High-fluence and high-flux performance characteristics of the superconducting Magnum-PSI linear plasma facility

Summary

This preprint presents the operational regime and experimental performance of the Magnum-PSI linear plasma generator upgraded with a superconducting magnet. The facility achieves steady-state ITER-relevant plasma divertor conditions with particle fluxes exceeding 10^25 m^-2 s^-1, heat fluxes up to 50 MW m^-2, and particle fluences reaching 10^30 m^-2. Machine performance is characterized and parameterized using both linear regression and artificial neural networks, demonstrating its capability for long-term plasma-facing material testing and Edge Localized Mode (ELM) simulation.

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EUROfusion WPPFC-PR(18) 21321 H.J.N. van Eck et al.

High-fluence and high-flux performance characteristics of the superconducting Magnum-PSI linear plasma facility

Preprint of Paper to be submitted for publication in Fusion Engineering and Design

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 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.

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Title, Authors, Highlights, and Abstract

High-fluence and high-flux performance characteristics of the superconducting Magnum-PSI linear plasma facility

H.J.N. van Eck*, G.R.A. Akkermans, S. Alonso van der Westen, D.U.B. Aussems, S. Brons, I.G.J. Classen, H.J. van der Meiden, T.W. Morgan, M.J. van de Pol, J. Scholten, J.W.M. Vernimmen, E.G.P. Vos and M.R. de Baar

DIFFER - Dutch Institute for Fundamental Energy Research, De Zaale 20, 5612 AJ Eindhoven, the Netherlands *Corresponding author: [email protected]

Highlights • The linear plasma generator Magnum-PSI is available for plasma-material interaction studies for fusion. • Magnum-PSI has shown its capability to reach the relevant plasma parameters for the ITER divertor. • Particle fluxes greater than 10^25 m^-2 s^-1 and heat fluxes of up to 50 MWm^-2 are obtained. • Particle fluences of up to 10^30 particles m^-2 have been achieved. • Linear regression and artificial neural network analysis have been applied.

Abstract The Magnum-PSI facility is unique in its ability to produce and even exceed the heat and particle fluxes expected in the divertor of a fusion reactor, combined with good access to the plasma-material interaction region for diagnostics and relatively easy sample manipulation. In addition, it is possible to study the effects of transient heat loads on a plasma-facing surface, similar to those expected during so called Edge Localized Modes. By virtue of a newly installed superconducting magnet, Magnum-PSI can now maintain these conditions for hours on end for truly long term tests of candidate plasma facing materials. The electron density and temperature in the plasma beam center as a function of different magnetic fields up to 1.6 T, gas flow and source current are determined: particle fluxes greater than 10^25 m^-2 s^-1 and heat fluxes of up to 50 MWm^-2 are obtained. Linear regression and artificial neural network analysis have been used to gain insight in the general behavior of plasma conditions as a function of these machine settings, enabling extrapolation for future experiments. The plasma conditions during transient plasma heat loading have also been similarly characterized. These capabilities are now being exploited to reach fluence of up to 10^30 particles m^-2 at ITER-relevant conditions, equivalent to a significant fraction of the divertor service lifetime for the first time.

Keywords Linear plasma devices; Plasma-surface interactions; High heat flux; Edge Localized Modes; Divertor; Artificial neural network analysis

1. Introduction and 2. Experimental setup

1. Introduction The development of a solution for the removal of heat and particles from the reactor is a key area of present-day fusion research, as it determines the performance, lifetime and safety of future fusion power plants. An important contribution to this research is provided by linear plasma generators, which can address the complex physics of plasma wall interaction in a systematic way, with controlled plasma parameters, flexible target geometry and good diagnostic access. The linear plasma facility Magnum-PSI is capable of exposing materials to steady-state plasma conditions similar to those foreseen in the ITER and DEMO divertor strike zones: 10^23 - 10^25 m^-2 s^-1 hydrogen plasma flux densities at an electron and ion temperature of 1-5 eV. It utilizes a superconducting magnet to generate an axial magnetic field up to 2.5 T which confines the high density, low temperature plasma produced by a wall stabilized dc cascaded arc [1] into an intense magnetized plasma beam (FWHM ≈ 10-25 mm) directed onto a target. In this way, extremely high ion fluxes (> 10^25 m^-2 s^-1) with heat fluxes up to 50 MWm^-2 can be achieved in steady state operation. This enables lifetime studies of fusion materials in a lab environment for the first time within a reasonable time frame (i.e. hours). Extremely high fluences over 10^30 D+ m^-2 have already been achieved with steady-state power densities over 10 MWm^-2.

In addition, the machine is capable of reproducing the transient heat and particle loads, with powers up to 1 GWm^-2, as they occur during so-called Edge Localized Modes (ELM) [2]. This combined plasma and heat loading can be used to study the synergistic damaging effects on a target material. Transient plasma loading can also be compared to laser loading using a high-power welding laser (LASAG FLS 352-302) to generate 0.1-3 ms heating pulses on the target. As such, Magnum-PSI, together with other linear plasma generators and laboratory heat facilities [3] are deemed essential to predict plasma facing component (PFC) performance at high particle fluence (> 10^27 D+ m^-2) and high number of thermal cycles (>10^6 ELM-like events) within the EUROfusion consortium [4].

These operations at high magnetic field strengths and over long time durations are achievable since the installation of the superconducting magnet at the start of 2017. Since then, an examination of the new capabilities of the machine was carried out. In this contribution, the operational regime and experimental capabilities of Magnum-PSI are presented.

2. Experimental setup To reach the required ion flux, a certain gas flow is needed, depending on the ionization degree of the plasma source. This gas flow can be as high as 20 standard liter per minute (slm). However, the neutral pressure near the target material should be almost entirely due to ions which are neutralized at the target plate and not due to neutrals coming directly from the source. This is achieved by using a three stage differentially pumped vacuum system [5] which minimizes the neutral influx to the target region while leaving the plasma beam undisturbed. In Figure 1 a schematic overview of the Magnum-PSI vacuum vessel is given. The three water cooled vacuum

2. Experimental setup (Continued)

chambers are enclosed by the superconducting magnet (not shown). The first chamber as seen from the right holds the movable plasma source. The movement of the plasma source makes it possible to change its position with respect to the first skimmer. The magnetized plasma beam flows through the first skimmer into the beam dump chamber where a water cooled beam dump can be placed between the plasma beam and the target. In this way the length of the target exposure can be set without switching off the plasma source or adjustment of the source parameters to the desired settings without exposing the target surface. In the third chamber the target material is exposed to the plasma beam. Each chamber is pumped with a separate pump combination consisting of two roots pumps and a backing pump with variable pump speeds up to 20.000 m^3 h^-1. Additionally, seeding gases (H2, D2, He, N2, Ne, Ar…) can now be introduced to this third chamber to adjust the neutral background pressure and composition at will, enabling detachment and seeding experiments [6]. By using this differential pumping scheme, the neutral pressure in the target region is low enough that the dominant source of neutrals in the final chamber is dominated by recycling from the target [7] and the plasma beam is transported from the source to the target with minimal losses.

Figure 1. Schematic overview of the differentially pumped Magnum-PSI experiment inside the superconducting magnet. Shown are (from right to left), the source chamber, beam dump chamber and target chamber each pumped by their own pumping station (S1, S2 and S3). The source chamber holds the plasma source which is mounted inside a movable water cooled tube (a). The magnetized beam flows through the skimmers (b and c) from the source to the target (d) while most of the neutrals are scraped off and pumped away. A beam dump (e) can be placed between the plasma beam and the target. Thomson scattering yields electron density and temperature profiles near the source (f) and directly in front of the target (g). Gas inlet from the source and gas puffing are indicated with Qs and Qg respectively.

The magnetic field is generated by a superconducting magnet consisting of five NbTi superconducting solenoids wound on a 2.5 m long stainless steel coil former positioned in a cryostat offering a 1.25 m warm bore [8]. The coils generate a plateau shaped magnetic field adjustable up to 2.5 T while the distance between the coils allows

2. Experimental setup - Diagnostics and Target Handling

for 16 room temperature view-ports. The coils are cooled with liquid helium using a re-condensing system operated with cryocoolers, while the magnet system can be adjusted between any chosen field at will using high-temperature superconducting current leads. The superconducting magnet makes extremely high fluence exposures possible while the large warm bore leaves enough room for diagnostics.

A key benefit for linear plasma devices is their good access accessibility and large number of diagnostic windows which allows for many different plasma and surface diagnostics to be installed. The most important plasma diagnostic is Thomson scattering (TS), which determines the electron density and temperature profiles downstream from the source exit and directly in front of the target with a spatial resolution of 1.6 mm [9]. Recently several new diagnostics have been installed. The ion temperature and axial/rotational velocity of the plasma beam can be measured with Collective Thomson scattering (CTS) [10], while a 4-channel resistive foil bolometer is now available for quantitative measurement of the plasma radiated power [11]. A new quartz crystal mass balance (QCMB, Inficon front load single sensor/STM-2 PN 074-613-P1D) can measure deposition rates of material eroding from the target. Fast voltage and current measurements are now also available, enabling determination of changes during transient events such as the ELM-like simulations.

Information on the composition of the plasma in front of the target is obtained from single channel survey optical emission spectroscopy (Avantes AvaSpec-2048-USM2-RM) covering the range 299-950 nm, while spatially resolved spectroscopy can be performed with the aid of a 1 m Jarrell-Ash spectrometer with a flexible spectral range 175 nm wide. Cooling water calorimetry can be carried out to measure the power deposited on the target by the plasma beam, while a fast infrared camera (FLIR SC7500MB) together with a single-channel emissivity independent multi-wavelength pyrometer (FAR-Associate Spectro Pyrometer FMPI) can be used to determine the target surface temperature with a spatial resolution of around 300×300 µm pixel^-1. Fast events up to 1 MHz can be captured by a fast visible light camera (Phantom).

Magnum-PSI is capable of handling large targets, up to an area of 0.12 x 0.6 m^2 and weight of 20 kg. The Large Target Holder is highly flexible and can be tilted to very low angles (<3°), replicating the incidence angles of plasma onto the target material in a fusion reactor. Additionally a second target holder is available which can accommodate up to five samples of dimensions <40 mm diameter and 10 mm thickness, exposing each in turn at normal incidence to the plasma. This Multi-target Holder enables fast sample throughput without breaking vacuum to exchange samples each time. After plasma exposure, the target holder is retracted to the Target Exchange and Analysis Chamber (TEAC). Here, the connection to an ion beam line enables ion beam analysis to locally probe material composition and obtain elemental depth profiles without breaking vacuum, for instance to investigate fuel retention in nuclear fusion reactor walls. Laser-Induced Breakdown Spectroscopy (LIBS) is also available in the TEAC to determine elemental concentration as a function of depth post-mortem in vacuo [12].

3. Operational space characterization - 3.1 Experimental results

3. Operational space characterization 3.1 Experimental results The measurements presented here are performed with an electrically floating target, typically made of W, in the perpendicular position with respect to the plasma beam using the Multi-target holder. Only hydrogen plasmas in steady-state are considered. Electron density ne and electron temperature Te profiles have been measured with TS 20-50 mm in front of the target while the source is kept at its standard position (131 mm in front of the first skimmer). The accuracy of ne and Te is 3% and 6% respectively at ne=1.5x10^19 m^-3 for an accumulation time of 3 s. Discharges on different days using the same machine settings were found to reproduce the same ne and Te within typically 8% and 6%, respectively. The magnetic field B (T), gas flow Γ (slm) and source current I (A) were varied while the pump speeds were always kept in the range 80-100%. Within this range, variations in pump speed have only a minor effect on the plasma conditions. So far, magnetic fields up to 1.6 T have been commissioned.

Figure 2 shows a scatter plot of ne and Te in the beam center, with color indicating the setting of (a) magnetic field, (b) gas flow, and (c) source current. Values up to ne = 10^21 m^-3 and Te = 4.7 eV were achieved. Lines of constant ion flux (solid) and power flux (dashed) are given, which show that particle fluxes of up to 10^25 m^-2 s^-1 and heat fluxes of up to 50 MWm^-2 are obtained. The ion flux to the target is calculated from the Bohm flux [13]: Γi = 0.5 ne cs = 0.5 ne [(kB Te + γ kB Ti ) / mi]^(1/2), (1) assuming adiabatic flow with isotropic pressure (γ=5/3), equilibration between electrons and ions (Te=Ti), and a density drop of a factor 0.5 in the pre-sheath, i.e. between the measurement location and the target. The heat flux to the target is calculated by: q = Γi [(2.5 kB Te - e Vs - e Vps)(1 - Ri,E) + 2 kB Te (1 - Re,E) + χi + χr (1 - Rn)] = Γi [5.03 kB Te + e 14.5 (eV)], (2) where Vs = kTe/e ln(4ci/ce) = 0.5 ln[(2π me/mi)(1 + γTi/Te)] is the sheath potential drop for which we assume ci = cs, and the pre-sheath potential drop Vps = ln(0.5) kTe/e, χi = 13.6 eV, χr = 2.2 eV are the ionization and dissociation energy of hydrogen, and Ri,E = 0.40 and Re,E = 0.15 are the ion and electron energy reflection coefficients and Rn = 0.40 the neutral reflection coefficient for W [14]. The arrows indicate the trends for increasing the depicted parameter while keeping the others constant, e.g. an increasing magnetic field leads to higher ne and Te values. More details are given in Sec. 3.2.

3.2 Linear Regression Analysis

Figure 2. ne and Te in the beam center for various magnetic fields (a), gas flows (b) and source currents (c) shown in color. Lines of constant ion flux (solid) and power flux (dashed) are given. Values up to ne = 10^21 m^-3, Te = 4.7 eV, Γi = 10^25 m^-2 s^-1, and q = 50 MWm^-2 are achieved. Arrows indicate the trend of change in temperature and density when the depicted machine setting is increased, showing that increased magnetic field raises both ne and Te, while an increase of either gas flow or source current causes higher ne but lower Te. The length of the arrow shows the relative strength of the dependence on each machine setting.

3.2 Linear Regression Analysis In order to gain insight in the general behavior of plasma conditions as a function of the main machine settings, we fitted the data using a scaling law of the form: ne = Cn Γ^(aΓ,n) B^(aB,n) I^(aI,n), (3a) Te = CT Γ^(aΓ,T) B^(aB,T) I^(aI,T). (3b)

Such a scaling law can disentangle the effect of the different machine settings in a database where all three parameters change across varying data points. To this end, the plasma conditions and machine settings are first

3.2 Linear Regression Analysis (Continued) and Scaling Law Predictions

normalised by their respective units. Then, the logarithm of both sides of Eq. 3a,b is taken, which - when applied to all points in the database - yields two linear systems of equations. These are solved in linear least squares fashion to obtain the scaling exponents ai,j and constants Cj. The results are: ne = 10^(7.9±0.4) Γ^(1.3±0.1) B^(0.91±0.05) I^(5.2±0.2), (4a) Te = 10^(4.3±0.2) Γ^(-0.71±0.05) B^(0.96±0.03) I^(-1.6±0.1). (4b)

These scaling exponents were used in Figure 2 to determine the length and direction of the arrows indicating the single-parameter trends. For B and I, the arrows compare relatively clearly with the observable trends in the raw data, but for Γ, the trend found by the scaling law is completely hidden in the raw data by changes in B and I.

The quality of the scaling law fit is assessed in Figure 3, where the measured ne (a) and Te (b) are plotted as a function of the values predicted by the scaling law. The fits are able to reproduce the experimental data within a factor 10^±0.22 (+64%/-39%) for density and 10^±0.12 (+30%/-23%) for temperature (rms), with R^2 values of 0.75 and 0.65 for ne and Te respectively. This larger error compared to the reproducibility and accuracy uncertainties of the TS measurements is most likely caused by non-linearity in the system behavior that cannot be captured by a simple scaling law. Still, the scaling laws capture the global trends in the data and can be used for extrapolation to other values. Assuming the scaling holds at higher fields than explored here the maximum parallel heat and particle fluxes achievable by Magnum-PSI can be estimated as 226 MWm^-2 and 7.1×10^25 particles m^-2 s^-1 respectively (2.5 T, 200 A, 20 slm). This would enable exposures at heat loads above 10 MWm^-2 for an ITER-relevant grazing field line angle to the target (α = 2.5 - 3.0° [15]).

Figure 3. Comparison of scaling law predictions with measured values of electron density (a) and temperature (b). The rms residual between the fit and measurements is 10^±0.22 for ne and 10^±0.12 for Te.

3.3. Data fitting using artificial neural networks

3.3. Data fitting using artificial neural networks

The linear regression in log-log space is in principle fitting to a product of one-term exponential functions in multiple dimension, which cannot map all complexity of the data. In order to be able to do this, alternative methods can be used [16,17]. In this study we implemented the artificial neural network (ANN), which is a flexible method that does not require a model a priori, and can map the complexity of data with a high accuracy [16]. More information about how the ANN method was applied here can be found in the Appendix. The ANN fitting results in Figure 4 show that by increasing the magnetic field, both ne and Te rise, consistent with Eq. (4a,b). The arc current causes a decrease of Te, while it increases ne, which is also consistent with Eq. (4a,b). Hence, the results reveal the same trends as the linear regression (LR) analysis. In contrast, it shows non-linearity in log-log space. The performance of the fitting increased significantly compared to the LR, which is evident from the comparison of the fitting results (LR/ANN) and the measured values, see Figure 5. The relative error (RMSE) dropped from 0.30 to 0.21 (46%) in Te and from 0.54 to 0.43 (26%) in ne. This obtained RMSE between the data and the ANN fit is still larger than the observed error in reproducibility of the data by a factor ~5, which means that either the current form of ANN is not much more effective in capturing non-linear trends in the data compared to the scaling law, or the scatter in the data is strongly underestimated.

Figure 4. The electron temperature (Te) and density (ne) as function of the magnetic field B and arc current I at constant gas flow (5 slm). The measured values are plotted along the fitted data (filled contour levels).

Figure 5. The fitted electron temperature and density (ne,fit/Te,fit) as function of the measured values (ne,data/Te,data).

3.4 Characterisation of ELM-like pulses in Magnum-PSI

3.4 Characterisation of ELM-like pulses in Magnum-PSI Magnum-PSI is equipped with a high-repetition rate ELM replication system [2]. On top of the steady state source current, a capacitor bank system, consisting of 28 identical sections, can be discharged through the plasma source to produce transient plasma pulses with high heat and particle fluxes. This capacitor bank system allows for high repetition pulses (>100 Hz) and flexible pulse shaping by varying the timing and voltage of the individual capacitor sections. To characterize these pulses in Magnum-PSI, a systematic scan in the machine parameters was performed. The magnetic field B was varied between 0.8 and 1.2 T [0.8, 1.0 and 1.2 T], the source gas flow Γ between 8 and 14 slm [8, 10, 12 and 14 slm] and the capacitor bank voltage U between 400 and 2000 V (in steps of 200 V), providing a database of 46 different pulses types. Only one capacitor section was used per pulse. Using multiple sections per pulse would enable pulse shaping and even more intense pulses. The temperature and density of each pulse type was measured using time resolved TS [9], measuring a TS spectrum at 50 different timings (relative to the pulse trigger) on a train of 50 identical pulses. The target was retracted far back from the TS position to avoid influencing the pulse characteristics.

The shape of the pulses was found to be independent of B and Γ, but to vary significantly with the capacitor bank voltage U. Figure 6 shows the pulse shapes for both density and temperature for three different voltages U = 400, 1200 and 2000 V. The density pulses are more elongated in time than the temperature pulses, with higher voltages giving longer pulses. The maximum achieved temperature in each pulse does not necessary coincide with the maximum density.

3.4 Characterisation of ELM-like pulses in Magnum-PSI (Continued)

Figure 6. Time resolved temperature (left) and density (right) of ELM-like pulses in Magnum-PSI. Three pulses with the same B and Γ (1 T, 10 slm) but different capacitor voltage (top row: 400 V, middle row: 1200 V, bottom row: 2000 V) show a large variation in pulse shape and duration.

The maximum temperatures and densities achieved in the data base varied from 3-18 eV and 1.5-2.8 10^21 m^-3 respectively. A LR analysis was performed to determine how the maximum measured temperature and density, Te,max and ne,max, scale with the machine parameters B, Γ and U. This regression analysis, including statistical uncertainties on the scaling parameters, results in the following two power laws: Te,max,fit = 10^(-0.18±0.28) B^(0.41±0.26) Γ^(-0.34±0.18) U^(0.55±0.07) (5a) ne,max,fit = 10^(0.36±0.12) B^(0±0.11) Γ^(0.78±0.8) U^(0.04±0.03) (5b)

The maximum temperature scales positively with B and U, and negatively with Γ. The maximum density of each pulse is virtually independent of B and U, but scales almost linearly with Γ. This is consistent with nearly complete ionisation of the gas in the source during the pulses [2]. Figure 7 compares the measured Te and ne maxima with the regressed maxima Te,max,fit and ne,max,fit. Whereas the maximum density seems to be relatively well described by a power law, the maximum temperature shows significant deviations, with measured temperatures saturating around 20 eV.

4. High fluence experiments

Figure 7. Comparison between the measured maxima in ne and Te, and the fitted values according to the regression analysis.

4. High fluence experiments The updated capabilities of Magnum-PSI enable new venues of exploration, at higher fluence, higher fluxes and with new diagnostic capabilities than were previously possible. As an example of the high-fluence capabilities a water-cooled monoblock chain identical to that used in [18] was exposed to a variety of plasma conditions in Magnum-PSI, including H, He, D and D+He plasma (89:11 gas ratio). In the longest (D) exposure this target received a fluence of 1.01×10^30 m^-2 while also matching the expected DT-phase operating temperature of 1200 °C [19]. This enabled for the first time experiments to probe lifetime performance of the monoblock, comparable to ITER conditions and with similar electron and ion temperatures as would be expected at the strike points during operation. The total fluence was equivalent to around 12 months of ITER operation [19], achieved in 19.7 hours (Figure 8). The full results will be published elsewhere.

5. Conclusions and Appendix

Figure 8. Peak ion fluence in the divertor for several different tokamaks over 5000 typical plasma discharges. The red dot-dashed line represents the highest reported fluence in literature achieved in any linear device [20] while the green dashed line represents the fluence in Magnum-PSI reported here. Adapted with permission from [21] © 2018 ITER Organization.

5. Conclusions The operational regime of the linear plasma generator Magnum-PSI has been explored after the arrival of the superconducting magnet. The results, electron densities up to 10^21 m^-3 and electron temperatures up to 4.7 eV leading to particle fluxes up to 10^25 m^-2 s^-1 and heat fluxes up to 50 MWm^-2, combined with the ability to maintain these conditions for hours on end, make the facility highly relevant for plasma wall interaction studies for fusion reactors such as ITER and DEMO. Linear regression and artificial neural network analysis have been used to gain insight in the general behavior of plasma conditions as a function of machine settings. Both techniques yielded similar results. On top of the steady state operation, a capacitor bank system can be discharged through the plasma source to produce transient plasma pulses with high heat and particle fluxes. A systematic scan in the machine parameters was performed to characterize these pulses.

Appendix The ANN was set up using the TensorFlow toolbox in Python [22]. Essentially, ANNs consists of connected nodes, so-called neurons, arranged in several layers. Each neuron is activated by a non-linear function φ (ReLu in this paper [23]) working on the sum of weighted inputs w · x from all neurons of the preceding layer plus a bias b (i.e., o = φ(w · x + b)). Its output o is transmitted to all neurons from the succeeding layer. In this manner, input parameters in the first layer, are transmitted through the ANN to generate predicted parameters P at the

Appendix (Continued), Acknowledgements, and References (1-7)

output layer. In this study, an ANN with two hidden layers of 5 neurons (56 free parameters of weights and biases) was trained by supplying the network with measurement data of Magnum-PSI (inputs Im and outputs Om). The training data was used to adjust the weights and biases in each neuron using the Adam optimizer [24] (a gradient descent method including learning rate scaling and momentum addition), which minimize the loss function E = 1/2 |Om - P(Im)|^2 with a learning rate of 0.0005. In order to avoid overfitting, L2 regularization [25] was applied with a regularization constant of 0.001. Moreover, to assess the quality of the fitting, the dataset of Magnum-PSI was split in two parts, a training set and validation set of 70% and 30% of the total data, respectively, i.e. a deviating root mean squared error (RMSE) for the validation set compared to the training set indicates overfitting. The training was performed on 50.000 batches of 50 random samples each. Lastly, the concept of ensemble averaging of networks [26] was applied to increase the fitting performance, and to obtain an estimate of confidence across the parameter domain. The average was defined as y_hat = (sum_{i=0}^n w_i x_i) / (sum_{i=0}^n w_i), in which w_i = 1 / sigma_i^2, and sigma_i is the RMSE of each network, and the variance is sigma_y_hat^2 = 1/(n - 1) · (sum_{i=0}^n w_i (x_i - x_bar)^2) / (sum_{i=0}^n w_i). For each output parameter, 25 ANNs were trained, and before the training of a new network, the data was shuffled and regrouped in a new training and validation set.

Acknowledgements We acknowledge Jonathan van den Berg and Karel van de Plassche for their input on ANNs. The actively-cooled monoblock chain was supplied by the ITER Organization and F4E as part of a Eurofusion-funded experiment to investigate the effect of ITER-relevant fluences on the properties of tungsten. 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. DIFFER is a partner in the Trilateral Euregio Cluster TEC.

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