Ion temperature clamping in Wendelstein 7-X electron cyclotron heated plasmas

The neoclassical transport optimization of the Wendelstein 7-X stellarator has not resulted in the predicted high energy confinement of gas fueled electron-cyclotron-resonance-heated (ECRH) plasmas as modelled in (Turkin et al 2011 Phys. Plasmas 18 022505) due to high levels of turbulent heat transport observed in the experiments. The electron-turbulent-heat transport appears non-stiff and is of the electron temperature gradient (ETG)/ion temperature gradient (ITG) type (Weir et al 2021 Nucl. Fusion 61 056001). As a result, the electron temperature T e can be varied freely from 1 keV–10 keV within the range of P ECRH = 1–7 MW, with electron density n e values from 0.1–1.5 × 1020 m−3. By contrast, in combination with the broad electron-to-ion energy-exchange heating profile in ECRH plasmas, ion-turbulent-heat transport leads to clamping of the central ion temperature at T i ∼ 1.5 keV ± 0.2 keV. In a dedicated ECRH power scan at a constant density of 〈n e〉 = 7 × 1019 m−3, an apparent ‘negative ion temperature profile stiffness’ was found in the central plasma for (r/a < 0.5), in which the normalized gradient ∇T i/T i decreases with increasing ion heat flux. The experiment was conducted in helium, which has a higher radiative density limit compared to hydrogen, allowing a broader power scan. This ‘negative stiffness’ is due to a strong exacerbation of turbulent transport with an increasing ratio of T e/T i in this electron-heated plasma. This finding is consistent with electrostatic microinstabilities, such as ITG-driven turbulence. Theoretical calculations made by both linear and nonlinear gyro-kinetic simulations performed by the GENE code in the W7-X three-dimensional geometry show a strong enhancement of turbulence with an increasing ratio of T e/T i. The exacerbation of turbulence with increasing T e/T i is also found in tokamaks and inherently enhances ion heat transport in electron-heated plasmas. This finding strongly affects the prospects of future high-performance gas-fueled ECRH scenarios in W7-X and imposes a requirement for turbulence-suppression techniques.


Introduction
The Wendelstein 7-X (W7-X) experiment [1][2][3] is a stellarator with predicted good equilibrium properties and high normalized pressures of up to β ∼ 5%. Its three-dimensional magnetic configuration has been optimized such that neoclassical transport losses due to finite magnetic ripples have been minimized. For the reactor's relevant low-collisionality 1/ν and √ ν transport regimes, the neoclassical transport scales according to: and (1.2) [4]. Here, n and T represent the species density and temperature, respectively. The reduction of the effective magnetic ripple ε eff < 1% in W7-X has minimized the neoclassical transport losses in the reactor relevant 1/ν regime. This neoclassical transport optimization has been experimentally demonstrated in plasmas in which the turbulent heat transport is suppressed by means of steep density gradients. Thanks to the beneficial 3D geometry of W7-X [5], both the ion temperature gradient (ITG) and trapped-electron-mode (TEM) turbulence may be reduced or even suppressed when the ion temperature and density gradients align [6,7] and the (ion) neoclassical transport becomes the more dominant transport mechanism. These conditions were achieved after a train of ice pellets transiently produced a peaked density profile. In these plasmas a central ion temperature of more than T i,0 = 3 keV could be achieved at a central density of n e,0 = 8 × 10 19 m −3 , with hydrogen as a fuel and with only 5 MW of electron cyclotron resonance heating (ECRH) [8][9][10]. The improved confinement was lost after relaxation of the density profile over a particle-confinement timescale of several 100 ms, and oftentimes due to an MHD event [8]. Despite this transient nature, neoclassical transport simulations have shown that this high performance would not have been possible in a neoclassically less-optimized stellarator [8,10,11] and hence, the neoclassical optimization of W7-X was demonstrated. The energy confinement scaling of the most successful plasmas is 40% larger than given by the International Stellarator Confinement Scaling ISS04 [12,13]. This paper discusses a transport regime in which turbulent transport is not suppressed, and the performance is limited with respect to the ISS04 scaling. So far, this has been the case for almost all stationary plasmas in W7-X with ECRH heating and standard divertor-or main-chamber gas fueling. These plasmas feature flat density profiles, and their transport is dominated by anomalous transport. Their confinement scaling lies at or is less than the ISS04 scaling, depending on the density in these plasmas [14]. At low densities, the confinement timescales are similar to the ISS04 scaling i.e. τ E,ISS04 ∼ n 0.51 , whereas, at high densities that approach the radiative density limit, an increase in density no longer scales beneficially following τ E ∼ n α , with α ≈ 0. Beyond the radiative density limit, increasing the density further becomes detrimental and α < 0. The decrease of α with density is gradual rather than abrupt, such that for almost the entire accessible density range, increasing the density leads to an increase in the stored energy [14]. Typically, in such plasmas, a radiative front is held outside the normalized minor radius of r/a ∼ 0.8 until the radiative density limit is reached, as shown in appendix A. In the confinement region r/a < 0.8 the radiation losses are very small indeed and well below the 5% level of the ECRH input power. Indeed turbulent transport, and not radiation losses, limit the heat transport and are responsible for the so-called ion temperature clamping observed in these plasmas.
The maximum line-averaged density achieved so-far in W7-X in a gas-fueled ECRH heated plasma is n e = 1.4 × 10 20 m −3 with P ECRH = 6 MW and second-harmonic ordinary resonance heating (140 GHz, B = 2.5 T) in a plasma with a low impurity content (Z eff ∼ 1.3) following boronization wall conditioning [15], although its confinement scaling was low at τ E /τ E,ISS04 ∼ 0.6 (τ E = W dia /P tot , where P tot is the total input power). Nevertheless, such plasmas are impressively stationary, with the longest high-power pulse (P ECRH = 5 MW) and detached divertor conditions lasting for 30 s [16,17]. At a lower input power P ECRH = 2 MW, and under attached divertor conditions, a pulse length of 100 s was even achieved [2,18].
The density profiles in such plasmas are flat to slightly peaked, as can be seen from e.g. the density profiles shown in this paper. Based on the assumption that neoclassical transport is the dominant transport process, the fear was expressed in [19], that hollow density profiles are inevitable in W7-X centrally heated plasmas, given the recycling properties of the device. However, in actual experiments, no evidence of hollow electron density profiles has been found, indicating that turbulent rather than neoclassical transport may dominate the particle transport. This has been confirmed by impurity transport experiments. In [20] no Z-dependence of the impurity transport was observed, although it had been expected, based on neoclassical transport predictions. Moreover, in an ECRH experiment at low electron density, it was shown that the impurity transport time (τ imp ) lies well below its neoclassical prediction [21], and no sign of impurity accumulation was seen. Furthermore, in a follow-up ECRH power-step-down experiment, it was shown that τ imp decreases with an increase of the ratio of T e /T i when P ECRH is increased [22]. The latter is a signature of ITG-type turbulence, and the experimental findings are consistent with linear turbulence calculations using the GENE code [23] (as will be shown in this paper). Now turning to the heat transport, the electron temperature in gas-fueled ECRH plasmas can be varied widely from ∼1 to 10 keV, depending on density and input power, as seen in figure 1. At low electron densities in W7-X with central electron root confinement, neoclassical transport contributes significantly to the total power balance (PB), as was reported in [24][25][26]. However, at increasing densities, it was shown that the electron heat transport is dominated by turbulence, in which the electron heat diffusivity χ turb,e is larger than the neoclassical diffusivity by up to an order of magnitude. PB analysis shows that χ turb,e = χ PB,e = 0.6 ± 0.2 m 2 s −1 , with only a small dependence on the magnetic configuration [27], and no clear sign of a critical normalized electron temperature gradient (a · ∇T e T e ) crit = a/L T e, crit or threshold. In [27] it is therefore concluded that the electron turbulent transport is largely diffusive. In the same work, heat pulse propagation (HPP) studies showed that the electron turbulent transport is likely driven by ETG and/or ITG turbulence in the core with, indeed, a small degree of electron transport stiffness with χ HPP,e /χ PB,e < 2.
The ion heat transport in stationary gas-fueled plasmas with ECRH heating is the subject of this publication. Already noted in [8] is the fact that the ion temperature in gas-fueled ECRH plasmas is saturated or 'clamped' at T i ∼ 1.5 ± 0.2 keV, as seen in figure 1. Counter to the post-pellet plasmas in [8], in which T i > 3 keV was transiently achieved, the clamping of T i appears virtually irrespective of the applied ECRH power and the electron density and electron temperature values obtained. Moreover, all of these plasmas feature flat to slightly peaked density profiles and therefore no density-gradient-aided turbulence suppression. Figure 1 shows that virtually the same T i ∼ 1.5 ± 0.2 keV is achieved in four configurations with various degrees of neoclassical optimization, where one would expect a clear separation on the basis of neoclassical simulations between low and high ε eff configurations, as shown by the grey symbols in the figure. The details of the configurations are given in table 1. The neoclassical transport simulations were conducted with the Neoclassical-Transport-Solver -Suite (NTSS) using mono-energetic transport coefficients for both configurations as calculated using the Drift Kinetic Equation Solver (DKES) as in [28,29]. For the simulations, a wide range of densities with flat density profiles , and a for W7-X representative centrally deposited ECRH heating with P ECRH = 4.5 MW are assumed. It should be noted that in addition to the configuration insensitivity, the clamped central T i found in the experiments lies well below the neoclassical predictions; another indication that different types of transport are at play.
The question arises as to why the electron-heated plasmas feature this clamped central ion temperature. Is the central  (see table 1 for a description of the configurations) as a function of (a) electron temperature T e , (b) line averaged density n e . Also shown in (a) and (b) are the neoclassical simulations for P ECRH = 4.5 MW for the 'standard' (grey triangles) and 'high mirror' configurations (grey squares). In these simulations, the highest temperatures can be achieved in the standard configuration (T i filled, and T e open symbols), thanks to its better neoclassical optimization and smaller effective magnetic ripple ε eff . temperature limited simply because the heat per particle transferred to the ions does not increase with an increase in the density or heating power? Or is it caused by the off-axis nature of the exchange power, so that no heat arrives at the core of the plasma? Or rather, does turbulent transport limit the ion temperature gradients , and is the clamping related to profile stiffness? As an answer to these questions, it will be shown in this paper that the T i clamping is the result of a combination of effects: (a) the limited and broad ion heating due to power transfer from electrons in ECRH heated plasmas, (b) the expected increase of heat transport according to the gyro-Bohm scaling and (c) the exacerbated turbulent heat transport due to the effect of an increasing T e /T i ratio on ITG turbulence in such plasmas. The rest of this paper will address each of these aspects in turn, giving the full details of the simulations and experiments used to reach this conclusion.

Ion heating in ECRH plasmas
In order to select the target experimental conditions for the ion heat transport study, we first look at the variation of the ion heating profiles under typical experimental conditions. In electron-heated plasmas, the ions are heated indirectly through the electron-to-ion exchange power p e-i , which for illustration purposes for a single-species plasma (where n e = n i · Z), and following [30], is given by: where the units of T e and T i are keV and n e is 10 19 m −3 , and where τ ei is the electron-ion collision time, τ ee is the electron-electron collision time, m p is the proton mass, m e is the electron charge, M is the atomic mass number, Z is the atomic charge number, Λ ee is the electron-electron Coulomb logarithm, and q e is the electron charge. The approximations are shown to demonstrate the basic parameter dependencies and are not used in the calculations presented in this paper.
To illustrate the ion heating levels and ion power 'deposition' profiles that can be achieved, the energy exchange p e-i is calculated from representative synthetic profiles of T e , T i and n e , as shown in figure 2, using truncated Gaussian profile shapes. These profiles are explicitly taken as the inputs to the p e-i calculations only, and do not represent any transport analysis, nor indicate whether they are achievable in W7-X. The ion temperature profile has been kept fixed to represent the 'clamped' T i,0 = 1.5 keV, whereas for the electron profiles, the central T e,0 is varied from 2 keV to 6 keV and a representative central density n e,0 = 7 × 10 19 m −3 is chosen. On axis, the calculated p e-i,0 increases with T e until it saturates at T e ∼ 4 keV, but the exchange power profile shape continues to broaden for the entire T e range considered; see figure 2(b). In other words, there is a limit to how much the central ion heating can be enhanced by increasing the temperature difference, due to the (T e −T i ) T 3/2 e term in p e-i , but the heated volume can be increased. The ion heat flux Q i is defined by A · Q i(r) = r 0 p e-i dV dr dr, where A is the flux surface area at r. As an example, figure 2(c) shows that at the central location r/a = 0.3, Q i saturates for T e > 3 keV, whereas further out at r/a = 0.6, it can continue to rise to T e = 6 keV. However, for electron-heated plasmas, the central ion heating can be enhanced by increasing the electron density, as is illustrated in figure 2(d) for fixed values of T e,0 = 3 keV and T i,0 = 1.5 keV. Due to the n e 2 term in p e-i, the on-and off-axis heat flux Q i increases simultaneously. In experiments, fixing T e,0 = 3 keV would require that n e and P ECRH are simultaneously increased.
To conclude, in electron-heated plasmas, the ion heating profile is broad and the heat flux peaks off axis. Whether a broad heating profile can lead to high central temperatures strongly depends on the type of transport at play. In the case of non-stiff diffusive transport this would necessarily lead to broad and flat temperature profiles as were found, for example, for electron heat transport in [24,31]. However in the case of strong profile stiffness, as is found, for example, in tokamak H-mode plasmas (e.g. [32][33][34]), the achievable central temperature does not strongly depend on the shape of the heat deposition profile; instead, it is largely determined by the strength of the edge pedestal pressure p ped . The latter lifts up the stiff core profile with p ped /p 0 ∼ constant, and T ped /T 0 ∼ constant.

Profile preparation
In order to compare simulated ion and electron temperature profiles with experimental data in W7-X, the measured profiles are required. The electron temperature is measured using Thomson scattering (TS) [35,36] and validated using electron cyclotron emission (ECE) radiometry [37,38] diagnostics. The latter depends for its measurement volume localization on calculations using the ray-tracing code Travis [39] and the magnetic field from the equilibrium code VMEC [40]. The line-average plasma density is measured by a singlechannel interferometer [41], and the plasma density profile is measured by TS. The ion temperature profile in W7-X is measured by an x-ray imaging crystal spectrometer (XICS) diagnostic [42][43][44] and a charge exchange recombination spectroscopy (CXRS) diagnostic [45]. To enable CXRS T i measurements, short 10 ms beam blips (compared to τ E > 100 ms of neutral beam injection (NBI) heating) are used. The impact on the plasma stored energy is less than ΔW dia = 5% (see figure 11). The CXRS ion temperature, the ECE, and the Thomson electron-temperature measurements show excellent consistency in the outer halves of the profiles (r/a > 0.5) with good e-i equipartition. The XICS temperature measurement is, however, hampered by as-yet unresolved uncertainties in the instrument profile of the spectrometer. In order to match the T i vaules measured by XICS to those measured by CXRS, as well as to the T e values measured by TS & ECE outside r/a > 0.5, the XICS T i profiles are given a single offset of ΔT i = −100 eV in all the XICS profiles presented in this paper.
Fits of the experimental profiles are used as inputs for further analysis. The equilibrium for mapping profiles is obtained using the VMEC code [40] with the kinetic profile information as input for an iterative equilibrium calculation. The n e , T e , and T i profiles are fitted using the LOWESS algorithm (locally weighted scatterplot smoothing) (see e.g. [46]) combined with a 'leave-one-out' (median) filter to deal with outliers. LOWESS carries out a locally weighted regression of variable y on variable x inside a windowed range and saves the smoothed variable. It is computationally intensive, but offers a stable fit to scattered data. The fit errors are determined by a Monte Carlo error estimation, in which each data point is allowed to move inside its own error margins and the fitting is repeated N times, thus obtaining a set of fits from which the standard deviation σ can be estimated; the 2σ error margins are shown in the profile plots in figures 3, 7 and 15. The LOWESS filter width, the outlier window used for data-point weighting, was set to r/a = 0.1 for the Thomson T e and CXRS T i profiles. For the TS density profiles a broader filter width of r/a = 0.2 was used due to larger statistical and systematic errors. As the XICS T i profiles are the result of an Abel inversion [42,44] no further fitting of this data was applied, but the plotted error margins are a result of the statistical spread of the profiles inside the averaging time window.
Residual profile inconsistencies are observed in the outer regions of the profiles, where T e = T i is expected. In order to obtain a meaningful PB we therefore set T e = T i in the outer region of the profile beyond the point where T e and T i first cross. As good T i profile quality can only be guaranteed for r/a < 0.8, the PB analysis in this paper is restricted to the range within r/a = 0.6. Note that as ion heat transport is studied here, the electron temperature is deliberately set equal to the ion temperature, rather than vice versa. In [27], where the electron transport was studied, the reverse was done by setting T i = T e from the point where T i > T e in the outer region of the plasma.

Neoclassical transport compared to experimental findings
In tokamaks, neoclassical transport has an inverse temperature dependence based on proportionality for banana-orbit-like transport. Using χ NC,tok ∼ ρ 2 pol /τ i , where τ i is the ion collision frequency, one can derive χ NC,tok ∼ n/ √ T or χ NC,tok ∼ T −3/2 if constant pressure is assumed. On the contrary, neoclassical stellarator diffusivity has a positive temperature dependence and scales strongly, according to T 7/2 , and somewhat weaker, according to T 5/4 , for the 1/ν (1.1) and √ ν (1.2) collisionality regimes, respectively [4]. Nevertheless, for the optimized W7-X configuration, the low ion-power density in electron-heated plasmas combined with pure neoclassical transport does not lead to ion temperature clamping at T i ∼ 1.5 keV as observed in experiments. Indeed, figure 1 shows that the neoclassical transport with the lowest effective magnetic ripple ε eff = 0.8% in W7-X should produce T i > 3keV for densities roughly greater than 7 × 10 19 m −3 . The ion temperature would then indeed saturate, but at roughly double the ion temperature than that observed experimentally. Figure 3 shows an example of the experimental profiles of a hydrogen-fueled ECRH plasma with n e,0 = 7 × 10 19 m −3 with P ECRH = 3.9 MW, a total radiative power P rad = 1.8 MW, and T e,0 = 3.3 keV, T i,0 ∼ 1.6 keV in the standard configuration with ε eff = 0.8% and Z eff = 1.3. The ECRH heat deposition profile is calculated from the launch geometry using VMEC for equilibrium and the TRAVIS code for ray tracing [39]. The radiation loss profile is estimated from bolometer inversion profiles and is located towards the edge of the plasma [47,48], as can be seen in appendix A. The stored energy and normalized pressure of this plasma are W th = 0.5 MJ with a normalized pressure of β ∼ 0.5%, and τ E,exp /τ ISS04 = 0.65.
Also shown are simulated profiles using the NTSS transport code [28] with the central ECRH deposition profile and a fixed density profile (fit) taken from figure 3(b). The neoclassical mono-energetic transport coefficients are calculated using the DKES code [29]. In the first run only a small amount of anomalous transport is assumed as χ ano = 0.1/n e < 0.1 m 2 s −1 across the profile for both ions and electrons, to avoid using unrealistically small neoclassical diffusivity D 22 at the plasma edge, following a similar approach to that described in [29]. Figures 3(c) and (d) show that in this predictive run, the transport is dominated by electron and ion neoclassical heat transport for the core plasma r/a < 0.75. As a result, the NTSS code in this case not only predicts a much higher central T i,0 (and T e,0 ) than those of the experiment, but the T i and T e profiles are also much broader than observed experimentally. This simulated plasma therefore has a much higher global performance with W th,NC = 1.6 MJ, β NC ∼ 1.5%, and τ E,NC /τ ISS04 = 2.1. This agrees with the findings of [29], in which similarly low but not identical levels of turbulent transport were assumed.
For the NTSS simulations to match the experimental global performance and profiles, the anomalous heat diffusivity must be increased by an order of magnitude to χ ano = 1.25/n e ∼ 0.7-1 m 2 s −1 . In this case, the neoclassical transport is overshadowed by the anomalous transport, as can be seen in figures 3(e) and ( f ). Similarly to the situation in the experiment, the plasma performance suffers strongly from anomalous transport, and in these simulations W th,anom = 0.5 MJ, the normalized pressure β anom ∼ 0.5%, and τ E,anom /τ ISS04 = 0.65, replicating the performance found in the experiment. Even though we have applied an ad hoc model for the turbulent transport, the high level of anomalous transport that is required to match the experimental findings clearly implies that the heat transport in the ECRH plasma in figures 3(a) and (b) is likely dominated by turbulent rather than neoclassical transport.
Electron turbulent transport was experimentally studied in [27]. In an electron heat transport study using ECRH modulations at density of n e,0 ∼ 4 × 10 19 m −3 , the PB and HPP transport could be separately identified. The analysis in a standard configuration plasma found that that the average PB diffusivity in the core plasma was χ PB,e ≈ 0.6 ± 0.2 m 2 s −1 . Furthermore, the electron turbulent heat transport appeared largely diffusive, (1) as no clear critical normalised electron temperature gradient (a · ∇T e T e ) crit = a/L T e, crit was found, which meant that it was hard to distinguish between ETG or TEM types of turbulence as the driving transport mechanism; (2) HPP experiments using wide parameter variations showed that the electron turbulent transport features only a low degree of transport stiffness with χ HP,e /χ PB,e < 2. Moreover, the electron heat transport shows only a small configuration dependence and no strong density dependence, and only a weak positive power dependence was found. The study of the ion turbulent heat transport is the topic of the paper at hand.

Modelling of ion turbulent heat transport
The anomalous ion-heat-transport in fusion experiments is generally determined by ITG turbulence, which means there is a limit on the inversed gradient length a/L T i . In tokamaks, this causes a high degree of ion profile stiffness [49][50][51][52][53][54], such that their energy confinement is largely controlled by the achievable edge (ion) temperature, or the so-called pedestal temperature. In [55] the destabilization of the ITG modes in stellarators is compared to that in tokamaks by means of linear gyro-kinetic calculations using the GENE code [23]. The authors of that paper discovered remarkably similar results for both confinement concepts. Important factors for the ITG growth rate are the ratio T e /T i and the normalized density gradient a · ∇n n = a/L n . The temperature ratio T e /T i has a strong destabilizing effect on the ITG modes, whereas a/L n has a stabilizing effect in the absence of trapped electrons. The latter is of utmost important when considering avenues that can suppress ITG turbulence, as is done in e.g. post-pellet experiments [7,8,56]. In W7-X, with its beneficial 3D properties [5,6], a so-called stability valley with elevated a/L T i = a/L n can be achieved when ITGs and densitygradient-driven TEMs, or so-called iTEMs, are simultaneously suppressed [6,7]. For a comparison between the ECRH plasma experiments and the low-density gradients described in this paper, gyro-kinetic calculations were applied with kinetic electrons as well as kinetic ions. Both linear as well as nonlinear gyro-kinetic calculations were conducted. As non-linear gyrokinetic calculations are very expensive in terms of computer time, a smaller subset of simulations was conducted. Both the linear and nonlinear runs were performed for the most unstable flux tube, where the most unstable flux tube was selected from several runs at different poloidal angles. Note that the simulations presented here act as a qualitative comparison to the experimental data and that a quantitative comparison has currently not been conducted.
In the linear simulations, the flux-tube average calculations are conducted with the normalized density gradient fixed at a/L n = 0.5 and the normalized electron temperature gradient at a/L T e = 0. Although in experiments a/L T e a/L T i , the assumption a/L T e = 0 is representative, as the impact of a/L T e on ITG turbulence is small. Figure 4(a) shows the linear growth rate of such calculations using the W7-X 'standard' equilibrium for a wide range of temperature ratios T e /T i = 1-5.5. Quite clearly, the ratio T e /T i enhances the degree of transport stiffness, i.e. the slopes of the curves in figure 4(a). Hence, electron heating can indirectly intensify ion transport as T e /T i is increased.
Nonlinear flux surface gyro-kinetic simulations can calculate the normalized heat flux Q i /Q GB required to sustain a given a/L T i . The gyro-Bohm diffusivity χ GB and hence the gyro-Bohm heat flux Q GB are defined, for example in [57]: where ρ i = m i T i /eB −1 is the ion Larmor radius, c i = eT i /m i is the ion sound speed using the ion temperature in eV, m i is the ion mass in kg, P i is the ion pressure, and a is the effective minor radius. The nonlinear calculations are conducted with a normalized density gradient a/L n = 0 and a normalized electron temperature gradient a/L T e = 0. Qualitatively, the nonlinear calculations are consistent with the linear calculations, although the critical gradient (a/L T i ) crit (zero crossing of the simulations through the ordinate), appears to be increased with respect to the linear calculations. This nonlinear upshift of (a/L T i ) crit compared to linear gyro-kinetic simulations was first reported in [58] and is also known as the Dimits shift.
The important result is that both linear as well as nonlinear calculations show that the ratio T e /T i exacerbates the ITGinduced transport and increases the degree of ion temperature profile stiffness. In predominantly electron-heated plasmas, usually with T e /T i 1, plasma heating can strongly enhance ion turbulent transport and help in saturating or clamping the achievable ion temperature.
As already reported in [57], the choice of magnetic configuration may affect the ITG stability. However, for the four configurations shown in figure 1, ion temperature clamping occurs at the same level of T i ∼ 1.5 ± 0.2 keV. In the context of ITG turbulent transport this may imply that either (1) the turbulence response is very similar between these configurations, e.g. [6], or (2) the initial underlying profile stiffness differences may be obscured by the strong T e /T i effect described above. Therefore, characterizing the perturbative ion transport in W7-X configurations requires a different tool than the simple PB analysis presented in this paper. For example, ion-heat-pulse-propagationstudies require a hardware upgrade to faster spectrometers and the data acquisition of our CXRS diagnostic. Using e.g. NBI modulation experiments, one could then follow an equivalent strategy to that described for electron perturbative transport in [27]. This spectrometer upgrade is planned to be implemented and will hopefully be available in the next experimental campaign.
In the remainder of this paper we will select only the standard configuration with the best NC transport reduction to study the turbulent ion transport in detail. We first investigate how well the ion temperature clamping as seen in W7-X electron-heated plasmas can be explained by assuming gyro-Bohm-level turbulent transport without the additional ITG features described by the theory above. A dedicated set of experiments will then be selected with a variation of the ion heat flux that is as wide as possible, to see whether, from a simple PB argument, evidence for ITG signatutes such as profile stiffness or turbulence-enhancing T e /T i can be observed.
For the gyro-Bohm modelling we use the NTSS code and the density profile shape from the fit in figure 3(b), as well as a representative level of 50% plasma radiation in the outer plasma volume r/a < 0.8-1. As a boundary condition for the separatrix, T i = T e = 100 eV is assumed. For the electron transport we assume a power independent diffusivity χ e,turb = 0.7 m 2 s −1 , which represents the upper limit of the anomalous diffusivity found in [27]. For the ions we assume a gyro-Bohm diffusivity χ i,turb = χ gB that follows equation (3.1).
In the simulations we vary the central electron density from 2-9 × 10 19 m −3 and apply electron heating using the typical ECRH deposition profile for X2 heating from figure 3(a). For each density and power level we allow NTSS to calculate the T e and T i profiles using the neoclassical and anomalous transport coefficients described above, where χ i,turb = χ gB is allowed to vary dynamically with T i across the plasma cross section. The simulation results are shown in figure 5. Interestingly, some of the features found in the experiment are seen in this simple simulation exercise. The central ion temperature indeed saturates at a level close to T i,0 ∼ 1.5 keV. Moreover, there appears to be only a small density dependence on the T i saturation, certainly when we take a power-dependent radiative density limit into account following [14]. The difference in the power dependence on the saturation level seen in figure 5(a) may be due to the fact that a fixed χ e,turb = 0.7 m 2 s −1 is chosen, whereas [27] reports a weak power dependence of χ e,turb . The normalized pressure β = p /(B 2 /2μ 0 ), where p is the volume-averaged plasma pressure, is somewhat higher than that found in the experiment, where typically β ∼ 0.5% for the highest density and input power used in the simulations.
A realistic upper limit for the installed ECRH power in W7-X is 15 MW. In [29], a projection was conducted that assumed mostly neoclassical transport and a turbulence model for the edge plasma. Keeping the overpredictions of the neoclassical transport simulation in figure 3 in mind, we would like to see what the gyro-Bohm model would predict for the higher ECRH levels for a comparison with the results in [29], and to get insight in future performance. Using the same model as that used in figure 5, and following the same approach as in [29], figure 6 'predicts' the performance with upgraded ECRH The critical density n c = 0.5 * P 0.6 is the density above which a radiative collapse will occur for a given input power P and is derived from [14]. The simulation points where n e > n c are not included. power, in terms of confinement normalized to the ISS04 scaling τ E/ τ ISS04 as well as the achievable normalized pressure β . The density profiles are scaled up to the experimental limit of the ECRH-O2 heating scheme, which is n e,0 = 1.6 × 10 20 m −3 . This ion gyro-Bohm transport model extrapolates the central ion temperature to be T i,0 ∼ 2 keV at P ECRH = 15 MW, and when T e approaches T i at the higher density, the confinement and normalized pressure fall well below the projections of [29]. The model produces a slightly more beneficial power scaling and a weaker density scaling than the ISS04 scaling, and the results may therefore even be 'optimistic'. Naturally, the model is for demonstration purposes, and for this reason no sensitivity analysis is provided. We will next study ion heat transport by means of a power balance study of ECRH-heated plasmas. Using a well-selected set of experiments, we study the local heat transport and investigate whether any of the ITG features, such as the T e /T i effect, can be seen in the experiment.

Ion transport in an ECRH power scan
To allow a probe of the ion heat transport, a detailed PB comparison is conducted of both a hydrogen and a helium fueled plasma in appendix A with ECRH power steps ranging from 3.9 to as low as 1.2 MW. Due to the higher critical radiative density limit of helium, compared to that of hydrogen plasmas, a broader power scan is possible in helium. For this reason, helium plasmas are better suited to probing the ion transport, as a wider variation of the exchange power is possible at a constant high density. The high density of n e = 7 × 10 19 m −3 is required to ensure that ion root transport is guaranteed for all power steps. At lower plasma densities, electron-to-ion root transitions occur at varying positions in the profile, depending on the power level (see e.g. [22]). Such transitions complicate the study of the anomalous heat flux Q turb = Q exp − Q NC. Furthermore, the transport gap, or the ratio Q turb /(Q exp − Q NC ), grows in W7-X ECRH plasmas as the density increases, further improving the accuracy in determining Q turb . Finally, in appendix A, it is shown that the transport properties of the Hand He-fueled plasmas are virtually the same. Therefore, the larger power scan in the helium-fueled plasma is used to probe the ion transport in these electron-heated plasmas. The helium fuel purity is 70% He and 30% H, but this is high enough to have a beneficial effect on elevating the critical density.
The power scan from 3.9 MW down to 1.2 MW in the helium plasma shows that with decreasing P ECRH , the central electron temperature decreases from 3 keV to 1.3 keV ( figure 7(a)). The ion temperature variation is smaller and T i,0 reduces from 1.7 keV to 1.2 keV. The density profile remains virtually unchanged for the entire power scan ( figure 7(b)). The T e , T i , and n e profile fits and their error bars (shaded area in figures 7(a) and (b)) are used to calculate the subsequent parameters and their error bars 1 in figure 7(c) onwards 1 The error ranges of the derived parameters are obtained by propagating the T e , T i , and n e errors in the NTSS code using three data inputs: (1) the fits as and the rest of this document. The ambipolar radial electric field, as calculated by NTSS, remains in the ion root during the scan (figure 7(c)), as confirmed by CXRS and Doppler reflectometry (DR) measurements of E r . The calculated neoclassical heat fluxes Q NC, Q i,NC , and Q e,NC stay much lower than the total experimental heat fluxes Q exp , Q i,exp , and Q e,exp , (figures 7(d)-( f )), and thus turbulent transport stays dominant when P ECRH is varied in the scan. The turbulent ion heat flux Q i,turb = Q i,exp − Q i,NC varies from 0.8 MW down to 0.1 MW from the highest to the lowest ECRH power level (normalized to n i values in figure 7(g)). The response of the ion temperature to the decreasing ion heat flux appears curious at first: figure 7(j) shows how the T i profile changes shape during the power scan: outside r/a ∼ 0.5, the normalized ion temperature gradient a/L T i increases, whereas inside this radius it decreases with increasing ion heat flux Q i,turb . The turbulent ion heat diffusivity ·χ i,turb (figure 7(i)) is calculated using Q i,turb = n i · χ i,turb · ∇T i . In the ECRH downward power scan, this heat diffusivity reduces from 1 m 2 s −1 down to 0.1 m 2 s −1 averaged over 0.2 < r/a < 0.8. As expected from the variation of the T i profile shapes, it is found that at a small radius of r/a = 0.3,  the inversed gradient length a/L T i shrinks with increasing heat diffusivity ·χ i,turb and at a larger radius of r/a = 0.6, it increases with increasing heat diffusivity.
The inverse responses of a/L T i at r/a = 0.3 and r/a = 0.6 respectively, to an increase in (a) the turbulent heat flux and (b) the diffusivity are summarized in figures 8 and 9, where in (c) and (d), the turbulent heat flux and heat diffusivity are also shown normalized to the gyro-Bohm heat flux and diffusivity as given by equations (3.1) and (3.2), respectively. The strong T i dependence of the gyro-Bohm normalization compresses the range covered, and for the highest ECRH power actually leads to a reduction of the normalized heat flux compared to the second-highest ECRH power in figure 8(c). Nevertheless, at this small radius, it appears, rather counterintuitively, that the reduction in the normalized gradient length a/L T i is due to an apparent 'negative' ion temperature profile stiffness. Clearly, a strong transport driver is at play that reduces the local gradient ∇T i /T i despite an increase in the heat flux. This observation is in qualitative agreement with the theoretical simulations, in which the ratio T e /T i enhances ITG turbulence, and at a stagnating heat flux Q i /Q GB can even lead to a reduction of a/L T i . Indeed, in the experiment the ratio T e /T i increases from 1 to 1.5 with increasing P ECRH at r/a = 0.3. Further out, at r/a = 0.6, the ratio T e /T i ∼ 1 for all four power steps, and the ITG simulations in figure 4 show that at low T e /T i , it is easier to drive a local ion tempeature gradient with a modest increase of (normalized) heat flux.
The gyro-kinetic simulation examples in figure 4 indicate that the increase of the ion transport stiffness due to the temperature ratio can be strong indeed and may impose a limit on T i . This additional driver for turbulence is inherent to electron-heated plasmas: an increase of the ECRH power enhances T e , which simultaneously enhances the exchange power p e-i as well as exacerbating the ITG turbulence and the degree of T i profile stiffness. These combined mechanisms cause additional clamping of ∇T i /T i , and their integrated effect can contribute to the clamping of the central T i value, as seen in the entire W7-X database of ECRH-heated plasmas in figure 1. A direct comparison of the experimental observations with the gyro-kinetic simulations is computationally expensive and will be the subject of future theoretical and experimental comparisons.

Conclusions and discussion
Ion temperature clamping in ECRH heated plasmas in W7-X is likely a result of various factors that lead to a reduction in the local ion temperature gradients and the global plasma performance. First, the ion heating through exchange power in electron-heated plasmas features a broad heating pattern with a subsequently low power density (figure 2), which under neoclassical transport conditions alreadyproduces low ion temperature profile peaking ( figure 3). Furthermore, the neoclassical transport is only a fraction of the total transport and in some cases represents as little as 10% of the total transport. As a result, the experimentally achieved T i -profiles are well below the neoclassical predictions (see e.g. figure 3). The impact of the ion turbulent transport is reasonably well modeled, assuming ion-gyro-Bohm heat transport. The saturation of the central ion temperature with increasing heating power and increasing density is well captured; however, obtaining the details of the ion temperature gradient response to increasing ion heat flux will require further characteristics of ITG turbulence.
A key result from linear and non-linear GENE simulations for the W7-X standard configuration is that the degree of profile stiffness increases with an increase in the ratio T e /T i , or, in other words, ITG turbulent transport is exacerbated by T e /T i. . In the power scan experiment discussed in this paper, indeed it seems that the "apparent negative profile stiffness" as seen at the radius of r/a = 0.3, see figure 8, may be caused by the enhancement of turbulence by the T e /T i effect as well by the saturation of Q i /Q gB . At larger radii, where T e = T i across the power scan, this effect is mitigated ( figure 9).
The enhancement of ITG turbulence with the T e /T i ratio is present in both tokamaks and stellarators [55] and appears to be present in all the magnetic configurations shown in figure 1.
However, it appears that in tokamaks, linear gyro-kinetic simulations which focus on the strongest growing mode can quantitatively describe the degree of ion transport stiffness enhancement due to T e /T i . Therefore, these linear calculations can be used in transport-predictive codes such as 'trapped gyro-Landau-fluid' (TGLF) [59]. However, for stellarators, due to their 3D geometry, the non-linear calculations show that the transport enhancement due to T e /T i is enhanced by initially less dominant modes; the T e /T i parameter affects all possible eigenmodes, including the subdominant ones, which are formally absent from the initial value solution of the linear gyro-kinetic equation in figure 4. In turbulence simulations, however, these subdominant modes also contribute to the determination of the ion heat flux level. It is therefore expected that the collective effect of the T e /T i parameter will be enhanced, as manifested in the nonlinear simulations.
As a result, a predictive transport model that could explain the clamping of the T i gradients would need to be based on nonlinear gyro-kinetic calculations, which are very costly, and a program such as TGLF will not be readily implementable for W7-X. Therefore, ad hoc transport models that use the outcome of nonlinear calculations and the stiffness enhancement due to an increase in T e /T i and its subsequent effect on temperature clamping could be useful tools going forward. In [60], for example, this was done by including the beneficial effect of introducing a density gradient on suppressing turbulence. This tool could be extended with the newly found detrimental effect of T e /T i on turbulence.
However, T i clamping can be broken, as has been shown experimentally. Figure 10 shows a few examples in which the clamping has been broken. The physics mechanism that acts on the turbulence suppression is thought to be the same in these examples; the introduction of a strong(er) density gradient, which aids the reduction or suppression of ITG turbulence and simultaneously limits the density-gradient-driven TEM turbulence. For reference, the figure also shows the power steps in helium-and hydrogen-fueled plasmas with the labels (1) and (2), as discussed in this paper. Both show that with everything else held constant, T i rises slowly from low to high ECRH power and the maximum T i value achieved, T i ∼ 1.6 keV, is similar between the two plasmas. Also, as a comparison with label (2a), a power-step experiment at half the density of used at label (2) is shown with n e,0 = 3.5 × 10 19 m −3 and a clamped T i ∼ 1.5 keV, as in [22].
A stationary elevated T i,0 = 2 keV was achieved (label (3) in figure 10) above the clamped value, a day after standard boronisation (not a powder-dropper) in a steady-state hydrogen-fueled plasma lasting almost 60 s with low power of P ECRH = 1 MW during the first 40 s and with an averaged density n e = 4 × 10 19 m −3 . It is suggested that a combination of fresh wall conditioning and low power electron heating helped to increase the normalized density gradient from a/L n ∼ 0.5 (e.g. figure 7) to a/L n ∼ 2 in the outer plasma region r/a = 0.5-1. The ion temperature may be increased through the mechanism of density-gradient-aided turbulence suppression. It is not understood why, in subsequent pulses with higher P ECRH = 4 MW and similar averaged density, the density gradient in the outer plasma region r/a > 0.5 reduced to a/L n ∼ 0.5 and subsequently the ion temperature was clamped at T i,0 = 1.5 keV. Suggested mechanisms that may influence the density profile shape include enhanced wall outgassing by ECRH, causing increased neutral recycling levels, and a possible 'density pump-out' caused by central electron heating that reduces the profile peaking.  (1) and (2), the first trials with a boron-powder dropper instrument (4) were conducted, in which the central ion temperature rose to T i,0 = 2.3 keV. The details of the boron-powder experiment and its influence on the kinetic profiles are described in [61]. Basically, the introduced boron helps to reduce the neutral hydrogen source. As a result, the edge density is reduced, while the core density remains unchanged. The resulting enhanced density gradient across the profile helps to suppress the turbulence. Moreover, impurities can stabilize the ITG modes. The reduction of the turbulence may also be due to the increase of impurity density as well as the change of edge density gradient. Unfortunately, shortly after the boron-powder enhanced T i phase, the ion temperature relaxed back to the pre-boron-power injection phase T i ∼ 1.6 keV. Only after multiple injection phases did the baseline T i somewhat rise above the clamped value. The price to pay is therefore an increased impurity content, with Z eff rising from 1.3 to 3.2.
The second example, label (5) in figure 10, is a transient increase of the ion temperature after ice-pellet injection to a level well above the clamped level, T i,0 = 3 keV [8,9,23], i.e. close the maximum achievable T i according to neoclassical simulations. After a train of pellets is injected, strong density gradients of up to a/L n < 3 are built. After the initial temperature collapse due to the pellet cooling, the ECRH power is increased from 2 to 4.5 MW and during the reheat phase T i and T e increase simultaneously and reach T e,0 ∼ T i,0 = 3 keV. A detailed PB analysis shows that the ion heat flux at this point is almost fully dominated by neoclassical transport, whereas the electron transport remains largely turbulence dominated. As both the density gradient and the ion root radial electric field rise after the pellet injection, a theoretical analysis using nonlinear gyro-kinetic simulations with the GENE code compared the effect of strong density gradients as well as a radial electric field on the turbulent transport. The results show that both can help to reduce the turbulent transport, but that in the case of the pellet experiments, the introduction of a strong density gradient is likely to be the main driving mechanism for the (ITG) turbulence suppression [7]. It is found that simultaneous TEM turbulence is not strongly induced by the enhanced density gradients, and instead, a so-called ion-TEM or iTEM is the dominant mode during the high-T i phase. Modeling shows that the turbulent ion heat diffusivity is reduced by an order of magnitude compared to the pre-pellet phase, explaining the enhanced ion temperature during this transient phase. Unfortunately, the high confinement phase is terminated on a particle confinement timescale of ∼100 ms as the density gradients relax back to the pre-pellet conditions.
For future scenario development, a remaining question is whether strong density gradients can be sustained in a stationary fashion. No doubt, the development of scenarios using steep density gradients to sustain high plasma confinement will use up a lot of future machine time at W7-X. A valid question therefore remains: how good a performance can be obtained in standard ECRH plasmas when the heating capacity is increased to P ECRH = 10 or 15 MW? The ion gyro-Bohm transport simulations in figures 5 and 6 show that the achievable ion temperature would already be saturated under such transport conditions. However, even at the highest density achievable by ECRH-O2 heating, 1.6 × 10 20 m −3 , the ratio T e /T i is not unity (figure 6(c)). A valid transport model would therefore also need to capture the effect of the T e /T i ratio on the ITG turbulence.

Appendix A. Experimental power balance study
An accurate PB is conducted, in which all the sources and sinks for the heat transport are considered. The experimental heat flux Q exp is the sum of the neoclassical Q NC and the turbulent heat flux Q turb . The steady-state PB, with separate sources and sinks for electrons and ions, is composed of: where the source Q ECRH is calculated by combining the power-density profiles p ECRH for all ECRH sources using the microwave ray-tracing code Travis [39]. The energy transfer between the electrons and ions Q e-i is a sink for the electrons and a source for the ions, and the power density profile p e-i is calculated from the kinetic profiles using equation (2.1). The radiated heat flux Q rad is the volume-integrated power density profile p rad obtained from a poloidal integration of the tomographic reconstruction of the bolometer multiple lines of sight [47,48]. Finally, a sink for the ions is the charge exchange loss Q cx between the hot ions and cold neutrals entering the plasma. Although the neutral source is difficult to estimate and forms an uncertain factor in the PB, the effect is only likely to be large near the plasma edge and will not significantly affect the balance at, or inside, the mid radius, as will be shown in this appendix. The neoclassical heat fluxes Q e,NC and Q i,NC are calculated with the help of the neoclassical transport solver NTSS, using the experimental profiles as inputs as well as DKES for the transport table. For a description of DKES, see [62,63]; for its application to W7-X, see [28] and the application of NTSS in [29]. As a target plasma for the PB, an ECRH power step-down experiment in a medium-density hydrogen-fueled plasma is chosen, for which the time traces of the major parameters are shown in figure 11(a). The upper bound of the ECRH power used in the experiment is limited to 3.9 MW due to the requirement to share the high-voltage power supply between the ECRH system and the NBI system used to provide 10 ms beam blips for the CXRS T i measurements. The choice of density of n e = 6 × 10 19 m −3 is a trade-off between various factors. First, the exchange power density p e-i is maximized at high densities due to its n 2 -dependence, but also has an optimum temperature difference ( figure 2). Second, an upper boundary for the density is set by the radiation limit for the lowest ECRH power step to ensure that P ECRH < P rad . And third, a lower boundary is set to minimize errors in determining the turbulence heatflux Q turb = Q exp − Q NC by avoiding zero crossings of the ambipolar radial electric field E r, and thus ensuring that E r is negative across the entire profile (ion root). E r profile measurements with DR [56] and CXRS [] have confirmed the ion root conditions across the full profile for each power step.
For the hydrogen-fueled plasma, the temperature and density profiles are given in figure 3 for the highest power level P ECRH = 3.9 MW in the scan. The central electron temperature of T e = 3 keV guarantees the optimum energy transfer at an ion temperature of T e = 1.5 keV, (see figure 2). Unfortunately, in the selected hydrogen plasma, the density is too high to conduct a wide ECRH power scan. Already at P ECRH = 1.7 MW, a high radiation front enters the confinement region. This effect is seen in figure 12(a), which shows the radiative power density profile for each power step. For the first two power steps, P ECRH = 3.9 MW and 3.3 MW, most of the power is radiated at r/a > 0.8; inside that radius, the volume integral of the radiated power profile is P rad,core < 100 kW. However, at the third power step (t = 4.5-5.5 s), the radiation moves in to r/a ∼ 0.5, and the kinetic profiles are strongly affected. Therefore, the selected hydrogen plasma does not meet our requirements.
Helium is considered as an alternative fuel, as helium plasmas have a higher radiative density limit compared to hydrogen plasmas. This is because the wall-impurity sources are reduced due to a lack of chemical sputtering by helium, compared to hydrogen radicals in the divertor. Figure 11(b) shows the waveforms achieved with power steps of 3.9, 2.4, 1.8, and 1.2 MW. Indeed, a plasma with a lower ECRH power down to 1.2 MW can be sustained at an even higher density level, compared to the hydrogen plasma. Figure 12(a) shows that for all power levels, the radiation front stays outside r/a > 0.8. Even for the lowest power step, the core radiation for r/a < 0.8 is small at P rad,core ∼ 150 kW. For the highest power level P ECRH = 3.9 MW, the T i and T e profiles as given in figure 15 are similar to that of the H plasma, whereas the electron density is somewhat higher at n e = 7 × 10 19 m −3 . Also, the plasma performance is similar between the helium-and hydrogenfueled plasmas with a diamagnetic stored energy for both of W dia ≈ 0.5 MJ +/− 0.05 MJ. As a result, the confinement times of both plasmas are virtually identical at τ E = 130 ms, and despite the small density difference, the ISS04 scaling is also similar at τ E/τ ISS04 ∼ 0.65 for the H and He fueled plasmas. These findings are consistent with the volume integral of the kinetic profiles, as (n e + n i ) H-fueled ≈   Divertor PB P res = P ECRH − P div − P rad for (a) the hydrogen-fueled #20180927.046 and (c) helium-fueled plasma #20180927.042 (right). The divertor heat load P div is reconstructed from IR thermography camera data integrated over all five double-divertor modules [17]. The radiated power P rad is taken from a poloidal averaged polarimeter-tomographic reconstruction and assumes toroidal symmetry. (b) and (d) The residual P res is balanced within ∼200 kW for the phases in which P rad < P ECRH up to the time point t = 7 s. Figure 14. (a) Neutral density as derived from H α spectroscopy from three different lines of sight of the CXRS diagnostic [45] (AEA21_A is a pure toroidal line of sight, and AEM21_S7 and AEM21_S8 are half poloidal, half toroidal lines of sight). The grey shaded areas are not errors, but rather an assessment with a lower and upper bound for the neutral density; the lower bound of this band is obtained by equating ionization and recombination using ADAS coefficients [66]. As this relates to the case of no inward neutral transport, this approach gives a lower limit for the neutral density. The upper limit is obtained by assuming that the neutral density pressure stays constant over the plasma. It is normalized using the edge data points and propagated inwards using the ion temperature from the XICS system (figure 7(a)). As the neutral pressure should, at most, be constant, this gives an upper bound. The error bars for the data are given as vertical and horizontal lines for each data point. The measured profile of n 0 is compared to a neutral model with a variation of the particle confinement time from τ p = 150 ms to τ p = 1 s. (b) The estimated charge exchange losses Q CX (from τ p = 150 ms to τ p = 1 s) compared to the experimental total heat flux Q exp,tot and Q i,exp from figures 7(d) and (e), respectively. The vertical dashed line represents the separatrix position.
(n e + n i ) He-fueled ; they yield a thermal stored energy in both plasmas of W th = 0.52 +/− 0.04 MJ.
Since a wider ECRH power range is possible in the heliumfueled plasma, the power steps in this plasma are used to study the temperature-clamping phenomenon, while a comparison of the H and He plasmas at PECRH = 3.9 MW is used to link to the wider post-boronization hydrogen W7-X database in figure 1.
Neither of the plasmas discussed is a pure single-species plasma, but contains a fuel mix of H and He. Figure 12(b) shows the ratio R H/H+He = n H /(n H + n He ) derived from charge exchange spectroscopy; for the H-fueled plasma, R H/H+He = 85%, and for the He-fueled plasma, R H/H+He = 25%-30%. In fact, to get pure single-species plasmas is time consuming in W7-X. The reason for this is that, on the one hand, the helium is not fully pumped in W7-X. Since the Hfueled plasma was preceded by He-fueled plasmas, a H/He mix is the consequence. On the other hand, and vice versa, due to the high hydrogen retention of the carbon plasma-facing components, H outgassing in a He-fueled plasma is relatively high if the previous plasmas contained H as a fuel. In the current conditions, high helium fuel purity can only be achieved (d) Total experimental volume-integrated heat flux A · Q tot (solid) compared to the total neoclassical integrated heat flux A · Q tot,NC (dashed), (A is the flux surface area). (e) Experimental volume-integrated ion heat flux A · Q i,exp (solid) as calculated from the exchange power, compared to the neoclassical integrated ion heat flux A · Q i,NC (dashed). ( f ) Experimental volume-integrated electron heat flux A · Q e,exp (solid) compared to the neoclassical integrated electron heat flux A · Q e,NC (dashed). (g) Volume-integrated turbulent ion heat flux normalized to the ion density A · Q i,turb /n i . (h) Profiles of T e /T i (i) turbulence ion heat diffusivity-A is the flux surface area; (j) normalized ion temperature gradienta/L T i and density gradient length a/L n where L x = x/∇x. after a time-consuming wall-conditioning program with repetitive pulses, for which no experimental time was allocated. (Note for reference that outside of this experimental day, only hydrogen plasmas are run and high hydrogen-fuel purity is usually obtained) For the core PB coming up in the next section we derive the ion density profile in the H/He fuel mixes from figure 12(b) as n i /n e = 0.9 and n i /n e = 0.65, respectively. Note that the R H/H+He profiles are flat for both plasmas and almost constant throughout the ECRH power steps. If we assume no other species than H and He are present in the plasma, then n i /n e = (z He + 1) /z He − Z eff /z He , and we derive Z eff = 1.3 and Z eff = 1.8, respectively. These values are consistent with the Z eff values obtained from bremsstrahlung spectroscopy.
Finally, the charge exchange losses are estimated. First, a divertor PB is considered, as seen in figure 13. The total power that arrives at the divertor tiles P div as measured by infrared (IR) thermography [64] is compared to the total ECRH power as well as the total radiated power P rad . The latter is reconstructed from bolometer tomography [47] by assuming toroidal symmetry. The residual (or unaccounted-for) power is given by P res = P ECRH − P div − P rad . Figure 13 shows that this residual power is of the order of 100-200 kW for both hydrogen-and helium-fueled plasmas, which is the uncertainty margin of the divertor PB. Only when the relative plasma radiation increases, such that P rad ∼ P ECRH , does the apparent discrepancy increase above this range, albeit the symmetry assumption of P rad may no longer be valid. As a result the non-absorbed charge exchange losses for the phases in which P rad < P ECRH may be, at most, of the order of P CX ∼ P res ∼ 100-200 kW.
The local charge exchange losses are furthermore estimated from the neutral particle density profile for the hydrogenfueled plasma ( figure 14). The reconstruction follows the methodology described in [65], using multiple passive H α lines of sight of the CXRS diagnostic [45] and assuming poloidal symmetry. No inversion is required, as multiple measurements are localized along each single line of sight using the Doppler broadening of multiple spectral components, which are subsequently related to the main ion temperature profile. Full details of the method are given in [65]. Depending on the particle confinement time assumed in the estimation, the charge exchange losses Q CX are of the order of 10-100 kW at the separatrix, and further inside, at r/a ∼ 0.8 (r eff ∼ 0.4 m), Q CX is estimated to be negligibly small compared to the total and ion heat fluxes Q exp and Q i,exp (from figures 7(d) and (e)). We therefore ignore the charge exchange losses in the further core PB analysis.
We now come to the PB analysis and the comparison of the helium-and hydrogen-fueled plasmas ( figure 15). Figure 15(c) shows the profiles of the ambipolar radial electric field E r as calculated by the NTSS code. As both plasmas feature ion-root transport with negative E r , the errors in Q i,NC and Q e,NC around root transitions are avoided. The experimental heat fluxes are shown in figures 15(d)-( f ) for the sum of the electron and ion fluxes, the electrons, and the ions, respectively. As a comparison, the neoclassical fluxes are also shown using dashed lines. Clearly, the turbulence heat flux dominates across the profile for r/a > 0.1, showing that the turbulent transport determines the energy confinement. Not shown in figure 15 are the radiative losses ( figure 12(b)), which are already accounted for in Q e,exp and are negligible compared to Q ECRH and Q e-i up to a radius of r/a ∼ 0.8. The charge exchange Q CX loss channel for the ions can be neglected in the analysis. The ion heat flux in figure 15(e) is higher in the hydrogen-fueled case, due to the Z/M dependency of p e-i (equation (2.1)). However as the ion density is lower in the helium-fueled plasmas, the normalized ion heat fluxes Q i,turb /n i are virtually the same in the hydrogenand helium-fueled plasmas, figure 15(g). Therefore, as the kinetic profiles and their gradients (figure 15(j)) look similar for the two plasmas, the ion heat diffusivity for the hydrogenand helium-fueled plasmas are also similar (figure 15(i)) and is of the order of 0.5-1 m 2 s −1 across the full profiles, i.e. well above the neoclassical diffusivity D 22,i . We therefore conclude from this PB comparison that no significant difference is observed in the ion heat transport between the H-and Hefueled plasmas. For this reason, we are justified in using the helium-fueled plasma in the ion transport study to probe the ion profile stiffness.