Calorimetry measurement for energy balance and energy distribution in WEST for L-mode plasmas

This paper presents the energy balance of 602 pulses from four different experimental campaigns for the WEST tokamak. Different magnetic configurations have been studied, with lower single null (LSN) and upper single null (USN) configuration with deuterium or helium plasmas. The energy balance is closed with an imbalance of about 5% of the total injected energy for most of the campaigns and for different magnetic configurations. The distribution over the whole machine is shown, with the outer first wall receiving most of the energy due to its large surface area with about 30% of the total heat load, and the divertor with 25% due to the heat loads deposited by the convected power in the scrape-off layer (SOL). Finally, the tomography inversion of the bolometry measurement allows us to disentangle the contribution of the radiated and convected power in the energy absorbed by each type of plasma-facing component. We show that in the USN configuration about 63% of the available energy in the SOL is deposited in the upper divertor (UDIV) through convected heat loads, while in LSN this value is spread over the lower divertor with 45% and the baffle and UDIV with about 10% for both.


Introduction
Power exhaust is a key issue for next-step fusion devices, such as ITER and DEMO.In particular, progress is required a See http://west.cea.fr/WESTteam.* Author to whom any correspondence should be addressed.
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. in understanding how the thermal loads are distributed on the various components (divertor, first wall, antenna…) in the vacuum vessel of present-day devices, in order to gain confidence in the modelling performed for next-step devices.The total energy injected into a tokamak during a pulse must equal that absorbed by the plasma-facing components (PFCs).Quantifying this balance is essential to providing important information for both plasma operation (wall protection) and plasma physics (particle and heat transport).In view of wall protection, an accurate energy balance is mandatory to push the experiment to maximum performance, towards high power and long plasma duration, while ensuring safe PFC operation.From the point of view of plasma physics, the heat load distribution over PFCs is essential to understand the physical processes at play and disentangle their contributions: convected power, radiated power, ripple losses, fast ions or electrons.Energy balance is however challenging to perform with the accuracy required, and in most present day devices, 25%-10% of energy is missing [1][2][3], furthermore, heat loads on the remote areas such as the vessel walls are still scarcely characterized.Recently in ASDEX Upgrade, a global energy balance with 5% of missing energy has been achieved based on calorimetry measurement with bolometric reconstruction and NBI loss calculation codes to close the energy balance in the remote areas [4].Performing the global energy balance based only on calorimetric measurements without modelling calculations is still challenging.
The WEST tokamak is perfectly suited to developing accurate and reliable energy balance with only calorimetry measurements.During the first five experimental campaigns (named C1 to C5), WEST operated with a mix of actively cooled ITER-like tungsten (W) PFCs and inertial W-coated graphite components in its lower divertor (LDIV) [5].WEST started its phase 2 of operation with the experimental campaign C7 with the LDIV fully equipped with actively cooled ITER grade PFC.The capability of performing high energy long discharges is crucial for gaining accuracy when assessing energy balance [6].WEST is also equipped with complementary thermal diagnostics: calorimetry and embedded measurement with thermocouples/Fiber Bragg grating.This wide set of complementary thermal diagnostics is a unique opportunity to perform heat load measurements and assess distribution, from the entire vessel scale with the calorimetry system down to the PFC scale with the embedded diagnostics.Energy measurement in the WEST tokamak is described in the section for actively cooled and inertial PFCs.Section 3 presents the energy balance and the associated distribution over the whole machine for a database of 602 pulses from different experimental campaigns and magnetic equilibriums.Finally, in the last section, the bolometry diagnostic is used to discriminate the radiated and convected contributions in the total measured heat load for each type of PFC.

Energy measurement in the WEST tokamak
WEST is a superconducting tokamak with actively cooled PFCs targeted at testing ITER tungsten divertor in a tokamak environment [5].To this end, the LDIV of WEST was progressively equipped with ITER grade divertor PFCs.The ITER grade PFCs of WEST are based on the ITER divertor technology with 35 actively cooled tungsten monoblocks assembled on a copper heat sink [7].During the first phase of WEST operation (from 2017 to 2021), the number of ITERgrade PFCs increased over the campaigns with 6 PFCs during C1 and C2, 12 PFCs during C3, 14 PFCs during C4 and 76 PFCs during C5 corresponding to 2 sectors (out of 12) fully equipped with ITER-grade PFC.During this phase, the LDIV was completed with inertially cooled graphite PFCs with a W-coating (∼15 µm).Each unit is composed of one component for the inner strike point (high field side) and one for the outer strike point (low field side [8]).Figure 1 shows the configuration of the LDIV before the campaign C5 with this mix of 2 sectors with actively cooled ITER-grade PFCs and 10 sectors with inertial W-coated PFCs.In 2022, WEST started its phase 2 of operation with the LDIV fully equipped with 456 actively cooled ITER-grade PFCs.The other parts of the machine are also water-cooled and they are illustrated in the figure 1 with a description of the PFC materials.Only the baffle (BAFF) components are not actively cooled due to leaks.All the PFCs are W-coated and only the vessel protections panels, located in remote areas receiving only radiated and charge exchange fluxes, feature a stainless steel at the surface.

Energy measurement for the actively cooled components
The active cooling of the PFCs is provided by a pressurized water loop divided into three parts as illustrated in the figure 1.The various PFCs correspond to 94 elements connected in parallel to the pressurized water loop.For example, the upper divertor (UDIV) contains 12 sectors of 30 • for a total of 360 • [2].The actively cooled PFCs can be classified in nine groups: (1) the LDIV partially or fully actively cooled depending on the campaign, (2) UDIV, (3) the BAFF only inertial in this study, (4) the inner first wall (IFW) composed by the inner bumpers and the vessel protection panels, (5) the outer first wall (OFW) only composed by vessel protection panels, (6) 2 lower hybrid (LH) antennae, (7) 3 ion cyclotron resonance (ICRH) antennae, (8) the antenna protection limiter (APL) not shown in the figure 1 and (9) the ripple and vertical displacement event (VDE) protections.The total surface of the components is about 136 m 2 , the IFW and OFW cover the largest part of the vacuum vessel, except for small gaps between sectors and the apertures if the unequipped ports, with a surface of 15 and 81 m 2 , respectively.
The PFCs outlet temperatures are exhaustively measured (94 sensors), while the inlet temperatures are measured in only two locations (upper part and global machine feeding pipe).The temperature measurements are made by using immersed Pt100 sensors outside of the vessel, one example of water heating on some components is shown for the pulse 54941 described in the figures 1(b) and (c).The flowrates are measured by VORTEX type flowmeters.Only 72 elements among 94, are equipped with flowmeters but thanks to symmetric cooling loop we can deduce the missing flowrate.The measured flowrates range from 1.4 to 13.5 m 3 h −1 depending on the components.These measurements allow to evaluate the thermal energy extracted by each part of the machine by (with the water flow, Cp the water heat capacity, T the inlet and outlet temperature and τ the transit time between the inlet and outlet temperature measurement): (1)

Energy measurement from the cooling phase of the inertial components
The temperature of the inertial PFC of the LDIV and the BAFF are monitored with IR camera [9], embedded measurement by thermocouple (TC) [10] and fiber Bragg grating (FBG) [11].Due to the difficulty of the emissivity evolving during the campaign [12] this study will rely only on the embedded measurements to derive accurate energy absorbed with the components.W-coated graphite components of the LDIV are equipped with 20 embedded TCs located at 7.5 mm below the surface [10] and 4 FBGs [11] embedded at 3.5 and 7 mm below the surface, an instrumented sector with 16 TCs is shown in the figure 2(a)).The BAFF is also equipped with 8 TC embedded at 5 mm from the surface in the W-coated CuCrZr component.Figure 2 shows an example of measurement for a tile equipped with 4 TC for the pulse 54941.
To derive the energy absorbed by the inertial PFCs during a pulse we use the temperature measurement during the cooling phase of the PFC between pulses as used at JET and well described in [1].The thermal contact between the inertial PFC and their support plate is poor, this leads to have slow cooling between pulses as illustrated in figure 2, allowing us to extrapolate the equilibrated temperature with a single exponential function, here determined between 600 and 2400 s, to the end of the pulse and use this temperature increase in the thermal energy calculation.The uncertainties of this method have been evaluated in the WEST case with three different comparisons.First, a 3D divertor tile instrumented by 4 TC has been modelled using the finite element code ANSYS and the energy determined from the cooling phase analysis has been compared to the energy used as input in the numerical calculations.Secondly, the energy determined in an experimental pulse with the cooling phase has been compared to the energy calculated from the heat flux (estimated from the embedded measurements, used to solve an inverse heat conduction problem to estimate the absorbed heat flux by the tile [10]).Finally, during the campaign C5 2 sectors of the LDIV were actively cooled, the energy measured by the calorimetry system described in the previous section and the energy determined with the cooling phase of the inertial components has been compared.An averaged uncertainty of about 15% has been determined for the cooling phase method from these comparisons.

Energy balance
The energy balance has been performed for 602 pulses in Lmode from four different campaigns (C3, C4, C5 and C7), see table 1.Only discharges with more than 10 MJ of injected energy have been analysed.The database is composed of 556 pulses in lower single null (LSN) configurations with both strike points on the LDIV and 46 pulses in upper single null (USN) configuration with both strike points on UDIV.All the pulses are deuterium plasmas except 91 pulses performed at the end of C4 with helium (He) plasmas [13].The injected energy is mainly from the LH antennae with about 15.9 GJ, 0.6 GJ from the ICRH antennae and 2.4 GJ of ohmic heating.For the campaign C7, only the first month of operation has been analysed as at some point of the campaign the pressurized water loop system has been modified to run with differential temperature for the PFC at 70 • C and the internal divertor coils at 50 • C to performed longer pulses higher than one minute.In this mode the inlet temperature is not constant with strong variation requiring further development for the analysis of the calorimetry measurements.During the C7 campaign we had also issues on the TC measurement of the BAFF and the  PT100 of the APL cooling loop leading to no measurement on these two groups of components.

Energy balance over campaigns and magnetic configurations
The figure 3(a)) compares the injected energy from the heating systems to the measured energy from the calorimetry system and the TC in the inertial PFCs for the 602 pulses of the whole database.The energy balance is excellent for the C4 and C5 campaigns for all magnetic configurations (LSN and USN) and also for helium plasmas, with only 5% of missing energy on average.These low values could correspond to the part of the machine where the absorbed energy from the plasma cannot be measured as the equatorial port in the OFW, some parts of the structure which are not monitored as the BAFF beam below the components.The C7 exhibits higher energy imbalance of about 17% due to the missing measurement of the BAFF and the APL (which are in the range of 9 and 1%, respectively).Considering these numbers, the missing energy of the C7 would have been in the range of 8% with all the measurements.Finally, the C3 campaign exhibits also higher energy imbalance despite the full coverage of the machine, this point will be discussed in the next sub-section.Figure 3(b)) shows the energy imbalance in percentage as function of the injected energy.The energy imbalance scattering is higher for low injected energy and almost constant for all the pulses with more than 30 MJ with different level for each campaign.This shows that, for pulses with higher injected energy, the energy balance will still be in the same range.

Energy distribution over the whole PFCs
Figure 4 shows the total energy measured as percentage of the injected energy for each PFC group for the different campaigns and magnetic configurations.The PFC receiving most of the energy is always the OFW with equivalent value for all the campaigns and magnetic configurations, only the campaign C7 exhibits slightly lower percentage with 26% instead of 31% on average.This high energy is due to his large surface and the radiated fraction which is mainly in the range of 50% [14], as these PFCs received only radiated  and charge exchange fluxes due to the high clearance, more than 20 cm, between the separatrix and the PFCs.The IFW receiving also only radiated power exhibits almost a constant value of 10% over the whole database, including C7.The second group of PFCs receiving a high fraction of the injected energy are the lower and UDIV during LSN and USN configuration, respectively.These energies are the combination of the radiated and convected heat loads from the scrape off layer (SOL).
In LSN configuration, for all the campaigns, the LDIV receives about 25% of the injected energy.Only the C3 campaigns exhibits much lower value of about 16%.These numbers are coherent with previous observations [15] of lower heat fluxes in the LDIV during C3 with embedded measurement as used for the energy measurement but also IR measurements.As for C3, the other groups of PFCs have equivalent percentage in comparison to the other 3 campaigns.The missing energy on the LDIV seems to be affected directly in the missing energy of the energy balance.
In USN, UDIV receives about 29% of the injected energy which is higher than the energy received by the LDIV in LSN configuration, for equivalent surface of about 6 m 2 and their symmetry.Still in USN configuration the LDIV receives only 6% contrary to UDIV receiving 10% in LSN configuration.This indicates that a part of the convected power in the SOL is intercepted by UDIV in LSN configuration.This point will be discussed in detailed in the next section.The BAFF receives about 9% and 5% in LSN and USN configuration, respectively.This difference indicates also that a part of the SOL is intercepted by the BAFF in LSN configuration.
The antennae are in the range of 3%-5% mainly from their lateral protection limiters due to the low external outer gap between the separatrix and the antennae of about few cm and the fast electron accelerated in front of the LH launcher and intercepted by the lateral protections.Finally, the last significant part of the energy goes on the ripple and VDE protections located on top of the machine.This energy is mainly due to electron ripple losses due to the strong ripple modulation at WEST [16].These measurements show that for long pulses studied here the averaged electron ripple losses are only in the range of 4 of 5%.Another point not illustrated in the figure is the good toroidal symmetry for the different groups of PFCs.

Radiated and SOL contribution over the PFCs
Plasma operation in WEST has been so far characterised by a relatively high fraction (∼50%) of input power dissipated by radiation [14,17].This exhaust channel is therefore important for the spatial distribution of energy on the WEST wall, with respect to the energy fraction channelled by plasma particles.In order to evaluate the radiation contribution to local energy loads on different wall elements, a multi-step treatment of bolometry measurements is deployed.First a synthetic projection basis was constructed relating local radiation emissivity to bolometer signals [17].Then a constrained tomography is applied, based on ad-hoc patterns distributed on reconstructed magnetic maps of the plasma (similar to patterns shown in [17] figure 9).Third, a second synthetic projection basis is applied to these inverted emissivity map, returning the local power flux (from radiation) to all local wall elements.Finally, this flux distribution is integrated in space over each macroelement of the wall, and in time, to return an estimate of the radiated energy absorbed by each wall element.(This entire framework is executed by an automated matlab solver called BOLO2wall).
This method can be directly benchmarked against calorimetry, for wall elements supposedly loaded by radiation only.The inner wall panel is only in contact with the plasma during initial and final ohmic limiter phases of discharges, whereas it is completely recessed from it during diverted L-mode plasmas (see figure 5(b)).For long diverted L-mode phases, the energy loads on this inner panel are thus largely dominated by radiation.Figure 5(a)) shows the comparison of the energy of the IFW measured with the calorimetry system and the radiated energy deposited on the IFW determined with the bolometry treatment.For all campaigns and diverted scenarios (LSN or USN), a quantitative agreement is found, within 10% of discrepancy, validating the bolometry treatment.This allows us to use this treatment for other groups of PFC to disentangle the radiated and convected energies in the calorimetry measurements.
Figure 6(a) compares the energy from the SOL deposited on all PFCs calculated with, in ordinate, the measured energy on LDIV + UDIV + BAFF + IFW + OFW + ANT + APL minus the radiated energy determined by BOLO2wall and, in abscissa, the energy available in the SOL (injected energy minus total radiated energy minus ripple losses from the energy measured for the PFCs RIPP/VDE).We have a linear tendency for each campaign showing the satisfactory energy balance.The C7 campaign in LSN is clearly below the other campaigns due to the missing data for the BAFF.
Figures 7 and 8 show the proportion of the radiated and convected energies for each group of PFC for all the campaigns and magnetic configurations.In LSN configuration, the convected energy from the SOL can be found mainly on the LDIV, as expected, for a percentage of about 45% of the total SOL energy.More than 20% is deposited on the OFW + ANT + APL mainly on ANT for the lateral APLs due to the small external outer gap in WEST as illustrated in figure 6(b)).Finally, the BAFF and the UDIV intercept also about 10% of the convected energy in the SOL.Contrary to the UDIV, this was expected for the BAFF due to the large part of the outer side of the LDIV which is magnetically shadowed by the BAFF and the low clearance of the BAFF edge with the separatrix.In USN configuration, the OFW + ANT + APL receive also about 20% of the available SOL energy but the UDIV goes up to 63% corresponding roughly to the sum of the deposited SOL energy on the BAFF plus the lower and UDIV in LSN.This difference can be attributed to the important clearance in USN (three times higher than in LSN) between    the separatrix and the lower part of the machine.For C4 in He LSN, the percentage of the SOL energy deposited on UDIV is increased to 16% with only 11% for deuterium plasma for the same magnetic equilibrium.This increase is coherent with the difference in plasma current with pulses at 300 kA with wider SOL for the He campaign in comparison to C4 in deuterium which was mainly at 500 kA.First comparison with edge modelling performed with SOLEDGE3X-EIRENE [18] on few pulses [19] showed that this difference between USN and LSN can be retrieved with edge modelling, more comparison will be performed in the future for different pulses of the studied database.
In addition to the database analysis the figure 9 compares the measured heating for two pulses with equivalent injected energy in LSN for the pulse 55517 (32.7 MJ) and in USN for the pulse 55778 (33.9 MJ). Figure 9(b) shows equivalent water heating for the IFW and OFW in the two magnetic configurations and a large increase of the heating for the UDIV components in USN configuration has seen previously with the database analysis.On the other hand, figure 9(c) shows the heating measured in an inertial tile of the LDIV located in the maximal heat flux area in the low field side.In LSN the poloidal distribution of the SOL heat load is clearly seen with different heating for the 4 TC poloidally spaced with heating from 180 • C for the TC at the outer strike point location to 10 • C for the TC far from the outer strike point location.In USN the TC heating are much lower and uniform with heating between 5 • C and 7 • C, coherent with heating by only plasma radiation.

Conclusion
A database of 602 pulses has been analysed, for each pulse the energy deposited on the whole tokamak has been measured with the calorimetry system for the actively cooled PFCs and with TC measurement embedded in the PFCs for inertial PFCs.The complementarity of these two thermal diagnostics allowed us to close the energy balance between the measured energy and the injected energy with a difference of about 5% on most of the campaigns and for all magnetic configurations with only calorimetry measurements.Moreover, this low value remains constant for pulses with injected energy from 30 to 160 MJ showing the robustness of the energy balance.
Thanks to the wide coverage of the calorimetry sensors with a full poloidal and toroidal coverage (94 thermal measurements and 72 flowmeters), the distribution of the energy over the whole machine has been determined.The distribution of the energy as a function of the magnetic equilibrium has been documented.The OFW appears as the group of PFCs receiving most of the energy, with more than 30% due to its high surface, then the lower or UDIV, depending on the equilibrium, is the second part of the machine receiving more than 25% of the injected energy.It has been found that ripple losses for the long pulses of the database are in the range of 4%-5%.Finally, thanks to the bolometry measurement and its tomography inversion, the contribution of the plasma radiation and the convected loads have been discriminated in the measured energy.In USN configuration about 63% of the available energy in the SOL is deposited in the UDIV though convected heat loads, while in LSN this value is spread over the LDIV with 45% and the BAFF and UDIV with about 10% for both.

Figure 1 .
Figure 1.(a) Inside view of WEST before the C5.(b) Main plasma parameters for the pulse 54941, (blue) plasma current (Ip), (red) injected power, (green) radiated power and (black) linear central density.(c) Water heating for 7 elements among 94 for the different type of components for the pulse 54941.

Figure 2 .
Figure 2. (a) IR showing the TC locations.(b) Temperature measurement during the pulse #54941 with the cooling phase between pulses, (black) a cooling curve is fitted with on the time slice illustrated in red from 600 to 2400 s and extrapolated to the end of the pulse to evaluate the energy absorbed by the component during the pulse.

Figure 4 .
Figure 4. Total energy absorbed by the different PFCs as a percentage of the injected energy, the values are summarized in table 1.

Figure 7 .
Figure 7.Comparison of the energy absorbed by the different parts of the machine and the contribution of the plasma radiation and the SOL over the campaigns in LSN and USN.

Figure 8 .
Figure 8. Energy from the SOL absorbed by the PFCs as a percentage of the measured energy, for all the campaigns in LSN and USN.

Figure 9 .
Figure 9.Comparison of the LSN pulse 55517 (line without marker) and the USN pulse 55778 (dash line with ∆).(a) Main plasma parameters, (blue) plasma current (Ip), (red) injected power and (black) linear central density.(b) Water heating of 3 types of components (red) UDIV (green) OFW and (magenta) IFW.(c) Measured heating of one inertial PFC of the lower divertor with 4 TC (different color) poloidally spaced.

Table 1 .
Energy measured for each PFC type and injected energy for different campaigns and magnetic equilibriums.