# Impact of inter-pulse wall outgassing on ITER plasma start-up

Federico Cursi, Julien Denis, Tom Wauters, Richard Pitts, Wouter Dekeyser, Martine Baelmans

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Federico Cursi, Julien Denis, Tom Wauters, Richard Pitts, Wouter Dekeyser, et al. Impact of inter-pulse wall outgassing on ITER plasma start-up. Nuclear Fusion, 2025, 10.1088/1741-4326/ae23e4. hal-05384085

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Distributed under a Creative Commons Attribution 4.0 International License
Impact of inter-pulse wall outgassing on ITER
plasma start-up

F. Cursi¹, J. Denis², T. Wauters³, R. A. Pitts³,
W. Dekeyser¹, M. Baelmans¹, the JET Contributors‡ and
the EUROfusion Tokamak Exploitation Team§

¹ KU Leuven, Department of Mechanical Engineering, Celestijnenlaan 300, Leuven 3001, Belgium

² Aix Marseille Univ, CNRS, PIIM, Marseille, France

³ ITER Organization, Route de Vinon-sur-Verdon, CS 90 046, St Paul Lez Durance 13067, France

E-mail: federico.cursi@kuleuven.be

**Abstract.** Low background pressures are expected to be required in ITER for successful plasma breakdown. After plasma implantation, the particles released from plasma-facing components (PFC) increase pressure in the main chamber, and it is therefore important to assess the expected timescales of post pulse fuel outgassing. This paper studies the reasons for different outgassing conditions in a large database of JET pulses obtained with a beryllium (Be) first wall (FW) and a tungsten (W) divertor, to estimate the minimum inter-pulse dwell time required in ITER. Outgassing is found to increase during the first few pulses of a day of operation in JET, due to increasing wall temperature and fuel inventory. The time evolution of experimental pressure curves is studied in a large dataset to identify general statistical trends. The code MHIMS, describing migration of hydrogen isotopes in materials, is then used to simulate a series of plasma discharges with inter-pulse outgassing in JET. The PFC are modeled as reservoirs in Be, W and stainless steel. The results agree qualitatively with experimental pressure curves and the initial outgassing increase is reproduced. The MHIMS reservoir model is then extrapolated to ITER, adapting the simulation setup with larger surfaces, a different plasma background, and longer pulses. This analysis features a comparison between the use of Be and W as FW materials, with the latter being key in view of the 2024 ITER re-baseline, which eliminates Be in favour of W for the main chamber armour. After 30 mins of inter-pulse outgassing, the hydrogenic pressure is 0.12-0.17 mPa with a Be FW. This value is reduced to 0.023-0.041 mPa when using a W FW, assuming no boronization. These pressures are much lower than the identified threshold of 0.5-1 mPa required for reliable ITER plasma start-up.

*Keywords:* Outgassing, Dynamic retention, Inter-pulse dwell time, Plasma-wall interaction, ITER

<footnote>‡ See the author list of C.F. Maggi et al 2024 Nucl. Fusion 64 112012 https://doi.org/10.1088/1741-4326/ad3e16</footnote>

<footnote>§ See the author list of E. Joffrin et al 2024 Nucl. Fusion 64 112019 https://doi.org/10.1088/1741-4326/ad2be4</footnote>
# 1. Introduction

The interaction between hydrogen isotopes (HI) and plasma-facing components (PFC) significantly impacts the operation of tokamaks, especially due to the process of particle recycling. During plasma operation, the PFC intercept an incident flux of plasma ions and atoms. Part of the incident particles are reflected back into the plasma, while others implant into the material, diffuse into the bulk and can be trapped in defects of the crystalline structure. The implanted particles can be released through the process of desorption [1], also called outgassing. The main processes occurring during HI recycling are illustrated in figure 1.

<figure><img src="image_2.png" /><figcaption>Figure 1: Physical processes in HI recycling from plasma facing materials of nuclear fusion reactors. Picture from reference [1].</figcaption></figure>

Particle recycling plays a crucial role in the operation of a fusion reactor. It is of key importance during the pulse for plasma density control since it provides the main fuel source (wall fueling) [2]. Additionally, the particles which are not released can be retained in the wall for a long time, contributing to long-term retention, which is particularly important in devices, such as ITER, using high throughputs of tritium fuel. However, the focus of this study is rather on dynamic retention: particles are implanted and retained during the pulse, and are subsequently released during inter-pulse outgassing [2]. This process is important for tokamak operation because it can affect the waiting time between pulses, as explained below.

Present experimental tokamaks are pulsed devices, relying on a transformer principle to inductively drive the plasma current [3]. The inter-pulse dwell time is defined as the waiting time between two plasma pulses. Together with the plasma pulse duration, it effectively determines the reactor duty cycle. Outgassing from the PFC after a plasma pulse could be a limiting factor for the inter-pulse dwell time, since it can affect the vacuum conditions at the subsequent plasma start-up.

Particles implanted during the previous pulse(s) are released in the main chamber through outgassing, inducing an overpressure in the vessel, which needs to be decreased through vacuum pumping in order to restore the vacuum conditions required for plasma start-up. Indeed, the hydrogenic pressure needs to be below a certain threshold in order for reliable plasma breakdown to occur. On ITER, this threshold is expected to be rather low, ~0.5-1 mPa [4, 5], so the inter-pulse dwell time of ~30 mins should be sufficient for the base pressure to decrease below this value. It is the aim of this study to estimate whether, considering wall outgassing, the hydrogenic pressure will be low enough within this inter-pulse dwell time. Plasma breakdown also needs other conditions to be satisfied, but the focus of this contribution is on the hydrogenic pressure only.

The gas released from the wall through outgassing after a plasma pulse can either be stored in the vessel in the form of pressure, or be evacuated through vacuum pumping. Assuming constant temperature during outgassing, these dynamics can be described by the gas balance equation [4]:

$$ \frac{V}{k_b T} \frac{dp(t)}{dt} = Q_{\text{outgas}}(t) - Q_{\text{pumped}}(t), \quad (1) $$

where $V$ [m$^3$] is the vacuum vessel volume, $T$ [K] is the neutral gas temperature in the vessel, $k_b = 1.38 \times 10^{-23}$ JK$^{-1}$ is the Boltzmann constant, $p(t)$ [Pa] is the pressure in the vacuum vessel, $Q_{\text{outgas}}(t)$ [D$_2$S$^{-1}$] (D$_2$=deuterium molecules, D=deuterium atoms) is the gas coming from wall outgassing and $Q_{\text{pumped}}(t)$ [D$_2$S$^{-1}$] is the gas evacuated from the vessel through vacuum pumping.

Tokamak outgassing has been studied both experimentally and through modelling in previous literature ([6–9]), where it was observed that the outgassing rate follows a power law of the type:

$$ Q_{\text{outgas}}(t) = K \times t^{-n}, \quad (2) $$

where $K$ is the initial outgassing rate (at $t = 1$ s), and the exponent $n$ is found in the range 0.6 to 0.8 [4]. As an example, an experimental pressure curve during outgassing right after JET pulse #88735 is shown in figure 2 (lower), where the log-log scale plot presents the typical linear trend indicating a power law.

In this paper, the process of inter-pulse outgassing is initially studied in JET experiments in section 2. Specific discharges are analyzed in section 2.1 to study how outgassing evolves during a typical day of operation. A larger dataset of discharges, described in section 2.2, is then analyzed with a statistical approach to study the dependence of outgassing on the preceding pulse parameters (section 2.3) and the typical power law trend of outgassing in time (section
<figure><img src="image_3.png" /><figcaption>Figure 2: Upper: Pressure evolution during pulse and subsequent inter-pulse outgassing of JET pulse #88735. The pulse starts at $t \simeq 0$ s, the outgassing starts at $t \simeq 35$ s. Lower: Pressure evolution only during the outgassing phase after JET pulse #88735. Outgassing here starts at $t \simeq 1$ s.</figcaption></figure>

2.4). The experimental analysis leads to interesting novel findings, but the results cannot be extrapolated to ITER. Therefore, the study continues with physical modeling using the numerical code MHIMS, described in section 3, to build a reservoir model of the JET PFC in section 4. The reservoir model is used first to reproduce the experimental findings in JET, and then deployed for extrapolation to ITER. In section 5, outgassing simulations for ITER estimate the hydrogenic pressure during inter-pulse outgassing. A comparison is made between the previous 2016 baseline, with a Be first wall (FW), and the current 2024 baseline [10], which eliminates Be in favour of W for the main chamber armour, assessing the impact of the recent ITER re-baselining activities on inter-pulse outgassing.

## 2. Experimental Analysis

In order to study outgassing in JET experiments, pressure measurements are taken from a penning gauge located outside of the vessel, on top of one of the midplane horizontal ports used for turbomolecular

pumping [11]. This pressure can easily be related to the outgassing rate, as explained below. During inter-pulse outgassing, the gas balance equation (1) can be rewritten as:

$$Q_{\text{outgas}}(t) = \frac{V}{k_b T} \frac{dp(t)}{dt} + Q_{\text{pumped}}(t). \quad (3)$$

However, after a few tens of seconds the time derivative term can be neglected due to the low pressure values and the relatively slow variation in time. This has been verified numerically for all JET discharges considered in this paper, finding that in most cases after 50 s the time derivative term is less than 2% of the pumped gas flow. Therefore, it can be assumed that:

$$Q_{\text{outgas}}(t) \approx Q_{\text{pumped}}(t) = \frac{S_{\text{eff,g}}}{k_b T_g} p_g(t), \quad (4)$$

where $S_{\text{eff,g}}$ [m$^3$s$^{-1}$], $T_g$ [K], and $p_g(t)$ [Pa] are the effective pumping speed, the neutral gas temperature, and the pressure at the penning gauge ('g') location. Equation (4) shows that, during the inter-pulse time, studying the trends of the pressure at the gauge location is equivalent to studying the trends of outgassing, apart from the multiplication factor $S_{\text{eff,g}}/k_b T_g$, which is known.

The pumping speed is a measure commonly used in the field of vacuum technology and is equivalent to the volumetric flow rate available to evacuate a vessel with a given vacuum pumping system [12]. The effective pumping speed is lower than the ideal pumping speed because it also accounts for the conductance of the ducts between the vessel and the pumps [12]. The effective pumping speeds in JET have been measured at the penning gauge location during dedicated gas test pulses in reference [9]. The effective pumping speeds of the neutral beam and the divertor cryopumps are respectively $S_{\text{eff,NBI}} = 76$ m$^3$s$^{-1}$ and $S_{\text{eff,div}} = 118$ m$^3$s$^{-1}$. The turbomolecular pumps are always active and their pumping speed is $S_{\text{eff,turbo}} = 9$ m$^3$s$^{-1}$, from references [13, 14]. During inter-pulse outgassing, since the plasma is off, the pressure can be assumed uniform in the vessel, hence the pumping speeds can be summed. The resulting total effective pumping speed is $S_{\text{eff,JET}} = S_{\text{eff,NBI}} + S_{\text{eff,div}} + S_{\text{eff,turbo}} = 203$ m$^3$s$^{-1}$.

Due to the pressure drop along the duct, the penning gauge measures a lower pressure compared to the pressure in the vacuum vessel. However, there is a simple linear relationship between the pressure in the vessel and at the penning location, hence the same trends can be observed. This linear relationship can be estimated from the calibration of the penning gauge against the baratron gauges, located below the divertor, during pulses without divertor cryopumping. This procedure is detailed in Appendix A, and a
calibration factor of 1.78 is found, meaning that $p_{vv} = 1.78p_g$, where $p_{vv}$ is the pressure in the vacuum vessel. The subscript 'g' will be henceforth be dropped since all quoted pressures are at the penning gauge location.

## 2.1. Reference Experiments

In this section, we study specific JET discharges to identify interesting trends in outgassing during a day of operation, and how it is affected by the preceding plasma characteristics. The same pulses analyzed here were also studied in reference [9]. A number of consecutive discharges with the same plasma scenario were performed to study fuel retention, hence they are particularly suitable for studying outgassing. The series analyzed here is #81606-#81624, but similar conclusions also hold for others from reference [9]: #82666-#82673 and #82592-#82626. Figure 3 illustrates the pressure curves during outgassing right after each pulse.

<figure><img src="image_4.png" /><figcaption>Figure 3: Pressure curves during outgassing right after each discharge of the series #81606-#81624. Please refer to the online version of the article for the color version of this figure.</figcaption></figure>

Focusing first on the green curves in figure 3, it is worth noting that during the first consecutive discharges (light green) outgassing increases. This is likely driven by two effects: the progressive increase of the PFC temperatures, given that these are not actively cooled in JET; and the increase in the fuel inventory of the wall. Nevertheless, outgassing eventually stops increasing and stays equal (dark green). Figure 4 shows the average temperature

measured from thermocouples in the bulk of the PFC at the end of each pulse. The temperature does increase in the first pulses, but it eventually reaches an equilibrium when it is high enough that the heat gained from the plasma can be evacuated through thermal diffusion during the inter-pulse dwell time. The progressive wall loading reaches an equilibrium when both temperature and inventory are such that the HI implanted during the plasma can be evacuated through outgassing between pulses. In reference [11], dynamic retention is also found to be reproducible in JET (Be-W configuration), except for the first pulses, which are indeed needed to reach the equilibrium condition described above.

<figure><img src="image_5.png" /><figcaption>Figure 4: Average bulk temperatures from thermocouples embedded in selected main chamber and divertor PFC at the end of JET discharges #81606-#81624</figcaption></figure>

The duration of most of the pulses in the series is ~25 s, of which ~5 s initially in limiter configuration, and the remainder in divertor configuration. Pulse #81613 (figure 3, dark blue) is instead a 13 s long pulse in limiter configuration, which ended prematurely. This means that both the divertor and the limiters received a lower fluence [$Dm^{-2}$] (time integral of particle flux density [$Dm^{-2}s^{-1}$]) due to the shorter time exposed, hence lower outgassing occurs. The opposite is true for pulse #81619 (figure 3, light blue), which was ended with a long limiter phase of 5 s with the plasma leaning on the outerboard guard limiters. As a result, the limiter received a higher fluence and stronger outgassing is observed. Most of the other pulses do not feature this limiter phase at the end of the pulse, or if they do, it is limited to less than 1 s. Nevertheless, outgassing after roughly 100 s is comparable to the other discharges.

The red and orange curves in figure 3 happen after pulses #81610 and #81612, both ending with a disruption. They present a very high peak pressure, likely due to two effects: 1) the recombination of the plasma will have a stronger impact on the pressure peak, due to the higher particle content of the plasma when a disruption occurs, compared to a soft landing; 2) the higher power incident on the PFC
transiently increases surface temperatures, leading to more outgassing. Indeed, a temperature peak corresponding to disruptive pulses can be observed in figure 4. The initial peak is followed by a steeper descent of pressure, leading to final pressure values comparable with non-disruptive discharges.

This analysis suggests that, at least in JET with Be FW and W divertor, once equilibrium is reached after a few initial pulses, outgassing does not change, given similar plasma scenarios. On the other hand, if plasma parameters such as the pulse duration or plasma configuration change, or if a disruption occurs, outgassing is affected. In the following sections, an attempt is made to generalize the trends and dependencies identified in this series to a wider dataset of more than a 1000 JET pulses, using statistical data analysis.

## 2.2. Dataset

A large database of 1292 JET discharges was selected from ~ 20000 pulses executed in several campaigns, spanning the period from which the Be FW and W divertor were installed up to pulse number #101491, which was performed in 2022. The discharges were selected according to several criteria: pure deuterium (D) plasmas, with a pulse duration longer than 5 s, with plasma current above 0.5 MA, toroidal magnetic field above 1.5 T, and plasma density above 10¹⁹ m⁻³. It was verified that the cryogenic vacuum pumping systems of both the neutral beam and the divertor were active in all these discharges, to have the same pumping conditions. The pressure curves during outgassing are shown in figure 5, where disruptive and non-disruptive discharges are clearly distinguished with pink and grey curves, respectively.

It is evident that all disruptive pulses lead to a high peak pressure, followed by a steeper decrease, ending up with a pressure similar to the rest of the experimental curves. This is consistent with what observed in section 2.1. The higher pressure peak due to disruptions was also observed in reference [15], in a different JET dataset. Therefore, this effect can be considered general. A few disruptive pulses in figure 5 do not behave as expected; they present a lower initial pressure ~1 mPa. These pulses disrupted very early; the plasma lasts for less than 10 s, hence both the inventory and the wall temperature are probably low, leading to low outgassing. This is also observed for a single non-disruptive pulse in figure 5, which only lasts 6 s. In all the other discharges, the plasma duration ranges between 15 s and 30 s.

This large dataset is used to first study correlations between pressure during outgassing and pulse parameters in section 2.3. Then, the same dataset is used to study the time evolution of outgassing using

<figure><img src="image_6.png" /><figcaption>Figure 5: Experimental pressure curves during outgassing from the JET dataset: 1053 non-disruptive pulses (grey); 238 disruptive pulses (pink)</figcaption></figure>

the characteristic power law trend in section 2.4.

## 2.3. Experimental Correlations

This section studies the impact of the preceding pulse parameters on the pressure during outgassing. We arbitrarily choose to look for possible dependencies in the peak pressure right after the end of the pulse (pmax), the pressure after 50 s (p50) and after 700 s (p700) of outgassing. These pressure values are fitted against different pulse parameters using robust statistical regression analysis. Several pulse parameters were considered as potentially relevant: energy from external heating, radiated energy from the plasma, average divertor and limiter bulk temperatures, plasma density during the flat-top phase and at the end of the pulse, plasma volume at the end of the pulse, pulse duration, time in limiter and divertor configuration, fuelling, pre-pulse background pressure, plasma current, magnetic field, energy confinement time. Given the large number of predictors, the statistical model chosen is a power law of the type:

$$y = A \prod_{i=1}^{N} x_{i}^{\theta_{i}}, \qquad (5)$$

with N predictors xᵢ. The fitting parameters are the multiplication constant A and the exponents of each predictor θᵢ. The pressure values were fitted for 1053 non-disruptive pulses out of 1292. As seen in sections
2.1 and 2.2, outgassing after disruptive pulses was found to behave rather differently, hence these were excluded from the dataset, in order to capture more general trends.

The most relevant predictors among the pulse parameters were identified based on the p-value resulting from t-tests on the coefficients (i.e. testing the null hypothesis that the coefficient is zero), and how removing the predictor affects the adjusted coefficient of determination $R_{adj}^2$, a goodness-of-fit measure. The p-value is a measure of the strength of evidence against the null hypothesis that a fitting coefficient is zero. A low p-value suggests that the observed data are unlikely under the assumption that the coefficient is zero, indicating that the predictor likely has a significant effect on the dependent variable. Therefore, the lower the p-value, the stronger the evidence that the predictor is relevant. The $R_{adj}^2$ is an adjusted value of the classic goodness-of-fit measure $R^2$ specifically meant to guard against overfitting, which is one of the risks of the classical least squares approach. Indeed, when adding a new predictor, $R^2$ can increase regardless of the actual relevance of the new predictor, as the new degree of freedom can allow to better overfit the data. On the other hand, the $R_{adj}^2$ is computed in a way that it does not increase if the new predictor is irrelevant.

Using this method, a strong linear correlation was found between the peak pressure $p_{max}$ [mPa] right after the end of the pulse and the plasma particle content $N_{pl,end}$ [D$_2$] measured 1 s before the end of the pulse:

$$p_{max} = (2.94 \pm 0.013 \times 10^{-20}) N_{pl,end}, \\ R_{adj}^2 = 0.941, \qquad (6)$$

with the plasma particle content computed as:

$$N_{pl,end} = n_{pl,end}V_{end}, \qquad (7)$$

where $n_{pl,end}$ [D$_2$m$^{-3}$] and $V_{end}$ [m$^3$] are respectively the particle density and the plasma volume measured 1 s before the end of the pulse. No other pulse parameter was found to be relevant for the prediction of the pressure peak. The plasma volume is taken from magnetic equilibrium reconstruction with the EFIT code. The particle density is computed as an average value by dividing the line integrated density measured with interferometry by the line-of-sight (LOS) length. For this fit, LOS 3 is used, which is 3.22 m long and goes through the plasma vertically close the magnetic axis. In order to verify the validity of this result, an analogous fitting was done with LOS 8, which is 2.08 m long and goes through the plasma horizontally close the magnetic axis. Less data was available from this LOS, so that the fitting was performed on only 835 pulses instead of 1053. Nevertheless, a similar result

was obtained with a fitting coefficient $2.14 \pm 0.013 \times 10^{-20}$ and $R_{adj}^2 = 0.936$.

This fit resembles an ideal gas law in the sense that $p_{max}$ is proportional to the number of particles present in the plasma $N_{pl,end}$ right before the end of the pulse. This suggests that the recombination of the plasma into a neutral gas also drives the pressure peak, at least partly, together with outgassing. When the plasma recombines, the pressure in the vessel equilibrates and this happens simultaneously with the beginning of outgassing. The recombined plasma has to be pumped out, which is consistent with an initial volume pumping phase [16], before outgassing becomes dominant. Therefore, the experimental fit is compared with an estimate of the pressure due to plasma recombination $p_{rec}$ [mPa] using the ideal gas law:

$$p_{rec} = \frac{1000 \times k_b T_{vv}}{1.78 \times V_{JET}} N_{pl,end} \\ = (1.98 \times 10^{-20}) n_{end} V_{end}, \qquad (8)$$

where $k_b = 1.38 \times 10^{-23}$ JK$^{-1}$ is the Boltzmann constant, $T_{vv} = 473$ K (200 °C) is the neutral gas temperature in the vessel, $V_{JET} = 185$ m$^3$ is the JET vacuum vessel volume (from references [13, 14, 17]), the factors 1000 and 1.78 are respectively the unit conversion from Pa to mPa and the calibration factor from the vacuum vessel pressure to the penning gauge pressure (see Appendix A). The fitting coefficients $2.95 \times 10^{-20}$ (LOS 3) and $2.14 \times 10^{-20}$ (LOS 8) found in equation (6) are close to the multiplication factor $1.98 \times 10^{-20}$ in equation (8), obtained from the ideal gas law. Of course, the exact numerical values are subject to the underlying assumptions. The fitting coefficients are uncertain due to the approximation of the density used. The multiplication factor from the ideal gas law is obtained assuming the neutral gas to be at the JET FW temperature. Most divertor tiles, being mounted on an actively cooled structure, are at a lower temperature [18], but these tiles have a small surface area compared to the main chamber. The JET vacuum vessel volume is also subject to some uncertainty, but this is expected to be rather small (<10%). For these reasons, it is difficult to derive an accurate quantitative estimate of what fraction of the pressure peak comes from recombination, compared to outgassing. Nevertheless, the fact that all these coefficients are very similar, and that a high adjusted $R_{adj}^2 > 0.9$ is found for more than 1000 different discharges, clearly indicates that a considerable fraction of the pressure peak originates from plasma recombination.
The fits found for $p_{50}$ [mPa] and $p_{700}$ [mPa] are:

$$ 
\begin{aligned}
p_{50} &= (2.51 \pm 0.363 \times 10^{-3}) \\
E_{\text{net}}^{0.291 \pm 0.008} p_{\text{back}}^{0.080 \pm 0.009} T_{\text{div}}^{0.161 \pm 0.018}, \\
R_{\text{adj}}^{2} &= 0.747;
\end{aligned} 
\quad (9) 
$$

$$ 
\begin{aligned}
p_{700} &= (2.48 \pm 0.53 \times 10^{-4}) \\
E_{\text{net}}^{0.354 \pm 0.012} p_{\text{back}}^{0.282 \pm 0.010} T_{\text{div}}^{0.086 \pm 0.024}, \\
R_{\text{adj}}^{2} &= 0.703.
\end{aligned} 
\quad (10) 
$$

$E_{\text{net}}$ [J] is the net energy transported through convection/conduction to the PFC, mostly to the divertor targets, which is estimated from the total energy from external heating and subtracting the radiated energy from the plasma. $p_{\text{back}}$ [mPa] is the pre-pulse background pressure i.e. the pressure measured by the penning gauge before the pulse starts. $T_{\text{div}}$ [K] is the average divertor bulk temperature, measured from thermocouples 1 s before the pulse starts. The $R_{\text{adj}}^2$ value is ~0.7-0.75, showing a weaker correlation compared to the previous fit for the pressure peak, but still pointing to a clear trend. Outgassing, almost certainly due to higher PFC temperatures, increases when a higher energy $E_{\text{net}}$ is directed to the divertor targets. The dependence on pre-pulse background pressure $p_{\text{back}}$ suggests that outgassing also depends on what happened prior to the pulse, since this is the final pressure of the preceding outgassing phase and is observed to increase and saturate during a day of operation. This is consistent with the outgassing increase during the first consecutive pulses of the day observed in section 2.1. The average divertor bulk temperature $T_{\text{div}}$ also has an impact, which is to be expected in a temperature-dependent phenomenon such as thermal desorption, but no significant dependence on the average limiter bulk temperature was found. This temperature rises throughout a day of operation due to consecutive plasma loading, since JET's PFCs are not actively cooled - see figures 4 and 8. Therefore, the absolute value of $T_{\text{div}}$ depends on the energy cumulated in the PFC during several preceding pulses. It should be noted that these temperatures are averaged over all tiles. It might therefore be that it is specific locations that are contributing more to outgassing, which would not be captured by an average temperature. This limitation will be addressed with physical modeling of JET's PFCs in a reservoir model in section 4.

It is important to note that no correlation was found between $p_{50/700}$ and $N_{\text{pl,end}}$, meaning that recombination does not impact pressure after 50 seconds, but only initially (equation (6)). Indeed, the neutral gas from plasma recombination is evacuated through the vacuum system rather quickly. The characteristic timescale of this process is $V_{\text{JET}}/S_{\text{eff,JET,vv}} \simeq 1$

s, where the pumping speed at the vacuum vessel $S_{\text{eff,JET,vv}} = 184 \text{ m}^3\text{s}^{-1}$ is computed with the calibration procedure described in Appendix A. Therefore, after only ~5 s the volume pumping phase is over and the pressure solely originates from outgassing. No significant correlations were found with any other of the pulse parameters listed at the beginning of this section. It is interesting to note that in both the previous sections 2.1 and 2.2 the experiments suggest a dependence of outgassing on plasma duration, which is not found in this regression analysis. However, this dependence is implicitly included in $E_{\text{net}}$, since, for the same input power, a longer pulse leads to a higher net energy to the targets.

This section only provides information on pressure at specific times during outgassing, but does not give any information on the time evolution of pressure, which is instead studied in the next section. The correlations found provide information about the dependency of outgassing on the preceding pulse parameters, but outgassing depends also on the previous pulses executed during the same day. This limitation will be addressed with physical modelling in section 4, where several consecutive discharges are simulated.

## 2.4. Pressure time evolution

The exponent of the outgassing power law (equation 2) was found to range from 0.6 to 0.8 [4]. Different physical processes can be considered to reproduce similar trends using analytical models of HI retention and release [6]: surface recombination controlled release results in $n = 2/3$, while surface diffusion controlled release leads to $n = 1.5$. When both these processes drive the release, reference [6] finds that the exponent $n$ changes in time, starting at ~ 0.5 and finishing at ~ 1.2 after 200 s. Only when considering consecutive plasma loading the exponent converges to a constant value in time of $n = 0.85$ [6]. An analytical model developed in reference [7] also found an exponent of $n = 2/3$ for timescales relevant for the JET interpulse dwell time (below $10^4$s). Outgassing in JET was also studied experimentally in reference [6], finding a constant exponent $n = 0.73 \pm 0.2$ for beryllium (Be) deposited on the carbon wall. Similar exponents have been found in more recent JET experiments with Be FW and W divertor, namely $n = 0.8$ in reference [9] and $n = 0.89$ in reference [2]. In general, experimental exponents seem larger than $n = 2/3$ found with analytical modeling when assuming recombination controlled release [6, 7]. This section aims to study the outgassing curves of 1053 non-disruptive pulses out of 1292, to examine how the coefficients of the power law compare with previous literature. As seen in sections 2.1 and 2.2, outgassing
after disruptive pulses behaves in a different way, hence these were excluded from this analysis.

Bayesian analysis is one of the most widespread and rigorous techniques with which to perform parameter inference and model comparison. It has often been used in the nuclear fusion field, as for example in mean-field plasma edge turbulence modelling [19, 20], but never to the authors' knowledge for retention or outgassing studies. Nevertheless, it is a coherent methodology for parameter inference on the coefficients of the outgassing power law, especially in a large dataset subject to uncertainties, and is hence chosen here as the most suitable method. Parameter inference with Bayesian methods not only involves the estimation of uncertainty over each fitting parameter, but also the identification of cross-correlations between them [19]. The latter is particularly interesting for this section since possible cross-correlations between the coefficients K and n of the outgassing power law have never been explored. The regression analysis in the previous section had the main objective of identifying general trends in the data, hence the least squares approach was considered sufficient.

In a Bayesian context, the degree of knowledge about a model M is expressed with probability distributions over the model parameter vector θ, which is the objective of the inference, based on experimental data D. If some degree of knowledge about the parameter values is already present before the inference, this should be expressed as a prior distribution π(θ|M). The backbone of Bayesian analysis is Bayes' theorem [19]:

$$\pi(\theta|D, M) = \frac{\mathcal{L}(D|\theta, M) \pi(\theta|M)}{\pi(D|M)}, \quad (11)$$

which allows computation of the posterior distribution π(θ|D, M) of the model parameters, starting from the prior distribution π(θ|M). This is done by multiplying π(θ|M) by the likelihood function L(D|θ, M), which is defined as the probability of observing data D, given the model M and the parameter set θ. The product of likelihood and prior distribution is normalized by the Bayesian evidence π(D|M), which measures the probability that a given model M explains the observed data D, integrated over all possible parameter values.

To make the inference here as objective as possible, uninformative priors are used, hence no knowledge is assumed on the parameter values. One advantage of Bayesian inference is that the model error can be included as one of the parameters of the inference, but assumptions on its distribution are required. Under the assumption that the error is random noise over the data, a Gaussian distribution with zero mean can be assumed. Therefore, only the

standard deviation of the error is part of the inference. The statistical model can therefore be expressed as:

$$y = f(x, \theta) + \epsilon, \quad \text{with } \epsilon = \mathcal{N}(0, \sigma^2), \quad (12)$$

where f is in this case the power law typical of outgassing curves, ε is the model error with respect to the experimental data, and its standard deviation is σ. Since the pressure varies over orders of magnitude during outgassing, using a purely additive error in absolute value is not appropriate. Therefore, the error is rescaled with the data and the model relative error εrel is inferred instead, such that ε = εrely.

The analysis is performed using the Bayesian framework developed in reference [19], which the reader is invited to consult for a more detailed description of the numerical techniques employed. Only a brief overview is provided here. The inference starts with a Maximum A Posteriori (MAP) estimation: the parameter values which maximize the posterior density distribution are found via maximization of the numerator of the Bayes' theorem. However, this only provides information about the most probable values of the parameters. Therefore, a Laplace approximation follows, where the posterior distribution is approximated around the result of the initial MAP estimation with a finite difference approximation of the Hessian matrix. Since the Hessian of the posterior distribution provides co-variances within parameters, this provides information on the uncertainty over the parameters, but also on any cross-correlations between them. The result of the Laplace approximation is used as an initial guess for the covariance matrix for a Markov chain Monte Carlo sampling technique, specifically an adaptive Metropolis-Hastings algorithm, which finally computes the posterior more accurately.

The initial part of the inter-pulse phase is dominated by volume pumping [16], as also explained in the previous section when discussing the impact of plasma recombination on the initial pressure peak. Therefore, with the aim of characterizing the outgassing process, Bayesian inference is only applied to the pressure curves starting from 50 seconds of inter-pulse time, after which outgassing is dominant. The resulting fitted power law for the dataset of JET discharges is:

$$\begin{aligned} p(t) = & K \times t^{-n} + \mathcal{N}(0, \sigma^2) = \\ & (17.61_{\pm 0.103})t^{-0.828_{\pm 0.001}} \\ & + \mathcal{N}(0, (28.3_{\pm 0.046})^2), \end{aligned} \quad (13)$$

where p [mPa] is the pressure measured at the penning gauge, t [s] is the outgassing time, and the model relative error is expressed as a percentage.

The resulting posterior distributions of the coefficients of equation (13) are illustrated in the
<figure><img src="image_7.png" /><figcaption>Figure 6: Results from Bayesian analysis of experimental outgassing curves, obtained using the framework developed in reference [19]. The posterior distributions of fitting parameters K, n and σ are in the subplots forming the diagonal of this matrix of figures. The cross-correlations between fitting parameters are on the off-diagonal subplots.</figcaption></figure>

diagonal subplots of figure 6. The MAP estimation for the power law exponent yields $n = 0.828$, which maximizes the posterior distribution of $n$ (see figure 6) and is therefore the most probable exponent among the outgassing curve database. This is consistent with previous studies on JET outgassing with Be-W configuration, for example $n = 0.8$ found in [9] and $n = 0.89$ in [2]. The cross-correlations between fitting parameters are shown in the off-diagonal plots in figure 6. K and n are found to be linearly correlated: a higher K results in a larger n, hence a steeper pressure decrease. This behaviour can be explained by a faster depletion of the wall inventory: a higher initial outgassing rate right after the pulse quickly depletes the implanted particles, resulting in a lower outgassing, hence lower pressure, later during the inter-pulse dwell time. This is consistent with the findings of section 2.1, where this trend was observed in specific individual discharges.

Attempts to correlate K and n with the preceding pulse parameters proved inconclusive, suggesting that simplistic mathematical correlations cannot fully capture the outgassing dependence on the preceding pulse parameters. Although the statistical correlations of sections 2.3 and the power law of section 2.4 provide interesting insights into outgassing at JET, they cannot be extrapolated easily to ITER. Therefore, physical modeling is found to be necessary at this point. The next section introduces the numerical code MHIMS, which will be used in sections 4 and 5 to

simulate outgassing in JET and ITER, respectively.

### 3. Modeling with MHIMS

The numerical simulation code Migration of Hydrogen Isotopes in MaterialS (MHIMS) was presented in references [21], [22] and [1]. The code describes a 1D domain of a material in which implantation, diffusion, trapping and desorption of hydrogen isotopes take place [1]. Inside the material, particles can be found in two different states: mobile particles, diffusing through interstitial sites due to concentration differences; and trapped particles, trapped in defects of the crystalline structure. The equations describing mathematically these processes and implemented in the model are the Reaction-Diffusion (RD) Equations [1]:

$$ 
\left\{
\begin{aligned}
\frac{\partial n_m(x,t)}{\partial t} &= \frac{\partial}{\partial x} (D(t) \frac{\partial n_m(x,t)}{\partial x}) \\
&\quad - \sum_{i=1}^{N_{traps}} \frac{\partial n_{t,i}}{\partial t} + S_{ext}^{i+}(x,t) \\
&\quad + S_{ext}^{at}(x,t), \\
\frac{\partial n_{t,i}}{\partial t} &= \nu_{t,i}^*(T) \frac{n_i(x,t)-n_{t,i}}{n_{IS}} n_m \\
&\quad - \nu_{dt,i}(T) n_{t,i}, \\
\text{BC at } x=0: \quad &n_m(0,t) = 0, \\
\text{BC at } x=L: \quad &D(T) \frac{\partial n_m}{\partial x}(L,t) = 0,
\end{aligned}
\right.
\quad (14) $$

where $n_m$ [m$^{-3}$] is the mobile particle density, $n_i$ [m$^{-3}$] is the density of traps of kind i, $n_{t,i}$ [m$^{-3}$] is the density of trapped particles in traps of kind i. $D(T) = D_0 \exp(-E_D/(k_b T))$ [m$^2$s$^{-1}$] is the diffusion coefficient, where $E_D$ [eV] is the barrier energy for diffusion, T [K] is the material temperature, $k_b = 8.62 \times 10^{-5}$ eVK$^{-1}$ is the Boltzmann constant. $n_{IS}$ [m$^{-3}$] is the interstitial site density i.e. the number of crystalline sites per unit volume where HI can diffuse. $\nu_{t,i}^*(T) = D(T)/\lambda^2$ [s$^{-1}$] is the trapping rate coefficient in traps of kind i, where $\lambda$ [m] is the distance between two interstitial sites. $\nu_{dt,i} = \nu_{dt,i}^0 \exp(-E_{dt,i}/(k_b T))$ [s$^{-1}$] is the detrapping rate coefficient at traps of kind i, where $E_{dt,i}$ [eV] is the detrapping energy of traps of kind i. Finally, $S_{ext}^{i+}$ [m$^{-3}$s$^{-1}$] and $S_{ext}^{at}$ [m$^{-3}$s$^{-1}$] are the volume sources of HI implantation, which are computed from the ion and atom implantation fluxes to the surface [1]. These sources have a spatial dependence on the implantation depth $x$ in the material, which is a Gaussian distribution with mean and standard deviation computed with the binary-collision code TRIM [23].

The simulated 1-D domain is the thickness L of the material layer in which these processes take place, assumed to be 100 µm for bulk surfaces [1] and 10 µm for co-deposits [24]. The domain is discretized in the $x$ direction with an exponential mesh of 1000
cells, such that the resolution at the surface is refined to capture correctly the implantation sources, which have a maximum range of ~10 nm. At the surface ($x=0$), it is assumed that the particle density is zero, imposing a Dirichlet condition: when a particle reaches the surface, recombination and desorption are assumed instantaneous [1]. At the bulk ($x=L$), it is assumed that the particle flux is zero, imposing a Neumann condition. In the case of co-deposits, the interface between the surface layer and the bulk material is found to behave as a barrier for particle diffusion, hence the Neumann condition is more suitable [1]. For PFCs with the same bulk and surface material, this condition is not expected to significantly impact the results [1].

The materials considered in this work are W, Be, and stainless steel 316L, found at JET outer main chamber [25, 26] - see figure 7. Several material properties must be defined in MHIMS, which are the free parameters of the RD equations (14). Important variables are the barrier energy for diffusion and the trapping properties of each material (trap types and densities, trapping and detrapping energies). These values are taken from the literature for the different materials: Be from [1, 27]; W from [1]; stainless steel from [28, 29]. The number and properties of traps are typically determined by fitting models based on RD equations to the results of thermal desorption spectroscopy (TDS) experiments [22]. In TDS, a material sample, previously implanted with deuterium, is gradually heated under controlled conditions, and the rate of desorbed molecules is measured as a function of temperature. The samples are either laboratory-implanted or collected from fusion devices after experimental campaigns (post-mortem analysis) [30]. A summary of the material properties used is given in tables B1 and B2 in Appendix B.

MHIMS requires for each simulated surface: material properties, temperature, and incident flux. This allows a reservoir model of JET and ITER PFCs to be constructed, where surfaces subject to similar conditions can be grouped into a single reservoir. MHIMS is then used to simulate consecutive pulses with inter-pulse outgassing for the different reservoirs, resembling what happens during a day of operation. As a result, the total outgassing expected in the vessel in between pulses can be obtained and the pressure computed using equation (4). The initial condition ($t=0$ s) for equations (14) is set in such a way as to reproduce the expected condition of the wall in the morning before starting operation. Starting from an empty wall, a long implantation phase is simulated to saturate the surfaces, followed by 10 hours of overnight outgassing. The final state of this initialization phase is the starting condition for the simulation of consecutive pulses with inter-pulse outgassing.

# 4. MHIMS simulations for JET

## 4.1. Modeling

As illustrated in figure 7, the different reservoirs identified in JET are: Be limiters, Be inner main chamber, Be co-deposits in the divertor, W high flux divertor, steel (outer) main chamber, W low flux divertor. The identification of the different reservoirs was based on the materials, on the different flux received by the surfaces and on the locations of the co-deposits. It should be noted that the JET main chamber is actually composed of several materials besides stainless steel, such as Inconel. However, this study focuses exclusively on stainless steel, as it is presumed to be the predominant material, and has more readily available data ([28, 29]). The fluxes used as input data for the MHIMS implantation phase are taken from a simulation performed in reference [1] of the plasma boundary of JET pulse #89044 (H-mode, divertor configuration) with the transport code SolEdge2D. The co-deposit location is known from ex-situ analysis of JET PFCs [30]: Be co-deposits are found primarily in the inner region of the divertor. These co-deposits can be partly responsible for dynamic retention of D [8]. A summary of the input data used for each reservoir is found in table B3 in Appendix B. The fluxes are averaged over each surface and assumed to be uniform. The ion flux on the main chamber is assumed to be concentrated in the plasma-wetted areas: the limiters. Therefore, given that the edge simulations assume toroidal symmetry, which is not the case in this region of the main chamber, the ion fluxes are rescaled to a smaller surface area. The remainder of the main chamber receives only atom flux.

The simulation is set up to resemble the series of discharges #82666-#82673 from reference [9]. The implantation phase lasts 22 s, which was the average time in divertor configuration, while the outgassing phase is 2700 s (45 min) long, as it was on average in the experiments. A total of 16 plasma pulses are simulated: 8 at constant temperature, to isolate the loading effect, followed by 8 at increasing temperature, to isolate the temperature effect.

Temperature data is taken from thermocouples in the bulk of the PFCs at the end of every JET pulse. Since these temperatures do not significantly decrease during the inter-pulse period [1], they are assumed constant throughout the outgassing phase. Figure 8 shows the temperature measured (circles) compared with the assumed temperature increase used as input for the different reservoirs in MHIMS (dashed lines). The Be co-deposits and W high flux reservoirs were assigned the average temperature from the divertor tiles close to the strike points location (1,3,5,6). The W low flux reservoir was given the average temperature
<figure><img src="image_8.png" /><figcaption>Figure 7: (a) Picture of JET PFCs adapted from reference [31] with identified reservoirs for MHIMS simulations. Please refer to the online version of the article for the color version of this figure. (b) Scheme of JET divertor tiles from reference [32]: the Be co-deposits cover tile 0 and partly tile 1; the W high-flux reservoir corresponds roughly to tiles 1, 3, 5, and 6; the W low-flux reservoir covers the remaining tiles.</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Figure 8: Bulk temperatures from thermocouples at the end of JET pulses #82666-#82673 (circles) compared with the assumed temperature increase used as input for the different reservoirs in MHIMS (dashed lines). (codep.=codeposits, div.=divertor, h.f.=high flux, l.f.=low flux)</figcaption></figure>

from the remaining tiles further from the strike points (4,7,8). The Be limiters are assumed to be the only part of the main chamber with increasing temperature, while the remainder (Be inner main chamber and steel outer main chamber) is assumed to stay at the initial temperature of 175 °C due to the low heat flux

received.

It might be argued that the PFC surface temperatures are likely higher than the values measured by thermocouples in the bulk. This is particularly true in the plasma-wetted areas, but only during the pulse, or at most immediately after. The plasma implantation phase is rather short, 22 s only, compared with the 45 minutes of outgassing. Therefore, the PFC surface temperatures are assumed to decrease to the bulk temperatures on a much faster timescale than the outgassing time. Moreover, the plasma-wetted areas are rather small in terms of surface. It is true, however, that these areas, although small, receive the highest flux. Nevertheless, these small high-flux areas also have the highest surface temperatures, leading to more outgassing during the pulse, which results in lower overall retention at the end of the pulse.

The outgassing rates obtained from the MHIMS simulations of each reservoir are summed to obtain the total outgassing rate in Ds⁻¹ released into the JET vacuum vessel. In order to be used in the gas balance equation (1), the total outgassing rate in Ds⁻¹ must be multiplied by a factor 0.5 to account for the unit conversion to D₂s⁻¹, since deuterium desorbs in the form of molecules [2]. Given the effective pumping speed S<sub>eff,JET</sub> = 203 m³s⁻¹ (from references [9, 13, 14]), the resulting pressure at the penning location p<sub>g</sub>(t) can be computed with the gas balance equation (4):

$$p_g(t) \approx \frac{k_b T_g}{S_{\text{eff,JET}}} Q_{\text{outgas}}(t), \quad (15)$$

where Q<sub>outgas</sub>(t) [D₂s⁻¹] is the total outgassing rate from the MHIMS simulation, and T<sub>g</sub> [K] is the neutral gas temperature at the penning location, assumed to be 293 K (20 °C).

## 4.2. Results

Figure 9 shows the total number of outgassed D particles from the different reservoirs over the simulated 45 min of outgassing time for the first and last simulated discharges. The quantity is computed by integrating in time the outgassing rate in Ds⁻¹ given as output from the MHIMS simulation. The results show that the main source of outgassing are the Be co-deposits, followed by the Be limiters, while the reservoirs in W and steel give a negligible contribution. This is primarily because Be has higher trap densities compared to W and steel (see table B2 in Appendix B). Moreover, the Be co-deposits, being located in the vicinity of the inner strike zones, receive relatively high particle fluxes. In reference [18], the co-deposits are found to heat up very rapidly during pulses where
the strike point was purposefully located nearby to enhance T desorption. This rapid heating is attributed to their poor adhesion to the surface. Nevertheless, they also cool down quickly once the plasma terminates [18]. Be limiters receive lower heat and particle fluxes compared to the divertor reservoirs, but still higher than the remainder of the main chamber, leading to an increase in temperature and outgassing. According to this analysis, therefore, even if W is located in high particle and heat flux areas (e.g. at the strike points), its impact on outgassing can be neglected in comparison with Be, as also found in previous studies [1, 7]. The steel outer main chamber, regardless of the large surface area (see table B3 in Appendix B), also makes a negligible contribution, due to low trap density of steel and low flux received. The total amount of outgassed D particles can be computed by summing the contribution from each reservoir, resulting in $1.6 \times 10^{22}$ D for the first pulse and $4.6 \times 10^{22}$ D for the last. These quantities are consistent with the range $1.5 - 3 \times 10^{22}$ D found experimentally in references [8, 11].

The resulting pressure at the penning location, computed with equation (15) for all simulated discharges, is shown in figure 10 and compared with the experimental curves from the whole dataset of 1292 JET pulses. In the first 8 simulated pulses, computed assuming constant temperature, the pressure increase is driven only by the progressive wall loading, but this remains very limited, since an equilibrium is reached after only 3 pulses. The temperature increase has a stronger impact in the last 8 pulses, where 6 discharges are required to reach an equilibrium. In reality, these two effects occur simultaneously, and equilibrium is reached after a few discharges, as found in the reference experiments described in section 2.1. As illustrated in figure 10, the simulated and experimental pressure curves are in qualitative agreement, with the simulations occupying the lower range covered by the experiments. The simulated pressure accounts only for outgassing and does not include the contribution from plasma recombination, which would affect only the initial pressure peak, as explained in section 2.3. Both the simulated and the experimental curves converge to a constant power law decay after some time. The power law is however slightly different: while experimental exponents were found to be $n \sim 0.828$, as seen in section 2.4, the simulated curves have $n \sim 0.66$.

# 5. MHIMS simulations for ITER

## 5.1. Modeling

For the ITER simulations, the MHIMS model is modified by adapting reservoirs and input operational data. Stainless steel is also present in ITER, but it accounts only for small surface areas in the diagnostic

ports and in between the FW panels. Considering the results of the JET simulation, the outgassing contribution from stainless steel in ITER will be negligible. The ITER divertor will comprise fully active cooled bulk W monoblocks and flat tiles [33]. The FW material will be discussed in section 5.2. Unlike JET, ITER will not have limiters. However, there will still be a distinction between plasma-wetted areas of the main chamber, receiving the full ion flux from the plasma, and the remainder only receiving the atom flux. For this reason, the ITER simulation retains a reservoir labeled as limiter, although this does not correspond to a separate physical component within the main chamber. Fluxes across the entire main chamber and divertor surfaces are taken from a plasma boundary simulation with the transport code SOLEDGE3X of a low current diverted hydrogen L-mode plasma, expected to be one of the typical scenarios exploited in the early phases of ITER operation [34]. Table B4 in Appendix B compiles a summary of the input data used for each reservoir. The effective pumping speed $S_{ITER}$ is computed starting from the analysis of reference [35], resulting in $82 \text{ m}^3\text{s}^{-1}$. The volume $V_{ITER}$ is $1400 \text{ m}^3$ [4]. The simulation is run in a similar fashion as for JET, except that the implantation phase is fixed at 400 s as characteristic of the typical pulse durations which can be run for low power, low current L-modes. Meanwhile, the expected ITER inter-pulse duration is expected to be quite close to that of JET, so the same 45 min period is assumed here. The wall temperature during outgassing is assumed constant at 70 °C, which is the temperature of ITER's PFC active cooling [36]. It is of course evident that PFC surfaces in plasma wetted areas will be higher, and often considerably higher, than this value. Such areas also receive high particle fluxes. However, these wetted areas represent only a very small fraction of the total wall surface. Moreover, the active cooling will ensure that all surfaces return to the cooling temperature very rapidly (few seconds) in comparison to the inter-pulse dwell time once plasma loading terminates.

## 5.2. First wall material: Be or W

Prior to the recent ITER-rebaselining activity [10], the ITER FW was entirely constituted of Be flat tile armour. This was the primary motivation for the conversion of JET, in 2011 [26], to the "ITER-Like" wall with majority Be PFCs in the main chamber. The first step in the analysis here is thus to perform an extrapolation to ITER assuming a Be FW. Since Be migration patterns in a Be main chamber ITER are theoretically expected to be similar to those found experimentally at JET [37], the outgassing analysis assumes that the same kinds of Be co-deposits will also
<figure><img src="image_10.png" /><figcaption>Figure 9: Outgassed D particles over 45 minutes of outgassing in MHIMS simulations for JET, for the first and last simulated discharges. Note the logarithmic scale on the y-axis. (m.ch.=main chamber, div.=divertor, codep.=codeposits)</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 10: Pressure during outgassing from MHIMS simulations for JET (1-16) compared with experimental pressure curves from non-disruptive (grey) and disruptive (pink) pulses.</figcaption></figure>

be formed, predominantly at the upper, inner divertor region.

These simulations can then be compared with the same analysis but with a full W wall which replaces Be in the 2024 re-baseline. In this case, a MHIMS

simulation is run in which all PFCs are in W (FW and divertor) and there are no divertor co-deposits. The same 70 °C cooling temperature is assumed, so that this is a simulation which is actually more pertinent to the DT-1 phase of operations in the new baseline [10]. In the early “Start of Research Operation (SRO)” phase of the re-baseline, W will primarily be used in the main chamber, but this will be a provisional, inertially cooled FW, to be replaced before DT operations begin. A diborane boronization system has also been included in the re-baseline as a risk mitigation measure in case plasma start-up on W surfaces proves challenging [10]. Section 5.4 will discuss the possible impact of boron layers on the outgassing simulations.

### 5.3. Results

The two models for ITER, respectively with a Be and W FW, are used to simulate repeated plasma loading with inter-pulse outgassing, as done for JET. The total number of outgassed D particles from each reservoir during the inter-pulse dwell time is shown in figure 11 for the Be FW case. Differently from JET simulations, Be co-deposits and limiters would not be the dominant sources of outgassing in ITER with Be FW, which instead is now the outer main chamber, the largest Be surface. This reservoir in JET is made of steel, which outgasses much less than Be, and is thus a negligible contributor. Regardless of the relatively low flux received, the large surface area makes the Be outer main chamber the main source of outgassing.
<figure><img src="image_12.png" /><figcaption>Figure 11: Outgassed D particles over 45 minutes of outgassing with MHIMS simulations of ITER (2016 baseline, W+Be), for the first and last discharges of a series of 16 identical simulated pulses. Note the logarithmic scale on the y-axis. (m.ch.=main chamber, div.=divertor, codep.=codeposits)</figcaption></figure>

Figure 12 illustrates the time dependence of the pressure computed from equation 15 using the outgassing rates from MHIMS simulations of the Be FW case, for a series of 16 consecutive discharges. The loading effect slightly increases the outgassing in the first discharges, but it rapidly reaches equilibrium. In contrast to the earlier JET simulations, the active cooling of the ITER PFCs eliminates the temperature effect and outgassing during consecutive pulses is very similar.

Finally, it is possible to assess whether the hydrogenic pressure is low enough for plasma breakdown after outgassing during the reference inter-pulse dwell time of 30 mins. The required pressure for reliable plasma breakdown in reference [4] is 0.5 mPa, while a maximum prefill pressure of 1 mPa would be allowed according to reference [5]. A conservative approach is taken here and the lower threshold is used, considering that prefill will be necessary and pressure may be higher due to impurity outgassing, which is not considered in this study. As illustrated in figure 12, with a Be FW, the hydrogenic pressure after 30 mins is 0.12 mPa for the first simulated discharge and 0.17 mPa for the last. Both values are lower than 0.5 mPa, suggesting that outgassing would not impose a strong limitation to inter-pulse dwell time in ITER, even with a Be FW, which is expected to be worse than full-W (see below) due to the presence of Be co-deposits and the much higher trap density in Be.

In figure 12, the pressure computed with MHIMS is also compared with an analytical solution of the

<figure><img src="image_13.png" /><figcaption>Figure 12: Pressure from MHIMS simulations for ITER of 16 consecutive discharges with Be FW (2016 baseline, continuous lines) and W FW (2024 baseline, dashed lines), compared with analytical pressure estimate from reference [4] (pink)</figcaption></figure>

gas balance equation during outgassing, from Wykes et al [4]. According to this estimate, the pressure would reach 0.3 mPa in 30 mins, a higher value than estimated here with MHIMS. There can be several reasons for this discrepancy. Outgassing in ITER might have been overestimated in reference [4], since it was computed by multiplying an outgassing rate
from an experiment in JET by a surface area scaling factor of 3.5, with an additional margin of 50% to be conservative. The outgassing rate from Be surfaces in JET was directly used for ITER, without accounting for the lower PFC temperature (due to the active cooling), which would decrease outgassing. Another difference is that the exponent used in [4] is $n = 0.73$, found from experiments in JET, while the MHIMS simulation finds $n = 0.67$.

Figure 12 also illustrates the MHIMS outgassing prediction for a full-W ITER. Outgassing from W is clearly significantly smaller than with a Be FW. The total quantity of outgassed D is an order of magnitude lower than in the case of Be walls, thanks to the lower trap density in W and to the absence of co-deposits. As a consequence, the resulting hydrogenic pressure after 30 mins is much lower: 0.023 mPa for the first simulated discharge, 0.041 mPa for the last.

There may be other limiting conditions for the inter-pulse dwell time, such as the impurity content in the neutral gas inside the main chamber [5]. Given that the hydrogenic pressure obtained from simulations is significantly lower than the required prefill pressure of 0.5-1 mPa, and considering that impurity outgassing should be only a fraction of the hydrogenic outgassing, the impurity fraction at prefill is expected to be rather low.

### 5.4. Discussion on potential impact of boronization on outgassing

Boronization is a wall conditioning technique in which a boron (B) film is applied to the FW of the device [38]. It has been found to be extremely useful in current devices in facilitating plasma start-up on W surfaces [10, 39, 40]. Its primary function in this case is to reduce the presence of low Z impurities in the start-up plasma (particularly oxygen). Boron is a low-Z material like Be, but it remains to be determined whether it behaves similarly to Be from the point of view of outgassing. Simulations for ITER show that B deposited on main chamber surfaces will erode and co-deposit in the inner divertor similarly to Be [10]. Similar migration patterns are observed in experimental metal tokamaks using boronization, like AUG [41] and C-mod [42]. This should in principle lead to stronger outgassing compared to the ideal condition in which only W is present. However, including boronization in the outgassing modelling presented here in a rigorous way is not currently possible, since there are not enough studies on HI outgassing from B. A further aspect to bear in mind is that boronization is not expected to be used frequently on ITER. At most, it could be performed once per two weeks (corresponding to short term maintenance periods when the toroidal field can be decreased), but

is hoped that it would be required only infrequently, for example to facilitate plasma start-up after long term maintenance [10]. In addition, the lifetime of B layers deposited during boronization is expected to be comparatively short, as they will be eroded by plasma ion and charge-exchange neutral fluxes. Therefore, most of ITER discharges are likely to be performed in a majority W environment, consistent with the assumption made here for the MHIMS outgassing simulations for ITER. Recent experimental results from WEST indicate that short-term retention and outgassing are not significantly affected by a fresh boronization [43], although this does not exclude the possibility that the observed outgassing was already dominated by boron introduced prior to the boronization. A similar modeling approach has been applied to isotope changeover experiments in WEST [44], although only the W divertor was considered as the primary reservoir. The simulated vessel pressure, based solely on divertor outgassing, was found to be an order of magnitude lower than the measured value. While direct extrapolation from WEST to ITER is not straightforward, it is reasonable to expect that including B outgassing in the MHIMS simulations could lead to a similar pressure increase. Nevertheless, even assuming a tenfold increase in outgassing due to the addition of B layers, the predicted vessel pressure after 30 min remains below 0.5 mPa.

## 6. Conclusions

This paper investigates the potential impact of inter-pulse outgassing on plasma start-up in ITER. The methodology is first to examine a large experimental outgassing database from the JET tokamak operating with W-Be plasma-facing components. The main identified experimental trends are reproduced with simulations of JET outgassing using the MHIMS diffusion-trapping code. Encouraged by the reasonable agreement found between simulation and experiment for JET, the same code, with appropriately adapted input parameters, is applied to ITER, with both Be and W main chamber armour. This allows positive conclusions to be drawn concerning the likelihood that outgassing between pulses on ITER should ensure low enough main chamber pressures for plasma breakdown.

Analyzing specific JET discharges (section 2.1), it was observed that outgassing increases during the first few pulses of the day due to increases in wall temperature and fuel inventory. This occurs until an equilibrium is reached, after which outgassing is reproducible in JET, provided a similar plasma scenario is used. Different scenarios (plasma configuration, pulse duration, disruptions) can affect outgassing, although not to a significant extent.
Statistical regression analysis on more than 1000 JET discharges identified clear dependencies on pulse parameters (section 2.3), despite the large size of the dataset (described in section 2.2). Note that previous literature focused primarily on the study of only a few selected outgassing curves. In this respect, the analysis presented here is, to the best of the authors’ knowledge, the only attempt to expand to a very large dataset. This database is used to study the typical outgassing power law $p(t) = K \times t^n$ using Bayesian parameter inference. It is found that the coefficients K and n are not independent, but linearly correlated. A larger initial outgassing (high K) leads to a faster depletion of the inventory stored in the wall, hence a faster decrease of outgassing in time (high n). The most probable exponent in the dataset is found to be n=0.828, which is consistent with previous outgassing studies in JET [2, 9].

The statistical correlations found for JET cannot be meaningfully extrapolated to larger devices such as ITER, hence a physical modelling approach was deemed necessary. The numerical code MHIMS is used to construct a reservoir model of JET PFCs and simulate consecutive discharges with inter-pulse outgassing. The simulation finds that the fuel inventory build-up rapidly reaches equilibrium, while the increasing PFC temperature impacts outgassing more substantially. The main contribution to outgassing comes from Be surfaces receiving high flux: the main chamber limiters and the Be co-deposits in the divertor. Outgassing from W and steel is found to be negligible compared to Be. Overall, the good qualitative agreement of this reservoir model with experiments provides confidence that it can be employed for extrapolation to ITER. Moreover, this is a promising methodology for future retention studies, for example for predictions of long-term retention, T inventory, and impurity outgassing.

Outgassing is simulated in ITER comparing the use of Be (2016 baseline) and W (2024 baseline) as FW materials. In ITER, the wall temperature can be assumed constant during operation in the nuclear phase thanks to the actively cooled PFCs, making the temperature effect negligible. Only the fuel inventory build-up during consecutive discharges slightly increases outgassing. Using a Be FW, the hydrogenic pressure after 30 min of outgassing (the expected inter-pulse dwell time in ITER) is ~0.12-0.17 mPa. Outgassing is one order of magnitude lower with a W FW: the hydrogenic pressure after 30 min is ~0.023-0.041 mPa. Switching from Be to W as FW material can therefore reduce both the retention and the outgassing of hydrogen isotopes. Even in the worst-case scenario simulated here, using the Be FW, the hydrogenic pressure remains significantly below the

required prefill pressure of 0.5-1 mPa. When a W FW is considered, the pressure decreases by approximately one order of magnitude, although the contribution of B is not considered in this analysis. Assuming that the inclusion of B layers could lead to a tenfold increase in outgassing, the resulting pressure after 30 min would still remain below the threshold. Therefore, according to the analysis presented here, it may be concluded that fuel outgassing will likely not be the limiting factor for inter-pulse dwell time in ITER.

## 7. Acknowledgements

This work has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200 — EUROfusion). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union, the European Commission or the ITER Organization. Neither the European Union nor the European Commission nor the ITER Organization can be held responsible for them.

## Appendix A. Calibration of pressure measurements

A schematic representation of the locations of the midplane penning gauge and the subdivertor baratron gauge can be found in references [11, 45]. To estimate the pressure difference between the penning gauge location and the vacuum vessel, the pressure measured by the penning gauge can be calibrated against that measured by the sub-divertor baraton gauges, during discharges where only turbomolecular pumps are active. When there is no cryopumping through the divertor, the baratron gauges should be at the same pressure as the penning gauge, since no net flow happens through the sub-divertor duct. However, the gas temperature in the vessel is different from that in the sub-divertor duct. In a vacuum system in the molecular flow regime, a temperature difference leads to a pressure difference due to thermal transpiration, or thermal effusion [12]. The ratio of pressures due to this effect can be computed with the following formula, adapted from [12]:

$$ \frac{p_{vv}}{p_{bar}} = \sqrt{\frac{T_{vv}}{T_{bar}}}, \qquad (A.1) $$

where $p_{vv}$ [mPa] and $p_{bar}$ [mPa] are respectively the pressures in the vacuum vessel and at the baratron gauges location, and $T_{vv}$ [K] and $T_{bar}$ [K] are the gas temperatures at these locations.
The signals from the penning gauge were compared to the baratron gauge signals for the series of discharges #82592-#82622 (also studied in reference [9]), where only turbomolecular pumping is active. The slow turbomolecular pumping also leads to a slower variation of pressure in time, which allows for a better comparison. The ratio of the two measurements was found to be ~1.4 for all the pulses, meaning that the baratron gauges measure a pressure 40% higher than the penning gauge. To account for the transpiration effect, it is assumed that the gas temperature in the vacuum vessel is at the wall baking temperature, 473 K (200 °C), while the temperature at the baratron gauge location, situated outside the vessel, is assumed to be 293 K (20 °C). This leads to a pressure ratio of 1.27, according to equation (A.1). The total calibration factor is then 1.4 × 1.27 = 1.78, which the penning signals must be multiplied by to obtain the vacuum vessel pressure.

Given that $p_{vv}=1.78p_g$, the pumping speed at the vacuum vessel can also be derived starting from equation (4), using the relation:

$$Q_{\text{outgas}}(t) \approx \frac{S_{\text{eff,g}}}{k_b T_g} p_g(t) = \frac{S_{\text{eff,vv}}}{k_b T_{vv}} p_{vv}(t). \quad (A.2)$$

Rearranging this expression yields:

$$S_{\text{eff,vv}} = \frac{1}{1.78} \frac{T_{vv}}{T_g} S_{\text{eff,g}}. \quad (A.3)$$

Therefore, given a pumping speed at the gauge location $S_{\text{eff,g}} = 203 \text{ m}^3\text{s}^{-1}$, the corresponding pumping speed at the vacuum vessel is $S_{\text{eff,vv}} = 184 \text{ m}^3\text{s}^{-1}$.
## Appendix B. MHIMS Input Data

This appendix summarizes the model parameters used for the MHIMS simulations with reservoir models of JET and ITER, respectively carried out in sections 4 and 5.

<table><caption>Table B1: Trap-independent material properties used in MHIMS simulations. A description of most quantities is given in section 3, when explaining the reaction-diffusion equations (14). $K_{sol}$ [-] is the number of interstitial sites per atom and $\rho$ [m$^{-3}$] is the material density.</caption><thead><tr><th>Material</th><th>λ<sub>mat</sub> [pm]</th><th>ρ<sub>mat</sub> [m<sup>-3</sup>]</th><th>K<sub>sol</sub></th><th>D<sub>0</sub> [m<sup>2</sup>s<sup>-1</sup>]</th><th>E<sub>diff</sub> [eV]</th><th>ν<sup>0</sup><sub>t,i</sub> [s<sup>-1</sup>]</th><th>E<sub>t,i</sub> [eV]</th><th>n<sub>IS</sub> [m<sup>-3</sup>]</th></tr></thead><tbody><tr><td>W [1]</td><td>111.7</td><td>6.34e28</td><td>6</td><td>1.90e-7</td><td>0.20</td><td>D<sub>0</sub>/λ<sup>2</sup><sub>W</sub></td><td>0.20</td><td>K<sub>sol</sub>ρ<sub>W</sub></td></tr><tr><td>Be [1]</td><td>157.7</td><td>12.2e28</td><td>2</td><td>1.34e-6</td><td>0.40</td><td>D<sub>0</sub>/λ<sup>2</sup><sub>Be</sub></td><td>0.40</td><td>K<sub>sol</sub>ρ<sub>Be</sub></td></tr><tr><td>Steel [28, 29]</td><td>243.0</td><td>9.91e28</td><td>1</td><td>1.00e-5</td><td>0.61</td><td>D<sub>0</sub>/λ<sup>2</sup><sub>steel</sub></td><td>0.61</td><td>K<sub>sol</sub>ρ<sub>steel</sub></td></tr></tbody></table>

<table><caption>Table B2: Trap-specific material properties used in MHIMS simulations. A description of each quantity is given in section 3, when explaining the reaction-diffusion equations (14).</caption><thead><tr><th>Material</th><th colspan="3">W [1]</th><th colspan="2">Be [27]</th><th>Steel [28]</th></tr><tr><th>Parameter</th><th>Trap 1</th><th>Trap 2</th><th>Trap 3</th><th>Trap 1</th><th>Trap 2</th><th>Trap 1</th></tr></thead><tbody><tr><td>E<sub>dt,i</sub> [eV]</td><td>0.85</td><td>1.0</td><td>1.5</td><td>0.9</td><td>1.3</td><td>0.9</td></tr><tr><td>ν<sup>0</sup><sub>dt,i</sub> [s<sup>-1</sup>]</td><td>1e+13</td><td>1e+13</td><td>1e+13</td><td>1e+13</td><td>1e+13</td><td>1e+13</td></tr><tr><td>n<sub>i</sub>(x) [at.fr.]</td><td>1.3e-3</td><td>3.5e-4</td><td>n<sub>3</sub>(0) = 0.15,<br>n<sub>3</sub>(x<sub>diff</sub>) = 0.01<br>(x<sub>diff</sub> = 1 µm)</td><td>0.095</td><td>0.071</td><td>0.01</td></tr></tbody></table>

<table><caption>Table B3: Input data used for MHIMS simulations for JET, per each reservoir: surface area, mean ion and atom fluxes, mean impact energy and mean impact angle. The mean values are computed by averaging over each reservoir. Results were taken from the SolEdge2D simulation in [1].</caption><thead><tr><th rowspan="2">Reservoir</th><th rowspan="2">Surface area [m<sup>-2</sup>]</th><th colspan="2">Flux [Dm<sup>-2</sup>s<sup>-1</sup>]</th><th colspan="2">E<sup>mean</sup><sub>imp</sub> [eV]</th><th colspan="2">α<sup>mean</sup><sub>imp</sub> [°]</th></tr><tr><th>Ions</th><th>Atoms</th><th>Ions</th><th>Atoms</th><th>Ions</th><th>Atoms</th></tr></thead><tbody><tr><td>Be limiters</td><td>11.08</td><td>8.59e+20</td><td>5.13e+19</td><td>119.42</td><td>74.21</td><td>59.93</td><td>39.46</td></tr><tr><td>Be inner main chamber</td><td>17.92</td><td>0</td><td>3.56e+19</td><td>0</td><td>72.33</td><td>0</td><td>38.08</td></tr><tr><td>Steel outer main chamber</td><td>59.39</td><td>0</td><td>5.66e+19</td><td>0</td><td>74.85</td><td>0</td><td>39.93</td></tr><tr><td>Be co-deposits</td><td>4.69</td><td>9.36e+21</td><td>2.40e+21</td><td>97.28</td><td>29.43</td><td>74.99</td><td>38.37</td></tr><tr><td>W high-flux divertor</td><td>6.17</td><td>6.55e+21</td><td>1.12e+21</td><td>293.56</td><td>71.52</td><td>70.08</td><td>39.57</td></tr><tr><td>W low-flux divertor</td><td>24.72</td><td>2.97e+20</td><td>7.75e+20</td><td>103.10</td><td>84.93</td><td>61.60</td><td>42.70</td></tr></tbody></table>
<table><caption>Table B4: Input data used for MHIMS simulations for ITER, per each reservoir: surface area, mean ion and atom flux, mean impact energy and mean impact angle. The mean values are computed by averaging over each reservoir. Results were taken from the SOLEDGE3X simulation in [34].</caption><thead><tr><th rowspan="2">Reservoir</th><th rowspan="2">Surface area [m<sup>-2</sup>]</th><th colspan="2">Flux [m<sup>-2</sup>s<sup>-1</sup>]</th><th colspan="2">E<sub>imp</sub><sup>mean</sup> [eV]</th><th colspan="2">α<sub>imp</sub><sup>mean</sup> [°]</th></tr><tr><th>Ions</th><th>Atoms</th><th>Ions</th><th>Atoms</th><th>Ions</th><th>Atoms</th></tr></thead><tbody><tr><td>Be limiters</td><td>82.73</td><td>1.83e+21</td><td>9.71e+19</td><td>63.64</td><td>103.69</td><td>52.83</td><td>30.49</td></tr><tr><td>Be inner main chamber</td><td>126.69</td><td>0</td><td>3.83e+19</td><td>0</td><td>92.86</td><td>0</td><td>36.19</td></tr><tr><td>Be outer main chamber</td><td>394.27</td><td>0</td><td>8.43e+19</td><td>0</td><td>124.77</td><td>0</td><td>33.48</td></tr><tr><td>Be upper main chamber</td><td>65.22</td><td>0</td><td>3.03e+20</td><td>0</td><td>21.45</td><td>0</td><td>36.80</td></tr><tr><td>Be co-deposits</td><td>38.11</td><td>1.75e+21</td><td>5.41e+20</td><td>64.03</td><td>23.45</td><td>57.91</td><td>38.75</td></tr><tr><td>W high-flux divertor</td><td>41.41</td><td>9.83e+21</td><td>2.97e+22</td><td>23.86</td><td>5.5</td><td>58.07</td><td>42.25</td></tr><tr><td>W low-flux divertor</td><td>126.69</td><td>6.34e+20</td><td>2.21e+21</td><td>95.20</td><td>14.19</td><td>58.49</td><td>42.36</td></tr></tbody></table>
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