 𝐿 𝑟1 and 𝐿 𝑟2 are considered equal. In the WEST tokamak environment, this assumption cannot be made due to the high reflective environment provided by metallic surfaces. In this configuration the reflected radiances variation must be calculated. The emissivity map is finally given by: 𝜀 =

(𝐿 𝑚1 -𝐿 𝑚2 )-(𝐿 𝑟1 -𝐿 𝑟2 ) (𝐿 𝐵𝐵1 -𝐿 𝐵𝐵2 ) (3)
Photonic simulations have been performed using the Monte Carlo raytracing code SPEOS CAAV5 [START_REF] Aumeunier | Infrared Thermography in Metallic Environments of WEST and ASDEX Upgrade[END_REF] to calculate the variation of reflected radiance ∆𝐿 𝑟 = 𝐿 𝑟1 -𝐿 𝑟2 [START_REF] Gaspar | In-situ assessment of the emissivity of tungsten plasma facing components of the WEST tokamak[END_REF].

Evolution of the emissivity distribution along the divertor during C4 (a) (b)

To follow the emissivity evolution during the C4 campaign, 160 pairs of pulses have been investigated from the pulse #54800 to #55987 coming from 20 different experimental days featuring significant temperature increase of the divertor. The pulses have been paired up with pulses of the same day to limit the emissivity variation between the two measurements. The selected pulses also fulfil the requirements on the TC measurement of Tinit > 95°C and heating between pulses higher than 30°C to have enough IR signal.

Figure 3 shows the emissivity map evolution for 7 pulses covering the C4 experimental campaign for the ISP tile #31 (top) and OSP tile #21 at the maximal heat flux location (therefore not at the same toroidal location as displayed in fig 1a). All the pulses are equivalent deuterium plasmas in terms of plasma current, density and injected power except for the last pulse which the last one of the helium campaign. For the deuterium plasmas the main difference for the 6 pulses is the magnetic equilibrium and especially the location of the outer strike point. The emissivity pattern exhibits sharp variations with poloidal and toroidal distribution, completely different on the ISP and OSP. The emissivity is found to be higher on the ISP than OSP, up to 0.6 on larger extend. On the ISP the high emissivity area also varies in the poloidal direction. On the OSP the low emissivity area is dominant and consistent with the outer strike point area featuring intensive sputtering processes over about few cm length (equivalent to the particle and heat flux decay length). The emissivity values displayed here are very close to emissivity measurement performed on pristine W coating 0.122 ± 0.006 [START_REF] Gaspar | Emissivity measurement of tungsten plasma facing components of the WEST tokamak[END_REF] with the same wavelength (3.9µm) at 200°C. Still on the OSP, the area of high emissivity corresponds to the start of the magnetic shadowing induced by the baffle located above the lower divertor. One can also note the complex and discontinues evolution of the emissivity pattern along the C4 experimental campaign.

Figure 4 (a) shows the emissivity distribution evolution during C4 from the pulse #54811 to #55987 with color variation from blue to red. The emissivity distribution is extracted in the PFU center regarding the toroidal coordinate. Figure 4 (b) shows the cumulated conducted energy to the lower divertor as function of the strike point location computed with the magnetic reconstruction (EQUINOX [START_REF] Blum | Reconstruction of the equilibrium of the plasma in a Tokamak and identification of the current density profile in real time[END_REF]). The conducted energy is calculated as function of time, with the radiated power taken from the bolometry system and subtracted to the total injected power integrated with 0.5 s time step and distributed with 1/4 ISP and 3/4 OSP on each strike point location during this time step (to be consistent with the IN/OUT asymmetry reported in [START_REF] Gaspar | Divertor power loads and scrape off layer width in the large aspect ratio full tungsten tokamak WEST[END_REF]). It is important to stress that the conducted energy plotted here have no consideration on heat flux decay length and the spatial resolution of the figure corresponds to the IR spatial resolution on these PFUs. One can note that the maximum cumulated energy is located between r=2.11 m and 2.15 m (corresponding to MB15-18) and r=2.21 m and 2.28 m (MB [START_REF] Aumeunier | Infrared Thermography in Metallic Environments of WEST and ASDEX Upgrade[END_REF][START_REF] Gaspar | Divertor power loads and scrape off layer width in the large aspect ratio full tungsten tokamak WEST[END_REF] for ISP and OSP respectively. The figures 3 and 4 illustrate the large variation of the emissivity during C4, especially on the inner side. The variations go from 0.12 ± 0.01, close to the pristine W-coating value, to 0.65 ± 0.05 showing a variation higher than a factor 5 for a single PFU that can be linked to an important variation of the surface state or structure as we can observe in the figure 1 b). It is important to stress that this variation (factor 5) is much higher than the emissivity variation due to temperature measured equal to 0.122 at 200°C and 0.148 at 550 °C as observed in laboratory [START_REF] Gaspar | Emissivity measurement of tungsten plasma facing components of the WEST tokamak[END_REF]. The emissivity distribution can be linked to pulse scenario and plasma parameters. In the figure 4 from the inner to the outer sides, the first arrow shows the increase of the emissivity from ~0.2 to ~0.5 constantly during C4 probably due to impurity accumulation 15 cm away from the inner strike point location, which is mainly at R = 2.13 m. The second arrow shows a strong decrease of the emissivity for 2.02 < R < 2.08 m from ~0.6 to ~0.4. This decrease happens during the last 4 days of C4 dedicated to helium plasmas, performed for PFU ageing study with the usual magnetic configuration (BT = 3.7 T, X-point height about 75 mm) but with plasma current (Ip) equal to 300 kA contrary to deuterium plasma mainly performed with Ip = 500 kA. These two main differences could strongly affect the erosion redeposition pattern in the inner side and explain the strong emissivity decrease probably by impurity removing in this area. The third location in the circle corresponds to an emissivity decrease at R=2.03 m for the last 13 helium plasmas performed with Ip=350 kA showing the sensitivity of the emissivity distribution to the plasma current. The fourth set of arrows illustrates the three principal outer strike point locations performed during C4. These locations can be also correlated to the locations where the emissivity is minimal at different moment in the campaign. These variations will be discussed in the next section.

Pulse to pulse emissivity variation near the outer strike point location:

During the C4 campaign, experiments have been performed with different X-point heights resulting in different outer strike point locations (from R=2.21 up to 2.29 m corresponding to MB24-28). Figure 5 shows the emissivity and conducted energy during 4 pulse sequences featuring fixed magnetic equilibrium (a, b, c and d) right after a change of strike point location. Emissivity and cumulated conducted energy before and after the pulse sequence (last pulse) are plotted in black and red respectively. The conducted energies for these pulses are: (a) 230 MJ for 12 similar pulses at R=2.27 m, (b) 720 MJ for 24 pulses at R=2.25 m, (c) 112 MJ for 8 pulses at R=2.29 m and (d) 2197 MJ for 106 pulses at R=2.235 m. These different periods correspond to experiment performed in the EU framework during C4 (a) PFU shaping experiment [START_REF] Grosjean | First analysis of the misaligned leading edges of ITER-like plasma facing units using a very high resolution infrared camera in WEST[END_REF], (b) predamaged PFU experiment [29], (c) sustained melting experiment [START_REF] Corre | Sustained W-melting experiments on actively cooled ITER-like Plasma Facing Unit in WEST[END_REF] and (d) the helium campaign [START_REF] Tsitrone | Investigation of plasma wall interactions between tungsten plasma facing components and helium plasmas in the WEST tokamak[END_REF]. The experiments (a), (b) and (c) have been performed with deuterium fueling and about 4 MW of LHCD heating, average core density was about 3.5 10 19 m - 3 and Ip = 500 kA. The main difference between the 3 sequences is the X-point height varying from 75 to 120 mm resulting in 3 different strike point locations. The pulse parameters of the helium campaign (d) are Ip=300-350 kA, average core density about 3.8 10 19 m -3 and PLH ~ 4 MW. The figure 5 shows the emissivity variation from 0.12 to 0.2 in few cm, equivalent to the heat flux decay length on the target. The comparison of the 4 selected experiments shows the correlation between the strike point location and the minimal emissivity location with an outer shift about 1 cm. The shift is inside the magnetic reconstruction uncertainty and coherent with the shift of few mm between strike point and maximal heat flux location due to the power spreading in the private flux region. Sequences(a), (b) and (c) show that a fast emissivity modification after only few hundreds of second of cumulated plasma duration. Case (c) even shows a 20% decrease of the emissivity at R = 2.295 m for only 8 pulses with a conducted energy of 112 MJ. On the other side, the sequence (d) shows a stagnation for the emissivity profile when the same plasma scenario is repeated even for a long period of time (about 2000s), here 106 pulses with a conducted energy of 2197 MJ contrary to the inner side where the emissivity continues to vary as shown in the figure 4. The minimal emissivity value seems to converge to the value of the pristine W coating about 0.12, consistently with the assumption of net erosion area and therefore a surface structure mainly composed of tungsten atoms. The figure 5 (d) shows also that the hollow freshly made during the period (c), at R = 2.295 m, disappears and exhibits a more uniform emissivity profile in this area consistently with the particle and heat flux decay lengths. The emissivity pattern obtained during sequence (d) is the result of two major changes: the magnetic equilibrium and plasma wall interaction processes with helium plasma, combined with a potential effect of boronization performed between these two sequences. The boronization and glow discharge effects will be discussed in the next section.

Effect of wall conditioning on emissivity

Wall conditioning is essential in fusion machine to achieve high plasma performance and reliable operational domain. The three conditioning techniques used in WEST is baking up to 200°C, glow discharge conditioning (GDC) [START_REF] Bucalossi | The conditioning procedures in Tore Supra after CIEL implementation[END_REF] using deuterium or helium and boron wall coating through GDC of diborane called boronization. Baking is generally performed before the campaign begin. Deuterium or helium GDC are performed all along the campaign several times per week depending on wall condition and start-up performances. During C4 a total of 210 h with 160 h and 40 h of deuterium and helium GDC have been performed, respectively. Boronization have been performed 13 times during C4 for a total duration of 52 h of diborane GDC. The standard procedure of boronization starts with a deuterium GDC (1 to 4 hours), followed by a helium GDC (30min to 1 hour), then the diborane GDC begins and takes about 2 to 6 hours, depending on the diborane consumption rate. The last step is composed by again a helium GDC (about 40min) and sometimes deuterium GDC (1 to 3 hours). After boronization the surfaces are covered by a boron layer and the impurity flux released from the wall is reduced temporarily. The layer is eroded by the plasma, in particular near the strike point locations, and lose progressively his capability of reducing the impurity influx particularly for the oxygen [START_REF] Bucalossi | Operating a full tungsten actively cooled tokamak: overview of WEST first phase of operation[END_REF]. As boron layer will cover the PFU after a bozonization, it is interesting to track the possible modification of the lower divertor emissivity after a boronization.

(a) (b)

The 15th and 17th of October 2019 two consecutive boronizations have been performed because of an air leak happened the 16 th of October with a vacuum vessel pressure increase from about 10 -5 to 2.10 - 2 Pa. The air leak from a visible camera window was fixed after several hours and followed by deuterium GDC before the second boronization. The total duration of different GDC during this period is 10 hours of deuterium GDC, 3 h 30 min of helium GDC and 15 h 30 min of diborane GDC. Figure 7 shows the estimated emissivity of the last pulse (black) before the boronizations and the estimated emissivity three pulses (red) after it. The pulses used to get the emissivity are twins, they have the same magnetic configuration and cumulated energy of about 40 MJ. No strong modification of emissivity is seen except a 30 % increase at R= 2.09 m suggesting an accumulation on bore in this area (3 cm away from the inner strike point). On the outer side, the emissivity profiles are very close before and after boronization. Unfortunately, the emissivity cannot be estimated right after the boronization due to the need of divertor heating to perform the measurement. Nevertheless, we can conclude that the emissivity in the divertor is weakly affected by the boronization after few pulses.

Emissivity distribution before and after C5

Figure 8 shows the emissivity distribution along the divertor in the PFU center obtained with in-situ method at the end of C4 after the helium campaign [START_REF] Tsitrone | Investigation of plasma wall interactions between tungsten plasma facing components and helium plasmas in the WEST tokamak[END_REF] (black) and C5 after deuterium campaign(red) with the cumulated energy conducted to the divertor before and during C5. Post-mortem measurement performed in laboratory with the same filter (3.9 ± 0.1μm) is also shown in the figure in blue. The testbed will be briefly described in the next section. The error bars correspond to the evaluated uncertainty due to the TC and IR measurements, here the uncertainty remains mainly on the IR measurement due to the low signal of the IR signal due to the narrow filter. First, the comparison of the emissivity distribution after C4 and C5 shows equivalent patterns, with a small increase of emissivity during C5 at the strike point areas and ~5 to ~10 cm away from the inner strike point area (RISP~2.13m) for ~2.02<R<~2.08m. Finally, the comparison of the in-situ assessment of the emissivity at the end of C5 (red) and the postmortem measurement (blue) shows equivalent pattern but important discrepancies in the amplitude. The post-mortem measurement exhibits higher emissivity on most of the PFUs. Only the high field side edge (R<2m) of the inner PFU and the low field side edge (R>2.35m) show equivalent emissivities with the in-situ measurements. The difference is ~0.06 at the inner and outer strike point where the in-situ assessment shows 0.13 ± 0.06 and 0.08 ± 0.03, respectively. This difference goes up to ~0.21 in the high emissivity areas where the emissivity is about 0.57 ± 0.08 (+37%) for the inner PFU and 0.35 ± 0.04 (+60%) for the outer PFU. Surprisingly the high emissivity area where the IR signal is higher are not the area with the best match. The post-mortem measurement has been performed 9 months after the end of C5 with the machine put back to the atmosphere, handling to remove the PFUs from the machine, storage under atmosphere and packaging to the laboratory. These several steps could modify the surface state of the PFUs leading to a variation especially in the high emissivity area where the impurity deposition is maximal. The differences could also come from the complementary sources regarding the IR emission and collection. First, a degradation of the IR transmission could lead to error on the in-situ assessment as the method relies on the IR calibration with a constant transmission during the campaign. But measurement of the optics after C5 reveals no significant change on the transmission of the IR systems during this campaign. Secondly, the in-situ emissivity calculated with the equation 3 uses a correction factor due to the evolution of the reflected radiance in the two thermal scenes used for the calculation. This reflected radiance variations have been evaluated with the photonic code SPEOS with simplified assumption as uniform low emissivity of the divertor. The consideration of non-uniform emissivity with high emissivity on the divertor could lead to a decrease of this correction. However, this correction of ~10% [START_REF] Gaspar | In-situ assessment of the emissivity of tungsten plasma facing components of the WEST tokamak[END_REF] is lower than the emissivity differences observed which is from 37 to 60% for the high and low emissivity area, respectively. Work is ongoing to disentangle the contribution of the different points. For the last point, work is ongoing to develop an inverse method based on the numerical twin of the WEST tokamak to estimate the emissivity distribution instead of using the double heating method [START_REF] Talatizi | Inverse radiation problem with infrared images to monitor plasma-facing components temperature in metallic fusion devices[END_REF] without assumption on their values or distribution.

Post-mortem emissivity measurement after the WEST phase 1

During the shutdown between C4 and C5 the W-coated PFUs and the unshaped ITER-grade PFUs of the sectors Q4B and Q3B, see figure 9 a) and c), have been replaced by ITER-like PFUs with toroidal bevel of 1° as expected in ITER. From the 76 PFUs only the PFU#18 of the Q3B sector has been kept for C5 and installed at the location #8, where heat load is maximum due to the ripple modulation, in order to perform melting experiment on the monoblock #28 [START_REF] Corre | Sustained W-melting experiments on actively cooled ITER-like Plasma Facing Unit in WEST[END_REF]. To complete the in-situ observations, the emissivity of the removed PFUs have been measured in laboratory, especially for the ITER-grade PFUs for which the emissivity cannot be monitored in the machine because they are actively cooled.

Two dedicated testbeds have been developed to measure the emissivity map of the full actively cooled and W-coated graphite PFUs. The double heating method is used to obtain the emissivity using the equation 3. As we control the testbed environments, we can consider here 𝐿 𝑟1 =𝐿 𝑟2 at the two temperatures, simplifying the emissivity calculation and reducing potential errors on the evaluation of the reflected flux evolution. For the ITER-like PFU testbed, the PFUs are heated though the PFU cooling tube using thermostatic bath. While for the second testbed, the W-coated graphite PFUs are heated in an oven. In both testbeds the PFUs are heated at 30°C and 70°C, each temperature the PFUs are measured by an IR camera in the wavelength range from 3 to 5 µm, contrary to 3.9 ± 0.1 µm in the machine, to optimize the signal noise ratio at this temperature level. The frame size is of 640x512 pixels, a 25 mm lens is used to get the full PFUs with a projected pixel about 0.7mm/pixel. A 50 mm lens with an extension ring is also used to have a field of view of about 4 monoblocks of the ITER-like PFU with a projected pixel about 0.08mm/pixel close to the very high-resolution IR view [START_REF] Houry | The very high spatial resolution infrared thermography on ITER-like tungsten monoblocks in WEST Tokamak[END_REF]. The uncertainty on the measured emissivities is about 4% and has been evaluated with Monte Carlo error propagation calculation considering errors on the PFU temperature of 1 °C and the IR calibration optimized for these measurements. This uncertainty will be displayed on some figures and removed for other for clarity. In any case the uncertainty on the measured emissivity remains much lower than the spatial distribution observed.

Emissivity pattern of the sectors Q4B and Q3B post-C4

A total of 30 PFUs have been measured with different PFU locations consecutive in the ripple modulation (20° period representing about 25 PFU) over two sectors. The set is composed of 14 ITERgrade PFUs and 16 W-coated graphite PFU divided into 2 components (located on the low and high field sides of the divertor). The emissivity maps obtained for these PFUs are shown in the figure 9 b) and d) superimposed to the pictures taken in the machine after the C4 campaign figure 9 a) and c). In addition to the exposed PFUs and for comparison, measurement have also been performed for unexposed ITER-grade and W-coated PFUs as shows in figure 10 b). The poloidal and toroidal distributions found on the W-coated PFUs (Q4B sector, figure 9 b) are consistent with the pattern found with in-situ measurement in the previous section (figure 3) with some differences on the high emissivity regions as discussed in the subsection 2.5. On the OSP region of the W-coated PFU (figure 9 b) the emissivity is found minimal down to 0.08 slightly lower than non-exposed W-coated PFUs from 0.09 to 0.15 (figure 10 b). This lower emissivity is due to a decrease of the roughness in this area and a cleaning of the surface in comparison to nonexposed PFU which are slightly polluted by their manufacturing (see next section 3.2). Because of the 0.5 mm toroidal bevel, the emissivity is higher in the magnetically shadowed areas (left hand part of the PFU for the OSP) up to 0.7 for the OSP PFU #22, due to impurity redeposition from neutral particles near the leading edge as observed in [START_REF] Balden | Erosion and redeposition patterns on entire erosion marker tiles after exposure in the first operation phase of WEST[END_REF]. The poloidal extension of the low emissivity area is about 10 cm. The toroidal extension of this area is coherent with the ripple modulation of the magnetic field: broader areas where the incident angle is minimal (<0.5°) around PFU#19 and thinner areas where the outer incident angle is maximal (>2°) around PFU#32 (as illustrated in figure 12, the grey area are the magnetically shadowed area). The other area with high emissivity is at the transition, in the far SOL and poloidal direction, from the wetted area (top part) to the magnetic shadowed area due to the baffle (bottom part). This area exhibits emissivity up to 0.75 on the whole toroidal extension of the divertor. In the magnetic shadowed area under the baffle, the emissivity lies between 0.3 (close to the wetted area) and 0.15 (10 cm away under the baffle). On the ISP region of the W-coated PFU (figure 9 b) the emissivity is found minimal down to 0.12 in the range of the unexposed PFU and slightly higher than observed on the OSP area. A first difference is observed on the poloidal extension of this low emissivity (net erosion) area, lower than 3cm for the ISP area and 10cm for the OSP limited by the baffle shadowing. Another difference is observed in the toroidal direction, contrary to the OSP region, the emissivity is found uniform on the ISP even for the ISP PFU#32 where the incident angle is minimal about 0.4° inducing strong magnetic shadowing due to the 0.5 mm bevel. On the ISP, plasma temperature, particle and heat flux are found to be lower, therefore local erosion and redeposition might also be lower on the ISP than the OSP. At the border with the private flux region, just below the ISP area, iridescent appears and high emissivity up to 0.8 is observed with variation from 0.12 to 0.8 within a few cm. In the private flux region, the emissivity is about 0.4 until the gap between the inner and outer PFUs. On the scrape off layer side (top part in figure 9 b), the maximal emissivity is about 0.85 with sharp transition within a few mm from the net erosion area. The emissivity pattern exhibits also a non-uniform variation with bumps and hollows. h MB#15 ISP (mm) -0,3 0,29 -0,06 0,27 -0,24 0,01 0,31 0,06 0,04 -0,37 0,67 -0,37 0,42 0,17

Average incident angle (°) 0,42 0,46 0,52 0,62 0,76 0,92 1,08 1,24 9 d) is quite similar to the shaped Wcoated PFUs. Once again, we found the low emissivity area at the strike point locations and sharp transition to high emissivity around these positions: in the outboard, in the baffle shadowing, in the private flux region and finally in the inboard, in the far scrape off layer area, few cm away from the inner strike point (see figure 10 a) and c)). However, the emissivity variation is higher with variation from 0.05 to 0.85 (factor 17) at a MB scale due to the complex plasma wall interaction because of the gap geometry, the various vertical misalignments and magnetic shadowing between PFUs As the ITERgrade PFUs are unshaped the knowledge of the PFU alignment is necessary to understand the emissivity pattern on the MB scale. To monitor the vertical misalignment (h) between adjacent PFUs, WEST is equipped with a 3D ball probe measuring arm which has a ± 18μm precision [START_REF] Gunn | Thermal loads in gaps between ITER divertor monoblocks: First lessons learnt from WEST[END_REF]. The misalignment measured for the 14 PFUs at the MB#15 and #25 locations (main strike point locations) have been summarized in the table 1, the toroidal shadowing induced by these misalignments are also shown with typical values of the incident angle at the different locations in the ripple modulation.

A complex pattern is observed especially in the outer area (see figure 11 a) featuring large toroidal variation in the plasma wetted area. For example (see figure 11.b), misaligned MBs (>0.2mm) exhibit a toroidal bump with emissivity of about 0.06 at the leading edge over the first 3 mm then a bump (up to 0.4 for PFU#7 (blue) and #8 (red), factor 7) about 5 mm away then slow decrease toward the trailing edge (down to 0.06 on PFU#8 (red) and PFU#17 (red) in figure 11 b)). This toroidal bump is observed on most of the PFU with overexposed leading edges and no shadowing from the upstream PFU (positive misalignment, see table 1) at the maximal loaded location for the PFU #07 and 08 and also close to the minimal loaded area with respect to the ripple modulation for the PFU#17. This pattern makes the IR analysis more complex as this pattern can evolve also during the campaign and with the strike point location [START_REF] Grosjean | Interpretation of temperature distribution observed on W-ITER-like PFUs in WEST monitored with a very-high-resolution IR system[END_REF]. The potential mechanisms leading to such feature, in particular the ion Larmor smoothing effect, have been studied in [START_REF] Grosjean | Interpretation of temperature distribution observed on W-ITER-like PFUs in WEST monitored with a very-high-resolution IR system[END_REF]. Still on the OSP area, the PFUs #14, #18 and #20 exhibit also strong emissivity up to 0.8 (figure 9.d) because of the recessed position of these PFU regarding the previous one (negative value of the misalignment, see table 1). The heat flux distribution and magnetic shadowing are computed with the PFCFlux code [START_REF] Firdaouss | Heat flux depositions on the WEST divertor and first wall components[END_REF] on the sector Q3B for the pulse #55987 with the ITER-grade PFU moved with the measured misalignments, as displayed in figure 12 (magnetic shadowing is shown in grey color). The resulting simulations show strong shadowing due to upstream PFU for PFU#14, 18 and #20, which is consistent with the high emissivity observed for the outer MBs (thses MBs are prone to intensive particle redeposition). More surprisingly the emissivity at the ISP is always low for the 14 PFUs even for the PFU#7 where the emissivity at the ISP is down to 0.06 even though the whole ISP MB should be shadowed. The number of ITER-grade PFU increased over the campaigns and the PFU location have been also reshuffled between the different campaigns for the physics needs of the WEST scientific program, see table 2. However, no strong correlation appears between the emissivity pattern and the PFUs history, showing that the emissivity pattern is mainly the picture of the last campaign exposure.

Campaign

(b) (a)

Figure 12. Normalized heat flux computed for the sector Q3B with the PFCFlux code [START_REF] Firdaouss | Heat flux depositions on the WEST divertor and first wall components[END_REF] for the pulse #55987 without asymmetry and 𝜆 𝑞 = 6𝑚𝑚 [START_REF] Gaspar | Divertor power loads and scrape off layer width in the large aspect ratio full tungsten tokamak WEST[END_REF] projected to the divertor (no spreading factor in the private flux region). The ITER-grade PFU have been moved according to the measured misalignment. The white area corresponds to the magnetic shadowed area especially visible for the PFU 14, 18 and 20.

Comparison of post-mortem measurements and emissivity distribution

After C3 and C4 experimental campaigns, W-coated PFUs with additional W marker coating have been analyzed using ion beam analyses and scanning electron microscopy techniques [START_REF] Balden | Erosion and redeposition patterns on entire erosion marker tiles after exposure in the first operation phase of WEST[END_REF]. The net erosion and deposition patterns in the inner and outer side of the WEST lower divertor were determined. As expected, strong erosion occurred at the inner and outer strike point area with an average net erosion rate of >0.1 nm/s over the campaigns. On the inner side, thick deposition composed of B, C, O and W of >10 μm for a 5-10 cm wide band is observed on the high field side with a sharp transition from the strong net erosion area. Outside this wide band moderate deposition is observed, even at the outer strike point location. These observations are in good agreement with the emissivity pattern observed with the in-situ (evolution during the campaign) and post-mortem measurements as illustrated in the figure 13. At both strike point location low emissivity about 0.1 close to the unexposed PFU (green crosses in figure 13 b) is found coherent with net erosion area. On the outer side, few cm away to the outer strike point (s350 mm), higher emissivity is found about 0.2 coherent with moderate deposition. On the inner side, the wide band of 5-10 cm observed on the C4 W-coated marker PFUs correspond to the high emissivity area up to 0.85 (for 100<s<220 mm).

In addition to emissivity measurements, roughness measurements have been performed at different location of the two PFUs at the inner and outer maximal loading location PFU#19 and #32, respectively see figure 13 a) and for the ITER-grade PFU#08 see figure 13 b). For the W-coated PFUs, the measured roughness is in the range from 1.3 to 1.8 µm, slightly lower than the unexposed PFUs measured at ~2.4 µm, except in the thick deposit area (from s~100 to ~220 mm in the figure 13) where the roughness increased up to ~4 µm with large standard deviation indicating non uniform roughness. This is coherent with strong deposition area and the subsequent surface modification observed with the in-situ emissivity measurement during the last 4 days of C4, experimental campaign performed with helium fueling (see figure 4 arrow #2). Equivalent pattern is observed for the ITER-grade PFU with roughness from 0.14 to 4.56 µm with low roughness in the strike point areas from 0.14 to 0.3 µm slightly lower to the values measured before installation and high roughness for the MB#6 to #12 up to 4.56 µm (see table 3). The standard deviation of the emissivity plotted in the figure 13 b) shows the strong emissivity variation at the MBs scale as for the MB#13 with emissivity from 0.05 to 0.85. Although, the high emissivities observed in the inner edge (s<100m), in the private flux region (s~280 mm) or in the outer side, in particular in the baffle shadowing area (s~450 mm), cannot be attributed to strong deposition or roughness increase. This could be explained by surface oxidation, as suggest the surface iridescence and post-mortem analysis that revealed the presence of W oxide in the deposit layer of ITER-grade PFU [START_REF] Martin | First post-mortem analysis of deposits collected on ITER-like components in WEST after the C3 and C4 campaigns[END_REF].

Emissivity pattern in the inter-PFU gaps

After the C4 campaign, one of the actively cooled ITER-like PFU has been moved from minimum heat load area (PFU#18) to maximum heat flux area (PFU#8) on the OSP (see figure 12), in order to melt the monoblock #28 during the next experimental campaign (C5) [START_REF] Corre | Sustained W-melting experiments on actively cooled ITER-like Plasma Facing Unit in WEST[END_REF]. This PFU has been exposed only to the C4 campaign (small heat loading and moderate erosion condition), with deuterium and helium plasmas, and C5 campaign with only deuterium plasma (high heat loading and intense erosion condition in the OSP). Figure 14 shows the emissivity measured for this PFU after each campaign and the cumulated energy conducted on the PFU with a spatial resolution corresponding to the MB size. After C5 the emissivity pattern has changed mainly into two areas, on the outer side from MB#23 to #30 corresponding to the plasma wetted area and on the inner side from MB#6 to #13 corresponding to the thick deposit area described in the previous section. For the inner side the emissivity decreased drastically after C5 especially for the MB#6 to #10 with emissivity 2 times up to 4 times lower than the post C4 measurements. This important reduction could come from a modification of the deposit observed in this region, further analyses are planned to characterize this area in terms of roughness, surface composition and deposit thickness with comparison to the post C4 PFUs not exposed to the C5 campaign. In the ISP area for the MB#14 to #16 the emissivity slightly decreases from ~0.1 post C4 to ~0.07 post C5. Finally, far away at the high field side of the PFU (R<2 m) and at the private flux region transition (R~2.15 m) the emissivity remains mainly unchanged.

Figure 15 shows the emissivity measurement with a zoom in on the OSP area from MB#23 to #30 with a spatial resolution of 0.08 mm/pixel. The emissivity strongly changed during C5 with an overall decrease from ~0.9 to ~0.1 because of the increase of the particle and heat loads.

• On MB#24, the emissivity decrease allows the visualisation of the 4 IR markers holes (prone to material redeposition). • On MB#25, corresponding to the main OSP location during the last part of C5, exhibits low emissivity on the whole MB surface coherent with net erosion area. • For the MB#26 to #30, the emissivity decreased in the MB center and increased at the leading edge, bottom part of the MB, during C5 despite the misalignment of +0.3 mm showing impurity deposition few cm away from the strike point location even with leading edge. Figure 16 shows the emissivity of the top and lateral surfaces of the PFU#8 after C5 for the full PFU and zoom in at both strike point areas. On the PFU sides, on both leading and trailing edges, the measurement shows low and high emissivity on the wetted (because of the 0.3mm vertical misalignment [ref alex]) and shadowed areas respectively. The high emissivity area suggests impurity deposition in the inter-PFU gap of 0.5 mm. This impurity deposition occurs from the MB#5 to #18 on the high field side and from MB#22 to #32 on the low field side corresponding to a poloidal extension higher than the strike point locations. Figure 17 shows the emissivity along the curvilinear abscissa for the MB at both strike point locations with identification of the leading and trailing edge. The measurement exhibits high emissivity ~0.8 up to 5 mm below the top surface for the outer leading edge and up to 0.4 for the outer trailing edge. For the inner side the emissivity is in the range of 0.6 on both edges with also 5mm depth in the gap. This depth corresponds to 10 times the gap size of 0.5 mm between two PFUs. Below this area, the emissivity decreases down to ~0.1 which indicates the limit of the plasma impact. On the OSP leading edge of the MB#28, we can distinguish a rectangle (2.3 mm depth and 9 mm width) corresponding to the surface in front of the PFU#7 groove where the W melting occurs [START_REF] Corre | Sustained W-melting experiments on actively cooled ITER-like Plasma Facing Unit in WEST[END_REF]. This area exhibits high emissivity even at the melting location probably due to deposition occurring during the month of operation after the melting experiment with the OSP away from the MB#28.

Conclusion

This paper summarizes the emissivity measurements performed on the plasma facing components of the WEST lower divertor inside the machine during the C4 (2019) experimental campaign for the Wcoated graphite PFUs and in laboratory after removing the W-coated and ITER-grade PFUs. The measurements clearly show a complex pattern with strong emissivity variation and his evolution during the campaign.

In the machine, the emissivity monitoring along the C4 campaign has been performed with the emissivity estimation for 160 pairs of pulses along the campaign. This monitoring has shown strong correlation of the emissivity distribution to the plasma operation, especially for the strike point location, plasma species and plasma current. On the inner side, emissivity increases from 0.12 to 0.65 has been observed 15 cm away from the strike point location. As well as fast modification of the emissivity distribution during the last 4 days with an emissivity decrease from 0.6 to 0.4 few cm away from the strike point location. During these days helium plasmas at Ip=300kA have been performed after a campaign with mainly deuterium plasmas at 500kA (with BT=3.7T). On the outer side the monitoring has shown that the emissivity distribution strongly depends to the strike point location with variation from 0.12 to 0.2 in the wetted area. When the strike point is moved at a new location the emissivity starts to decrease down to 0.12 locally (where Te>20 eV) and increase at the previous strike point location up to 0.2. These emissivity modifications occur in few pulses with additional LH heating of about 4 MW and cumulated conducted energy of few hundred of MJ. Finally, the emissivity monitoring has not shown strong modification of the emissivity due to the wall conditioning by deuterium or helium GDC or even boronization with equivalent emissivity distribution observed before and after three pulses after wall conditioning performed.

Post-mortem measurements have been also performed with dedicated laboratory testbeds. These measurements confirmed the in-situ observations in terms of complex spatial distribution and sharp spatial evolution of the emissivity from 0.05 to 0.85 at a MB scale. These measurements have shown emissivity variation over a ripple modulation with the measurement of 16 W-coated graphite PFUs and 14 ITER-grade PFUs. The emissivity pattern is coherent with the ripple modulation and the modulation of the shadowed area due to upstream PFU with high emissivity in the shadowed area. The ITER-grade PFUs have shown equivalent pattern to the W-coated PFUs with more complex distribution in the strike point area with strong toroidal variation from 0.06 to 0.4 in few mm in the toroidal direction. The comparison of the emissivity distribution with roughness measurements indicate that the high emissivity could be attributed to different causes. In the thick deposit area (mainly B, C, O and W [START_REF] Balden | Erosion and redeposition patterns on entire erosion marker tiles after exposure in the first operation phase of WEST[END_REF]) the roughness is in the range of the IR wavelength leading to an increase of the emissivity in addition to the compound of the deposit which are also a good emitter as B and C. The other areas with high emissivity could be due to oxide as the iridescent color suggest as well as first Raman measurements.

The number of ITER-grade PFU increased over the campaigns and the PFU location have been also reshuffled between the different campaigns for the physics needs of the WEST scientific program. However, no strong correlation appears between the emissivity pattern and the PFUs history showing that the emissivity pattern is mainly the picture of the last campaign exposure. This point combined to the strong emissivity variation (factor 17) with complex pattern with strong variation in the poloidal and toroidal directions imply the necessity to develop an in-situ procedure to measure the emissivity at a day scale to be able to derive accurate surface temperature from IR measurement over all the experimental campaigns

Figure 1 .

 1 Figure 1. (a) Top view of the machine with typical heat load pattern on the lower divertor due to the ripple modulation (20°), the sector distribution, the Ion Cyclotron Resonance Heating (ICRH) and Lower Hydrid Current Drive (LHCD) antennas and diagnostics. (b) Picture of the sector Q6A after the 2019 campaign (C4). A total of 10 W-coated graphite PFUs were equipped with 16 TCs which are indicated by their tile number on (b) and (c). In this section, we investigate TC measurements located on the outer #21 and inner #31 tiles. (c) Blackbody temperature measured by the IR view before the pulse starts (featuring homogenous tile temperatures) with the tile numbers and the diagnostics location.

Figure 2 .

 2 Figure 2. (a) Evolution of the initial temperature over the last 4 days of the C4 campaign, helium plasma, for OSP PFU #21 (red cross) and ISP PFU #31 (blue circle) PFUs. The green vertical lines correspond to the first pulse of each day. (b) Toroidal distribution of the initial temperature for the pulse #55987 for the 10 instrumented PFUs (red cross) PFU #21, (blue circle) PFU #31 and (black cross) PFU #13 to #29.

Figure 3 .

 3 Figure 3. Emissivity map for the ISP tile #31 (top) and OSP tile #21 (bottom) of the sector Q6A during C4 for the pulses: #54811, #54973, #55113, #55570, #55762, #55829, #55987 (C4 end).

Figure 4 .

 4 Figure 4. (a) Emissivity distribution along the lower divertor, for the ISP tile #31 and OSP tiles #21 of the sector Q6A, for 160 pair of pulses during the C4 campaign from the pulse #54811 (blue) to the pulse #55987 (red), with color graduation from blue to red. (b) Illustration of the conducted energy to the lower divertor at the strike point location with asymmetry of 1/4 ISP and 3/4 OSP as observed in [26] and no consideration of decay length (λq). (black) Conducted energy before the pulse #54811 and (red) between the pulses #54811 and #55987. (see Movie01 online)

Figure 5 .

 5 Figure 5. Emissivity distribution and conducted energy along the Q6A OSP tile #21 of the divertor for 4 experiments with different strike point location. Mean strike point location at: (a) R=2.27 m, (b) R=2.255 m, (c) R=2.29 m and (d) R=2.235 m. (black) Emissivity and conducted energy before the first pulse of the experiments and (red) emissivity for the last pulse and conducted energy over the experiment. (see Movie02 a/b/c/d online)

Figure 6 .

 6 Figure 6. (a) Emissivity distribution along the Q6A OSP tile #21 of the divertor with strike point location at R=2.255 m, (black) first pulse of the experiment, (red) typical pulse of the experiment. (b) Langmuir probe measurement for the pulse #55070, (red) electron density, (blue) electron temperature and (black) parallel heat flux estimated assuming Te=Ti (𝑞 // = 𝛾𝐽 𝑆𝐴𝑇 𝑇 𝑒 with γ=7).

Figure 7 .

 7 Figure 7. Emissivity distribution (black) before boronization and (red) three pulses after it, pulses #55541 and #55553, respectively.

Figure 8 .

 8 Figure 8. (a) Emissivity distribution along the lower divertor, for the ISP tile #31 and OSP tile #21 of the sector Q6A, for (black) the last pulse of C4, (red) the last pulse of C5 and (blue) ex-situ measurement after C5. (b) Illustration of the conducted energy to the lower divertor at the strike point location with asymmetry of 1/4 ISP and 3/4 OSP as observed in [26] and no consideration of heat flux decay length (λq). (black) Conducted energy from (black) C1 to C4 and (red) for C5.

Figure 9 .

 9 Figure 9. (a) Picture of the Q4B sector after the 2019 campaign (C4). Part of the divertor baffle can be seen at the bottom. (b) W-coated emissivity map from ex-situ measurement superimposed to the Q4B sector picture. (c) Picture of the Q3B sector after the 2019 campaign (C4). (d) ITER-like emissivity map from ex-situ measurement superimposed to the Q3B sector picture. The radial strike point extension are indicated with dotted lines in the pictures as well as the maximum heat load areas due to the ripple modulation in red.

Figure 10 .

 10 Figure 10. (a) Emissivity map after C4 for W-coated PFUs and ITER-like PFU from the location #7 of the sectors Q4B and Q3B, respectively (same location in the ripple pattern). (b) Emissivity map for non-exposed PFUs (9 Wcoated PFUs and one ITER-grade PFU). (c) Emissivity distribution for (black) non-exposed W-coated PFUs, (green) non-exposed ITER-grade PFU, (red) W-coated after C4 and (blue) ITER-grade PFU after C4 extracted from figure (a).

Figure 11 .

 11 Figure 11. (a) Emissivity map of the PFU #07, #08 and #17 with a zoom in on the OSP area. (b) Emissivity along the curvilinear abscissa sMB (toroidal direction) in the MB#27 center of the PFU (blue) #07, (red) #08 and (green) #17.

Figure 13 .

 13 Figure 13. (a) Emissivity map and picture of the W-coated tiles ISP PFU#19 and OSP PFU#32 on the Q4B sector after C4. Comparison of the emissivity distribution (red), roughness measurements divided by 10 (blue) and the deposition observed in [36]. (b) Emissivity map and picture of the PFU #08 (ITER-grade) on the Q3B sector after C4. Comparison of the average emissivity with standard deviation (red) and roughness measurements divided by 10 for each MB (green) before and (blue) after WEST exposure see the roughness values in the table 3.

Figure 14 .

 14 Figure 14. (a) Emissivity map for the same PFU from the sector Q3B after C4 and C5 located at the location #18and #8, respectively. Illustration of the conducted energy to the lower divertor at the strike point location with asymmetry of 1/4 ISP and 3/4 OSP as observed in[START_REF] Gaspar | Divertor power loads and scrape off layer width in the large aspect ratio full tungsten tokamak WEST[END_REF] and no consideration of decay length (λq). (black) Conducted energy during C4 and (red) C5. (b) Emissivity distribution along the same PFU from the sector Q3B after C4 (black) and C5 (red) located at the location #18 and #8, respectively.

Figure 15 .

 15 Figure 15. (a) Emissivity map (zoom in on the OSP area) for the same PFU from the Q3B sector after C4 (top) and C5 (bottom) located at the location #18 (lower heat loading) and #8 (higher heat loading), respectively. (b) Emissivity distribution after C4 (black) and C5 (red) in the middle of the PFU (dotted lines in (a)).

Figure 16 .

 16 Figure 16. Emissivity map of the PFU #8 after C5. (top) Full PFU with top and lateral sides with the 25 mm lens (0.7mm/pixel). (bottom) Zoom in for 4 MBs at the inner (left) and outer (right) strike point locations with the 50 mm lens (0.08mm/pixel).

Figure 17 .

 17 Figure 17. Emissivity of PFU #8 after C5 measured in the MB center along the curvilinear abscissa sMB with sMB =0 mm at the junction between the leading edge and the top surface. (a) Inner strike point MB (blue) #13, (red) #14, (green) #15 and (magenta) #16. (b) Outer strike point MB (blue) #25, (red) #26, (green) #27 and (magenta) #28.

Table 1 .

 1 Misalignment (h) measured at the OSP (MB#25) and ISP (MB#15) of the WEST sector Q3B before the C4 experimental campaign. Positive values are prone to strong erosion on the leading edge, while negative values are prone to particle redeposition A total of 14 unshaped ITER-grade PFUs have been measured after C4. Although no shaping, the overall pattern measured on the ITER-grade PFUs (see figure

	1,4	1,53 1,65 1,71 1,76 1,76

Table 2 .

 2 Location of the C4 PFU over the experimental campaigns.

	PFU location

Table 3 .

 3 Averaged emissivity and roughness measured on the ITER-grade PFU#08 of the sector Q3B after the C4 campaign.

Acknowledgments

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 and ITER Organization.


domain: spi phys

text:
Q Herbette

E Géron

T Dichi

G Pillet

J Lucas

Losses do not prevent wide band metamaterial true time delay line applications, GaAs MMIC experimental verification

Losses are often the impairing feature of metamaterial true time delay line devices. In this paper we analytically demonstrate that ohmics losses in this kind of structures as well as impedance mismatch depend on the bandwidth. These results allow to consider wide band application for radar systems. It is verified experimentally that metamaterial delay line devices are fit for wide band delay line applications for they allow low insertion losses, low return loss and tunable delay.

Introduction

The multiplication of on-board RF systems in aeronautics for instance, along with the reduction of space available, especially in drones, makes it interesting to have many RF systems sharing the same antennas. Consequently as each system working frequency bands can be different, wide band antennas are required. Phase array antennas can be operated at a given frequency by controlling the phase between each radiating elements to pilot the RF beam [START_REF] Mailloux | Phased Array Antenna Handbook[END_REF]. The phase difference between radiating elements is required to compensate the different electrical paths length, generally in air, to the target of each radiating element. Doing so leads to constructive interference by summing in-phase waves in the selected direction. Consequently, to operate phase array antennas over a wide band, a flat group delay in the frequency band, which is equivalent to a propagation, is required and is often referred as true-time delay [START_REF] Zhang | Compact composite right/left-handed transmission line unit cell for the design of true-time-delay lines[END_REF][START_REF] Kim | A stepped-impedance true time delay line using GaAs MMIC technology[END_REF]. The issues, for radar applications for instance, are compactness, insertion loss, bandwidth and delay value which must correspond, in air, to the order of magnitude of the distance between the radiating elements.

In the last decade or so, works show the interest of making delay line using metamaterials [START_REF] Zhou | Design Considerations of Miniaturized Least Dispersive Periodic Slow-Wave Structures[END_REF][START_REF] Murase | Group delay equalised monolithic microwave integrated circuit amplifier for ultra-wideband based on right/left-handed transmission line design approach[END_REF][START_REF] Zhang | Compact composite right/left-handed transmission line unit cell for the design of true-time-delay lines[END_REF][START_REF] Lucas | Using a 1d bandgap metamaterial to build up a delay line[END_REF]. While the concept of metamaterial appeared in 1968 [START_REF] Veselago | The Electrodynamics of substances with simultaneous negative values of ǫ and µ[END_REF] , the first practical realization can be traced back to 1999 when Pendry [START_REF] Pendry | Magnetism from conductors and enhanced nonlinear phenomena[END_REF] proposed a design working at microwaves frequencies meeting the concept. In 1968 Velasago studied theoretical materials presenting special properties such as both negative permeability and susceptibility hence the prefix meta because those materials are not found in the nature. Their principle is that of inference between waves scattered by periodically spaced elements as the atoms in a crystal. Here one can see the link with solid state physics. This principle was early applied to electrical circuits such as electrical lines compound, delay lines, filters or couplers [START_REF] Islam | Coupled-line metamaterial coupler having co-directional phase but contra-directional power flow[END_REF][START_REF] Caloz | Electromagnetic Metamaterials: Transmission Line Theory and microwave applications/The Engineering Approach[END_REF][START_REF] Kahng | Compact metamaterial zeroth-order resonator bandpass filter for a uhf band and its stopband improvement by transmission zeros[END_REF][START_REF] Géron | Electronically controlled asymmetric microstrip line coupler underpinned by an hybrid right-left-handed line[END_REF] in which electrical waves propagate. It is usual to say that metamaterials allow band-gap engineering [START_REF] Caloz | Perspectives on EM metamaterials[END_REF][START_REF] Eleftheriades | EM transmission-line metamaterials[END_REF][START_REF] Eleftheriades | Transforming Electromagnetics Using Metamaterials[END_REF]. That kind of design yields incremental delay potentially allowing large delays by adding elements. Unfortunately, these designs are generally characterized by high insertion loss and a low characteristic impedance of the obtained line preventing applications. Some work report that measured insertion loss in metamaterial structure are related to the bandwidth [START_REF] Nadége | Slow waves in locally resonant metamaterials line defect waveguides[END_REF].This had to be investigated to determine if it could allow practical wide band application.

In this paper, by analytically analyzing the relationship between bandwidth and both insertion loss and characteristic impedance, we show that it is possible to realize long delay line with a large bandwidth and good impedance matching by judiciously engineering the pass-bands of a metamaterial line. First we shortly give the basics of incremental metamaterial delay line application. The ohmic loss which is the preponderant factor in insertion loss is then analytically calculated. We show it varies proportionally to the inverse of the bandwidth. The same analytic approach is used to demonstrate that mismatch loss can be small for large bandwidth delay lines. Finally a wide band GaAs MMIC prototype presenting low insertion loss and delay compatible with antennas application ( i.e. delay equivalent to the propagation between radiating elements in air ) was realized to verify the theoretical performances.

Metamaterial lumped elements delay lines

A metamaterial lumped elements transmission line (MTL) is a periodic impedance structure whose periodicity length is small enough so that propagation can be neglected both between elementary cells and inside the cells themselves [START_REF] Caloz | Electromagnetic Metamaterials: Transmission Line Theory and microwave applications/The Engineering Approach[END_REF]. That kind of metamaterial can be modeled using a T impedance cell as presented in figure 1. We only consider here symmetrical cell metamaterial and we work at sufficiently low frequencies in order not to take into account the propagation between elementary cells.

Vn

Vn + 1

In In + 1 Z2 Z2 Z2 Z1 Z1 Z1 Z1
Elementary cell In this model Z 1 and Z 2 are any king of impedance. Using the chain matrix as in reference [START_REF] Eleftheriades | NEGATIVE-REFRACTION METAMATERIALS[END_REF] one shows that :

cos(θ) = Z 1 Z 2 + 1 (1)
Z 2 c = Z 2 1 + 2Z 1 Z 2 (2)
Where θ is the equivalent electrical length of the cell (ie the phase shift per unit cell: v n+1 = e jθ v n , j 2 = -1) and Z c the Bloch impedance of the built line. The Bloch impedance is the impedance of a periodical structure. In our case it is the ratio V n /I n anywhere on the considered infinite metamaterial line for a right or left propagating voltage-current wave. It is also practically the measured impedance from the generator when feeding the considered metamaterial line loaded with a resistor of value Z c . It can therefore be interpreted as the characteristic impedance of the metamaterial line. In what follows, we will use the term characteristic impedance when referring to Z c .

Vn

Vn + 1

L1 L1 C2 C1 C1
Elementary cell Any time cos(θ) goes beyond +1 or below -1, θ becomes complex and interference between the multiple scattered waves are destructive and extinction occurs.The electrical waves in the line are evanescent at the corresponding frequency. By judiciously choosing Z 1 and Z 2 , it is possible to engineer the frequency bands where the waves are evanescent (stop-bands) or propagating (pass-bands). When waves are evanescent the real part of θ is a multiple of π. When waves are propagating , θ is real and can even be negative, in which case the line is left handed. In so far the group delay G d = ∂ω ∂θ is concerned one could use indifferently a left or a right handed MTL. It would delay in the same way a wave packet. It is also possible to design a line presenting two bands. In those lines, the pass-bands are respectively left then right handed. By connecting the two bands one would increase the per cell delay, thus obtaining a greater delay per cell [START_REF] Collin | Foundation for microwave Engineering[END_REF][START_REF] Caloz | Electromagnetic Metamaterials: Transmission Line Theory and microwave applications/The Engineering Approach[END_REF]. Unfortunately that kind of structure is practically very difficult to tune. Finally we use a simple pass-band right handed structure whose cell is the simplest and is presented in figure 2 With the cell of figure 2 the pass-band circular frequency limits can be expressed as [START_REF] Lucas | Using a 1d bandgap metamaterial to build up a delay line[END_REF]:

ω 1 = 1 √ L 1 C 1 (3) ω 2 = 1 L 1 C 1 + 2 C 2 L 2 (4)
With that structure, loss-less capacitors and zero resistance inductors, one obtains the dispersion and extinction of figure 3. Here, one can see that there is no insertion loss in the pass-band when using ideal lumped elements and that only extinction occurs outside. With the linear estimation of figure 3 one obtains an order of magnitude for G d , the group delay per cell, which is also the incremental delay (ie step delay): To summarize those results, in the frequency band where the waves are propagating, the MTL line behaves as a standard propagation line with its standard parameters ie : characteristic impedance, propagation celerity, where the length unit is the cell. Consequently, without considering losses, it can be used to build a delay line, to obtain any delay stepped by G d the group delay per cell.

G d ≈ 1 2∆f (5)
Unfortunately, per cell insertion loss is often very high, thus limiting the applications of that kind of devices as delay lines by limiting the number of cells one can cascade.

Insertion loss in metamaterial delay lines

Former experiment [START_REF] Lucas | Using a 1d bandgap metamaterial to build up a delay line[END_REF] and simulations of this design show that losses are mainly due to the inductors internal resistance when a substrate with sufficiently low losses is used. We verified this point for GaAs (tan(δ) = 3 10 -4 ) and woven Teflon glass (tan(δ) = 9 10 -4 ). Let us rewrite equation 1 for the considered cell with inductors presenting an internal resistance r. Separating real and imaginary parts it comes:

ℜ e cos(θ) = C 2 C 1 + 1 -L 1 C 2 ω 2 (6)
ℑ m cos(θ) =rC 2 ω (7)
Only the imaginary part depends on r and is therefore responsible for the ohmic loss which is the expected result.

At first sight, considering again equation 7, it seems that ohmic loss increases with the frequency even without taking into account the rise of r with the frequency resulting from the skin effect. Surprisingly this result is not in agreement with simulations we performed, which led us to investigate more thoroughly. At a given frequency, r should be proportional to the L 1 inductor value. It is true for winded inductors meaning that both L 1 and r are proportional to the number of turns. It turns out to be true as long as the skin penetration does not increase too much the resistance. Practically, it is verified at low frequencies, or over small bandwidth, or for thin conductors as when using printed inductors with air bridges such as those used in MMIC [START_REF] Robertson | MMIC Design[END_REF] technology.

Let us assume that:

r = aL (8)
where a is a real positive number.

Solving the set of equation 3 and 4 with C 1 and C 2 as variables yields :

C 1 = 1 π 2 (2f c -∆f ) 2 L 1 (9)
C 2 = 1 4π 2 ∆f f c L 1 ( 10
)
where ∆f is the pass-band frequency width defined as ∆f = 1 2π (ω 2 -ω 1 ) and f c the central frequency :

f c = 1 2π ω 1 + 1 2
∆f . With equations 7, 9, 10 and eliminating L 1 it comes:

ℑ m cos(θ) = aω 4π 2 ∆f f c ( 11
)
which reads in the middle of the pass-band:

ℑ m cos(θ) fc = a 2π∆f (12)
This result is interesting. Indeed, considering equation 12, ohmic loss will increase with a which is intuitive. It will concomitantly decrease with the bandwidth which is not intuitive. It can be noted that considering a Left Handed structure and using the same analytic approach, the same behavior is obtained though with a different expression for ℑ m cos(θ) .

With equation 1, the ohmic insertion loss per cell in the middle of the pass-band finally reads as:

Ohmic Insertion Loss = 20 log 10 exp -.acos ∆f 4f c +  a 2π∆f (13)
In this equation f c stands for the pass-band central frequency and | | denotes the modulus. Figure 4 shows that for a = 2Ω/nH which is a typical value for MMIC (Microwave Micro Integrated Circuit) technology, the ohmic insertion loss is small (lower than 3dB) as soon as the bandwidth is greater than ≈500 MHz. One can see as well, that ohmic loss does not depend on the central frequency which is not obvious when considering equation 13. Consequently wide band applications for multi-systems antenna such as those presented in the introduction can optimistically be considered.

These results concerning ohmic insertion loss and group delay are most certainly very general for they have been also reported in reference [START_REF] Kahng | Compact metamaterial zeroth-order resonator bandpass filter for a uhf band and its stopband improvement by transmission zeros[END_REF] in a completely different kind of metamaterial. In this reference it stated without demonstrating it that losses must be related to the travel time of the waves in the material, which is related to G d , the latter depending as the inverse of ∆f (see equation 5).

Characteristic impedance

Of course metamaterial delay lines must be connected to other standard microwave equipment such as generators, amplifiers, filters, measurement apparatus, whose input and/or output impedance are classically 50 Ω. With equation 2, one can see that the characteristic impedance depends on Z 1 and Z 2 . If it is not close to 50 Ω, impedance matching will be required as in [START_REF] Lucas | Using a 1d bandgap metamaterial to build up a delay line[END_REF]. ∆f (via G d ) and f c are determined by the application requirements. Considering equations 9 and 10, one can only choose L 1 which is consequently the only degree of liberty to have some influence over Z c .

Using equations 9 and 10, Let us write Zc as a function of f c , ∆f and L 1 . It reads :

Z 2 c =π 2 (∆f ) 2 L 2 1 . 4f c 2 -1 4 (∆f ) 2 f 2 c (14)
It is interesting to note at this point that this value is valid whatever the frequency in the pass-band frequency width. Z c is constant in the pass-band.

As in section 3, the consequences of this result depends on whether a wide band application or a narrow band application is considered.

In the case of narrow band application (high group delay), the operating frequency of the delay line is far greater than the pass-band frequency width :f c ≫ ∆f . Consequently equation 14 can be approximated as :

Z c ≈ 2π∆f L 1 (15)
In that case Z c is proportional to ∆f whatever the value of f c which yields small characteristic impedance because ∆f is small. In the general case one has 0 < ∆f fc < 2 because the bandwidth is DC limited. Equation 14 can be rewritten as:

Z 2 c = 2πf c L 1 2 × ∆f fc 2 1 -1 16 ∆f fc 2 .
Finally one can plot as presented in figure 5 the normalized characteristic impedance as a function of the relative bandwidth ∆f fc as given by equation 16 :

Z c |Z L1 | = Z c 2πf c L 1 = ∆f f c 1 - 1 16 ∆f f c 2 (16) with 0 < ∆f f c < 2
In figure 5, as mentioned above, for small values of ∆f , and more accurately for ∆f fc < 0.5, the characteristic impedance at the middle of the pass-band is proportional to |Z L1 | = 2πf c L 1 which leads to small values of characteristic impedance. For greater values of ∆f fc , albeit not proportional, the characteristic impedance still increases with the relative bandwidth. This allows wide band delay lines without requiring impedance matching.

As an illustration of theses two situations, in reference [START_REF] Lucas | Using a 1d bandgap metamaterial to build up a delay line[END_REF]: ∆f = 100MHz, with f c = 2 GHz which yields

Experimental results using UMS GaAs MMIC Technology

In order to verify the precedent results and the feasibility of such delay lines, a prototype using the United Monolithic Semiconductors (UMS) PH25 GaAs process was realized. This process was chosen because it is open for shared runs. The goal was to obtain at least a 66 mm (3 10 8 /66 10 -3 =220 ps) air equivalent delay, compliant with inboard electronic antena applications, over a frequency bandwidth of at least 8-12 GHz. Considering figure 3, it can be seen that the group delay is stable only in the middle of the pass-band. So, to obtain a stable delay, it has been necessary to design a MTL presenting a larger pass-band frequency bandwidth than the required 8-12 GHz one. The reduction of the delay resulting from the larger bandwidth being eventually compensated by adding cells to increase the delay by G d as necessary. As the cost of an MMIC prototype depends on its size, we chose to use the standard 1.4×1.4 mm die which is the smallest compatible with the industrial packaging of UMS. Finally, we managed to fit a 10 cells MTL delay line with a (5-18)GHz bandwidth which makes it compliant with the required delay. The realized prototype is presented in figure 6. The geometrical constraints impact the performances by creating parasitic coupling. These coupling were taken into account using the PH25 components model provided by the foundry which are very accurate. We used theses model to simulate the design using the Advanced Design Software (ADS), 2016 version, from keysight technologies. Nevertheless these coupling effects did not prevent to reach the desired performances in spite of the meandering of the realized line. The prototype was designed for measurement using RF microwaves probes. The measurement were performed using a ROHDE&SCHWARZ ZNB40 VNA with Rosenberger Z40-X-GSG-150 RF probes. A classical SOLT calibration procedure was used with the coplanar CSR8 calibration substrate.

The measured S parameters show excellent agreement (Figure 7) with the simulated ones. From the S 11 measurement it is possible to verify that the delay line is nearly matched (Z c ≈ 60 Ω) . This point is necessary for wide band applications. By differentiating S 21 , the group delay presented in figure 8 can be calculated. The performances in term of delay are summarized in Table 1. In this table, the performances of a 50 Ω AsGa microstrip line long enough to exhibit the same delay are presented as a reference. One can see that it length is ≈ 62 times greater which demonstrate the efficiency of the MTL concept in so far the delay is concerned. Insertion losses are equivalent (-1.2 dB) but it is not a periodical structure and the above considerations do not apply and the delay relative variation is much lower. Such a long delay line can, unfortunately, not be embedded in a 1.4×1.4 mm die which is, here again, the reason why alternate ways to build up true type delay lines are researched. Finally, the performances of the prototype are, as with the simulation, compliant with the targeted performances.

Conclusion

We have presented the theoretical constrains of a wide band MTL delay line. Though wide band devices are in general more complicated to design, we have shown that in the case of MTL delay lines it is not the case. Indeed as soon as the bandwidth is large enough, insertion loss is low and the characteristic impedance can be large enough to avoid matching circuitry. For frequency bandwidth larger than 0.5 GHz, ohmic insertion loss is lower than 3dB and the characteristic impedance of these devices increases with the pass-band frequency bandwidth.

The delay in these MTL delay line devices can be controlled both by tuning the bandwidth or by simply adding cells. Those theoretical predictions have been verified on a prototype to demonstrate a Technology Readiness Level of 3.

Figure 1 :

 1 Figure 1: Metmaterial line: general symmetrical T cell model

Figure 2 :

 2 Figure 2: Right Handed pass-band MTL cell

Figure 3 :

 3 Figure 3: Dispersion (θ versus ω: blue) and extinction ( Vn+1 Vn versus ω: dashed red) in a Right Handed passband MTL

Figure 4 :

 4 Figure 4: Ohmic insertion loss per cell : a) as a function of the bandwidth ∆f , a = 2Ω/nH, b) as a function of the central frequency f c , ∆f = 100 MHz

Figure 5 :

 5 Figure 5: Normalized characteristic impedance versus relative pass-band width

∆f fc = 0. 5 .

 5 With L1 = 4.5 nH, |Z L1 | ≈ 56.5 Ω and Zc ≈ 56.5 × 0.05 ≈ 2.8 Ω. Consequently impedance matching was necessary. But for wide band application, for instance with ∆f = 10 GHz, f c = 10 GHz and L1 = 1 nH. One has |Z L1 | ≈ 63 Ω and ∆f fc = 1. This late value being greater than 0.5 we use ∆f fc and finally one has Zc ≈ 63 × 0.96 ≈ 60 Ω and no impedance matching should be required.

Figure 6 :Figure 8 :Figure 7 :

 687 Figure 6: UMS AsGa PH25 process 10 cells delay line prototype

Table 1 :

 1 [START_REF] Kahng | Compact metamaterial zeroth-order resonator bandpass filter for a uhf band and its stopband improvement by transmission zeros[END_REF] and S 21 parameters Performances of the prototype and reference line

	Bandwidth 8-12 GHz
		GaAs	GaAs
		MTL	microstrip
		delay line	line
	Total unfolded	400	25000
	length
	(µm)
	Group delay	71.7	70.44
	at 10 GHz
	(mm air)
	maximal delay	75.16	70.48
	(mm air)
	minimal delay	68.83	70.44
	(mm air)
	relative variation %	9.18	0.05
	(max-min )/min

Funding and acknowledgment

The authors would like to acknowledge Thales Systèmes Aéroportés for their funding and support to this project.