Maximizing the ion temperature in an electron heated plasma: from WEST towards larger devices

In electron heated plasmas, as the power increases, it is experimentally reported that the ion temperature (Ti ) saturates while the electron temperature (Te ) increases [Beurskens NF 2022]. As on AUG, W7X and elsewhere, Ti saturates around 1.5 keV in WEST L-mode electron heated plasmas while Te reaches 4 keV. Simulations within the integrated model METIS have been compared against a whole WEST campaign consisting mostly of L-mode plasmas with Lower Hybrid heating ranging from 1 to 5.5 MW. In METIS, the collisional equipartition is modeled as well as the turbulent heat transport using the neural network regression of the quasilinear gyrokinetic code QuaLiKiz. The observed Ti saturation is well captured by the modeling framework. The saturation correlates with a low ratio of the energy confinement time to the volume averaged electron-ion collisional heat exchange time. It is then shown that Ti saturation in electron heated plasma is due to an equipartition time higher than the energy confinement time. In larger devices, no Ti saturation is expected nor predicted by physics based integrated modeling used in this work, thanks to equipartition times sufficiently shorter than the energy confinement time.


Introduction
In predominantly electron heated L-mode plasmas, the saturation of the core ion temperature is reported while electron a See http://west.cea.fr/WESTteam.* Author to whom any correspondence should be addressed.
Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.temperature in the core increases with increasing power: in W7X and AUG with ECRH [1,2].In fusion reactors, the dominant heating provided by the alpha particles will be transferred preferably to the electrons, while the D-T fusion rates scales with the ion temperature as T 2  i in the range 10 < T i < 20 keV.It is therefore important to explore the respective roles of transport and heating on ions and verify our ability to model the competition between the heat source from collisional equipartition scaling as (T e − T i )/T 3/2 e and the loss term due to turbulent transport.
In the following, we show that, in WEST electron heated L-mode database, with the Lower Hybrid power (LHCD) ranging from 1 to 5.5 MW, as in electron heated (ECRH) AUG and W7X cases reported in [2], T i remains below 1.5 keV while T e reaches up to 4 keV.To explain these observations and underline the main parametric dependences of the competition between equipartition and transport, a reduced analytical model has been developed in appendix A where the ratio of electron to ion heat diffusivities is parameterized.Then most of the analysis uses the integrated modeling plateform METIS [3] where steady-state operation points are obtained.In the latter, the turbulent transport is modeled using the neural network version of the quasilinear gyrokinetic code QuaLiKiz [4], coupled with current diffusion and a self-consistent calculation of the equipartition.The validity of the neural network version has also been tested against few integrated modeling simulations using QuaLiKiz appendix C. The reference point of the analysis is a WEST pulse heated by 2.8 MW of LHCD that has been previously analyzed and successfully modeled in [5].
In METIS, a power scan from 1 to 3.8 MW at fixed density around our reference point, captures the central ion temperature saturation observed across the WEST database.Additionally, it is shown that the impact of changing T i /T e on the turbulent transport does not significantly modify the saturation of the ion temperature in our case.Indeed, as in AUG [2], the T i saturation is predominantly due to a weak equipartition and increased transport.Then, the role of the various players leading to enhanced coupling of ions and electrons are further explored: increased electron densities or increased major radius at constant q 95 .The dependencies of the central ion temperature saturation with these parameters scale very well with the ratio of volume averaged electron-ion collisional heat exchange time (defined in equation (A.23)) to the global energy confinement time as in [6,7].This means that the ion temperature saturation in electron heated plasmas is expected as long as the electron-ion collisional heat exchange time is larger than the energy confinement time.In presence of direct ion heating this correlation is modified and the ratio T i /T e can be more efficiently increased.Therefore, when extrapolating towards larger devices such as ITER or DEMO [8][9][10], thanks to denser plasma leading to shorter heat exchange time, as well as larger confinement times and some direct ion heating by alpha particles, the saturation of T i is not expected even in ECRH only DEMO [11].The central ion temperature has also not been observed to saturate in recent transport simulation with higher fidelity models [12] of ITER-like baseline scenarios and was not considered as a problem in the discussion of the heating mix of ITER [13].
In the following section 2, we will first describe the WEST L-mode database and characterize the central ion temperature saturation.Then, in section 3, the integrated modeling strategy and results are described.From our reference WEST case, the impact of various parameters is explored using METIS coupled to the neural network of the quasilinear gyrokinetic code QuaLiKiz: electron heating power, modified turbulent transport, density, direct ion heating power and finally plasma volume.The conclusions are given in section 4.

WEST L-mode electron heated database
WEST experimental data are natively archived in IMAS via Interface Data Structure (IDS) such as core_profiles, equilibrium etc [14].Most of the data treatment included in this chain are automated to make the results available to all in a systematic manner.For example, a polarimetry-constrained equilibrium is performed between pulses using NICE [15] and automated fits of the temperature and density profiles are provided.
Moreover, the IDS summary which is used to store time traces, is filled with relevant quantities for further database analysis such as, to name a few, plasma current, external and ohmic heating, total radiated power, neutron rate, line averaged electron densities and effective charge.These quantities can be time averaged over plateaus of total power intersecting plasma current plateaus whose duration exceeds 0.3 s [5,16] and are stored in an additional occurrence of the summary IDS.
The database contains time averaged quantities over 3609 plateaus coming from 1219 Deuterium pulses.They exhaustively cover two WEST experimental campaigns (C4 and C5), at the exclusion of the He sessions of C4 campaign [17].The pulses are mostly ohmic or LHCD/ICRH heated L-mode plasmas.All the selected plateaus for the following analysis (565) are at 3.7 T with plasma current I p = 0.5 MA, LHCD heating power P LHCD = 1 − 5.5 MW, and line averaged densities n = 2.5 − 6 × 10 19 m −3 .
In the following, we are interested in the electron and ion temperature profiles and in particular their central values.The electron temperature is measured by Electron Cyclotron Emission while the central ion temperature is inferred from the D-D fusion producing neutrons using interpretative METIS [3] simulations and a prescribed shape (T i ∝ √ n e T e ).This is currently the only way to evaluate the ion temperature on WEST but will soon be supplemented with data provided by an xray imaging crystal spectrometer.More detailed comparisons of the ion temperature evaluation using the neutron rate and charge exchange spectroscopy and/or spectral lines broadening in the x-ray range during the Tore Supra era (for which a neutral beam injection system was installed) are given in appendix D. The neutron rate are measured using 3 groups of detectors distributed equally in the toroidal direction which are constituted of 11 fission chambers and one He 3 ionization chamber.A calibration of such detectors was performed for Tore Supra using an in-vessel neutron source [18].The neutron rate provides no spatially resolved measurement for T i , but rather an integrated measurement with stronger weight in the plasma center.This is due to the cross-section scaling as ∼n 2 D T γ i with γ ⩾ 2.5 in the temperature range of WEST plasmas.In the reduced ion temperature range considered in this study with central T i below 1.5 keV, the temperature exponent is even above four.The deuterium density is inferred using the quasineutrality condition and an estimation of the impurity content.The electron density is taken from interferometry inversions (ten lines of sight) and the impurity content is estimated such that a light impurity (nitrogen) concentration is adjusted to match the resistive Z eff (allowing to reproduce the flux consumption in the ohmic phase) while the tungsten concentration (though not contributing significantly to the main ion dilution) is chosen to match the radiated power in the bulk plasma [19].It has to be noted that the Z eff measurements using the background bremsstrahlung signal in the visible spectra was not available for most of the discharges, thus the use of the flux consumption to infer the effective charge.This method is indirect and applicable in the inductive phase only.However, reasonable variations of Z eff would only provide marginal changes in the ion temperature evaluation from the neutron rate (due to the strong dependence of the D-D cross section with T i compared to n D ).
For this WEST reduced database of plateaus, the measured D-D neutron rate is plotted against the measured central electron temperature from ECE in figure 1 left panel.The inferred central ion temperature are also shown against the time averaged (over a plateau) central T e in the right panel.As reported in AUG and W7X [2], the inferred T i saturate (together with the measured D-D neutron rate) at ∼1.5 keV while the central T e reaches up to 4 keV.
Following these observations, integrated modeling will be applied to WEST plasmas and compared to the WEST reduced database in order to quantify the relative role of collisional equipartition and turbulent transport in explaining such central ion temperature saturation.

Integrated modelling results
3We have chosen a modeling framework where the following ingredients are present: (i) a theory-based quasilinear transport model catching the well-known instabilities like ITG, TEM, ETG, (ii) electron-ion collisional equipartition, (iii) selfconsistent equilibrium and current diffusion inside a fixed last closed flux surface.

METIS framework description
The framework used is METIS coupled to the 10D neural network of QuaLiKiz [4].It combines all the above ingredients and is further described in appendix B. The starting point for the simulations is the WEST discharge #55025 at 8.5 s with 2.8 MW of LHCD power at 0.5 MA and at 3.7 T. At a later time this discharge exhibits a central electron temperature collapse which was modeled and understood to be due LHCD absorption moving off axis in colder plasmas which subsequently impacts negatively the tungsten neoclassical transport [5].
Predictive simulations are based on an interpretative METIS simulation which is run over the full time history of the discharge of interest.This allows combinations of several diagnostics to be taken into account and quantities such as the ion temperature profiles, effective charge, tungsten content to be inferred while preserving an overall consistency with measurements, such as the measured neutron rate, the flux consumption in the ohmic phase, the line integrated and the radiated power.The shape of the LHCD power deposition radial profile as been parameterized by a Gaussian (here throughout this study we use a fixed radial shape for the electron heating that is rescaled in power scans) with a position of the maximum at the normalized toroidal flux as radial coordinate ρ = 0.325 and a half width at half height of 0.25.The choice of the parametrization for this deposition profile is based on previous ray-tracing/Fokker-Planck simulations with the C3PO/LUKE suite of codes [20] performed in [5] for this particular discharge.
The plasma composition is such that the nitrogen levels matches the effective charge of 2.34.A tungsten concentration (n W /n e = 1.48 × 10 −4 ) is used such that the radiated power fraction in the bulk for the reference case is around 35% and is consistent with radiated power measured from bolometry [19].Throughout this section, Z eff and the concentration of tungsten are kept fixed (the radiated power is consistently computed from the electron temperature profiles using cooling rates from the ADAS 50 database [21]) and the profiles of nitrogen and tungsten are homothetic to n e .
In contrast to the standard use of METIS where 0D scaling laws are considered together with parameterized profile shapes [3], here the time independent, 1D heat transport equations are solved for a given time of interest (see appendix B).Then, the ion and electron temperature profiles result from the competition between the heat turbulent transport from QLKNN-10D [4], the neoclassical ion heat flux [22], the heat sources from the fixed LHCD deposition profiles, the collisional equipartition, the ohmic heating and radiative losses.
The Neural Network regression of QuaLiKiz used to compute turbulent transport is based on a 10D hypercube set of 300 millions of QuaLiKiz simulations [4].A discussion of the training domain compared to WEST data is provided in appendix C. Due to an overestimation of the effect of collisions in the QuaLiKiz version (v2.4.0) on which the neural network has been trained [23], the collisionality is reduced using a multiplier value of 0.25.While the impact of collisions on turbulent transport cannot be simply reproduced using a scaling factor on the reduced collision operator of QuaLiKiz, this affects the quasilinear fluxes via reductions of the linear growth rates.Furthermore, this setting on collisionality has been suggested and validated for the modeling of JET plasma current ramp-up [24].
A similar setting for tuning the Electron Temperature Gradient (high wave number passing electron modes) contribution to the electron heat flux is chosen.The motivation behind this multiplier, comes from the way these high wave numbers are accounted for in the saturated electrostatic potential of a quasilinear model.Indeed, very few nonlinear simulations based on the real electron to ion mass ratio have been performed including ion and electron scale fluctuations [25,26] which limits the data available to tune the quasilinear rule for ETG transport.The latter is expected to be significant for sufficiently large ratios of ETG to ITG normalized linear growth rates, e.g.[27], equations ( 2) and (3).Following this work with integrated modeling and multi-scale gyrokinetic simulations, the ETG multiplier is set to 0.33 for all the simulations in this work unless stated otherwise.The impact of this parameter is further discussed in 3.3.
To validate the described settings for the neural network, comparisons between QLKNN-10D and QuaLikiz version 2.8.4 have been performed using the steady state solver of METIS (for few cases only due to much longer computational times) and produced similar results (within 15% difference for the electron temperature and 5% for the ion temperature profiles on our reference case).This comparison together with a discussion on the training domain of the neural network is given in appendix C.
Regarding boundary conditions in METIS for the electron temperature and density, due to limitations of the available experimental data, the fitting procedure is forced to zero outside the separatrix.This results in T sep = 50 eV and n sep = 1.1 × 10 19 in agreement with the experimental database of figure 8 [28] where n sep is taken from reflectometry measurements and T sep from the two point model applied to target Langmuir probe measurements.
Based on the key parameters identified in the simplified analytical model in appendix A, several scans of relevant quantities in the METIS-QLKNN-10D framework have been performed in the following sections.First the electron heating is scanned from 1 to 3.8 MW and reproduces the central ion temperature saturation reported in the WEST database.It also captures the power degradation observed experimentally.In parallel to the effect of collisional equipartition on the low central ion temperature, the role of turbulence and more specifically the electron to ion temperature ratio is also investigated.Then the impact of density, plasma volume and external ion heating are explored, in particular to understand under which conditions the T i saturation can be avoided.
In all of these scans, particle transport is not considered and the density profiles are taken from interferometry inversions for the reference case and kept fixed.The choice of not considering particle transport is mostly driven by limitations of the current modeling setup whether it is from missing neutral source feedback on volume averaged density or from the known limitations of the QLKNN-10D transport model regarding collisions and thus the difficulty in modeling density peaking [23], particularly in the case without core particle sources.These limitations will be lifted in future developments of this framework.
Finally, a summary of all these scans is provided and compared to an ITER-like case.

Power scan: electron heating
A scan in Lower Hybrid heating (electron heating only) is performed from 1 to 3.8 MW.For the nominal power of 2.8 MW referring to the experimental WEST discharge #55025 at 8.5 s, the agreement between the simulated electron temperature profile using METIS-QLKNN-10D and the measurement from electron cyclotron emission lies within error bars (figure 2 left panel, the measurements are the purple symbols and the corresponding predicted profile the purple dashed line).Note that ECE signal is noticeably polluted by the LHCD  fast electrons for ρ > 0.5.Hence no measurements are available for T e at ρ > 0.5.A Thomson scattering system will be installed in 2024.It has to be also noted that the central electron temperature is very sensitive to the shape of the LHCD power deposition profile and in particular to its central power deposition as discussed in [5].The corresponding ion temperature profiles for these simulations are also shown in figure 2 right panel.
Given the lack of T e measurement for ρ > 0.5 and of T i , it is interesting to validate further our modelling against the global energy confinement time and the measured D-D neutron rate.On figure 3 left panel, τ E for the WEST C4-C5 database is plotted against the additional power (external and ohmic).A power degradation close to P −0.73 is found, as in the ITER L-mode scaling law from equation (A.22) and WEST experimental points (more details on WEST scalings and on the two confinement branches in [16,28]).A systematic overestimation of the energy confinement time is observed with METIS+QLKNN-10D compared to the L-mode scaling law, which decreases with injected power (maximum difference of 20% at low power).The agreement with the D-D neutron rate (figure 3 right panel) is also particularly good given the strong sensitivity to T i .
On figure 4, left panel, the central T i is plotted against T e as on figure 1. Across the modeled electron heating power scan, it is observed that, while the electron temperature increases, the ion temperature at first slightly increases (P in = 1 − 2.8 MW) and then saturates for P in = 2.8 − 3.8 MW.The modeling results are quantitatively in agreement with the T i saturation observed experimentally (consistently with the D-D neutron rate).This is expected due to the reduction of the ion heating by collisional equipartition as T e increases (τ ei scales with T As proposed in [2,6,7], here as well, it is found that the ratio of the volume averaged electron-ion heat exchange time over the energy confinement time is a good proxy for the central electron to ion temperature ratio (figure 4 right panel).

Impact of the ion turbulent transport
Turbulent tranport (heat flux stiffness and threshold) is affected by T e /T i in a complex way depending on the dominant modes and the normalized density gradient which can result in lower/higher thresholds with increased T e /T i , e.g.[29,30].QuaLiKiz, hence its neural network regression, captures these effects.Regarding the problem of ion temperature saturation, it was found that the T e /T i dependence of turbulent transport was exacerbating this saturation [31].It is therefore essential to explore the impact of larger T e /T i on turbulent transport and quantify its impact against collisional equipartition in explaining the T i saturation.
To study the impact of the ion to electron temperature ratio on turbulence while not affecting the equipartition power nor the electron-ion collision frequency via changes in the electron temperature, the independent input parameter T e /T i has been modified in the transport code QLKNN-10D.This ratio is set fixed (radially for ρ ⩽ 0.7 where central electron heating allows large excursion of T e /T i while at the edge collisional equipartition constrains the T e /T i ratio to be close to 1) to 2 different values: 1 and 0.25.On figure 5, the predicted T e and T i profiles using QLKNN-10D T i /T e = 1 or QLKNN-10D T i /T e = 0.25 are compared in panels (a) and (b).The heat diffusivities are shown on the panels (c) and (d).It is found that the electron temperature is decreasing with increasing QLKNN-10D T i /T e due to increased electron heat diffusivities from ρ = 0.5 inward.The ion temperature follows the same trend and the central T i is slightly increased for QLKNN-10D T i /T e = 0.25 while the ion heat diffusivity is lower (figure 5(d)).
In figure 6 the results of a power scan ranging from 1 to 3.8 MW of external electron heating is shown for the two extreme values of QLKNN-10D T i /T e .It it found that the central ion temperature saturation is given by the achievable central electron temperature for the same input power.Furthermore the correlation between τ ei /τ E and T i /T e for the same power scan is modified when going from QLKNN-10D  T i /T e = 1 to 0.25.In the following the role of Electron Temperature Gradient turbulence is explored as the critical gradient is decreased with increasing T i /T e [32] at low R/L n .
The Electron temperature Gradient modes are included by default in QuaLiKiz.In the neural network training exercise [4], the ETG electron heat flux was defined as the flux arising from the spectrum at normalized poloidal wave numbers k y ρ s > 2 (using QuaLiKiz conventions) and QLKNN was trained on these ETG fluxes separately.Therefore it is simple to turn ETG contribution on or off when using QLKNN-10D for heat fluxes computations.
With the ETG contribution turned off, central T e is less modified with changing T i /T e in QLKNN-10D (figure 7) and is lower for 0.2 < ρ < 0.6 which goes in the opposite directions regarding variations of constrained T i /T e compared to cases with ETG contributions.Indeed, increased midradius T e is observed for QLKNN-10D T i /T e = 1 compared to QLKNN-10D T i /T e = 0.25, consistently with increased electron heat transport as QLKNN-10D T i /T e decreases.These simulations suggest that the additional electron heat flux from ETG can contribute significantly to the total electron flux.In the case without ETG contributions, the achievable central T e is similar with T i /T e = 1 and T i /T e = 0.25 and thus the resulting central ion temperature saturation (a maximum increase of 5% is observed for the reference case).Figures 7 and 8 show that in our WEST reference case, the impact of the electron to ion temperature ratio on ITG/TEM turbulence does not modify the saturation of the ion temperature but might be important when ETG turbulence is found to contribute significantly to the total electron heat flux.
In the following sections, ways to optimize the central ion temperature are further explored either from decreased collisional heat exchange times or increased energy confinement times.

Impact of the density
A scan in density is performed to increase the collisional equipartition rate.We recall that the steady states found using METIS-QLKNN-10D are only for the heat transport equations (as discussed in section 3).The density is kept fixed (based on the interferometry inversion of our WEST reference case) and in this scan it is modified with a multiplier on the whole radial profile.
While varying the density around the reference density of 4 × 10 19 m −3 from 8 to 2 × 10 19 m −3 , the central electron temperature increases at lower densities (see figure 9 left panel).On top of this density scan, a power scan has been performed at higher densities than the reference case (here 8 × 10 19 m −3 ).To achieve the same electron temperatures in this case, injected powers up to 10 MW have been used.For similar central electron temperatures, the achievable central ion temperature can be increased for higher density plasmas thanks to faster collisional equipartition.
Not only the collisional heat exchange time is modified due to the changes in density and power but also the energy confinement time which is increasing with the density in these simulations and decreasing with power.The link between these characteristic times and the ion to electron temperature ratios is shown in figure 9 right panel where the density and power scans are plotted together and overlap with the WEST database.It is found that, at fixed power (squares in figure 9), decreasing the densities (from red to blue) results in increase in τ ei /τ E due to increased τ ei , hence resulting in lower T i /T e .
Moreover, two power scans at a lower and higher density are performed to achieve similar central T e , namely, n = 4 × 10 19 m −3 with P LHCD ranging from 1 to 3.8 MW (lower triangles) and n = 8 × 10 19 m −3 with P LHCD ranging from 3.8 to 10 MW (upper triangles).Increasing power to achieve similar central electron temperature at larger densities results in lower energy confinement times, hence higher τ ei /τ E and lower T i /T e .Nevertheless, the central ion temperature achieved is larger in the higher density higher power case (upper triangles) at the expense of lower energy confinement times.

Impact of external ion heating
Direct additional heating on the main ions has been added in the simulations with a centrally located Gaussian deposition Figure 10.Reference case with 2 MW of power to the electrons (see figure 2).Temperature profiles obtained from steady state simulations with a ion heat source parameterized with a Gaussian which width is 1/4th of the minor radius and such that the power is deposited at 100% on the main ions.
profile having a half width at half height of 1/4th of the minor radius.The range of total ion heating varies from 0 to 2 MW.The reference case has a background of 2.8 MW of electron heating with the LHCD system.As expected (see figure 10), when the power directly coupled to the ions is ramped up, the central ion temperature is increasing independently of the electron temperature, the latter remaining between 2.9 and 3.4 keV.
Comparing to WEST experimental data (figure 11 left panel) with LHCD only, a deviation of the central ion temperature is observed.For up to 2 MW of injected power, the range of variation of the central ion temperature results in T i /T e reaching 0.8 for a given fixed central electron temperature.This clearly shows a transition due to the nature of the ion heat source, from collisional equipartition and thus directly related to T e , to direct ion heating uncoupled from the electron temperature profiles.
Finally, it has been checked that the global energy confinement time predictions in these steady state METIS simulations including turbulent transport with QLKNN-10D were still valid in a regime of mixed ion and electron heating.This is shown in figure 11 right panel and is indeed in good agreement with the scaling law from equation (A.22).

Impact of the volume
In the analytical model introduced in appendix A, the volume is an important parameter that allows to maximize the equipartition efficiency.On the other hand, larger major radius also leads to larger energy confinement times.Both play in favor of an expected weaker T i saturation in larger devices thanks to decreasing τ ei /τ E .
To explore this further, a scan in plasma size has been performed.The shapes are kept isomorphic, i.e. in this case: a typical WEST plasma shape with large aspect ratio, A = 5, triangularity δ = 0.5 and elongation κ = 1.4.Additionally, these scans have been performed also varying the plasma current to fix the edge safety factor (q 95 = 4.2) at a constant toroidal magnetic field of 3.7 T.
First, scans have been performed with constant injected power (figure 12 top left panel) and major radii ranging from 1.75 to 3.5 m.The ratio of ion to electron temperature is found to converge towards 1 as the major radius increases while the energy confinement time increases but the electron temperature is decreasing.The constant injected power with increasing R comes with an increased fraction of radiated power (keeping the tungsten concentration fixed) due to the radiated power scaling up with larger volume (figure 12 bottom right panel).
The large radiated fraction of the reference case (35 %) which unfavorably scales with the volume, motivated additional scans of the major radius while keeping the ratios of power over the plasma surface (P/S) or volume (P/V) constant.In such cases, increasing the size also leads to larger injected power, hence a degradation of the confinement time with power that can significantly compensate the increased confinement time from increasing R and plasma current (figure 13 right panel).In the case of P/V constant, modeled τ E is slightly increasing.For P/S and P/V constant, the electron temperature profiles are now increased together with the ion temperature due to the reduction of the radiated power fraction.
It has to be noted that the predicted energy confinement time is systematically higher than what is found using the Lmode scaling law at R = 3.5 m and could be attributed to the limitations of the training domain of the QuaLiKiz neural network.This is why larger values of R are not considered at this large aspect ratio and an ITER case is directly studied in the following section.
The results of these scans with constant q 95 , magnetic field and varying plasma current and major radius are grouped in figure 14 right panel using τ ei /τ E .They are found to follow similar trends with central T i /T e .The case with constant power features the largest variation of the ratio τ ei /τ E due to decreasing temperatures and thus decreasing electron-ion heat exchange time (for constant density in these cases).On the other hand, the opposite behavior is observed for the cases with constant power density P/V and P/S (figure 14 left panel) where the collisional heat exchange time is increasing and is compensated by increase in the energy confinement time.

Summary of all scans
To underline the significance of the link between the ratio of electron-ion collisional heat exchange time over the energy confinement time and the central ion to electron temperature ratio, all the relevant scans performed in this section are reported in figure 15.It is found that the power, density and major radius scan (the latter being performed for a constant q 95 , magnetic field and external power with P/S constant) are following the same trend.Additionally, increasing the external ion heat flux results in deviation of this trend as the competition between the source and transport is not anymore governed by the collisional equipartition only.Finally, to emphasize the results obtained for increasing major radius, an ITER-like case with an amplification factor Q = P fus /P in ∼ 10 taken from the ITER IMAS scenario database [33] has been analyzed (run 130 013 occurrence 1).This scenario describes a D-T plasma at nominal magnetic field B T = 5.3 T and plasma current of 15 MA.The temperature profiles were computed using the QLKNN-10D transport coefficients (including also a scaling for the pedestal pressure [34]).It has to be noted that the input data are within the training domain of the neural network up to the pedestal top  All results of the different scans performed in section 3 are reported in this figure showing the ratio of the collisional equipartition rate over the global energy confinement time versus the ratio of central ion to electron temperature.An ITER-like case is also highlighted and described in the text.ρ = 0.95 which is also discussed in appendix C. Further validating the transport model, the energy confinement time predicted for this case is 3.06 s whereas the ITERH-98(y,2) scaling law predicts 2.99 s.Additionally, the amplification factor reached is of the order of Q ∼ 8 in this simulation due to more peaked ion temperature profiles (with similar central value) compared to the reference ITER-like case where the profile shapes are following the shape of the Bohm/gyroBohm transport coefficients.The external heating consisted of NBI and ICRH with a total of 53 MW and ∼ 114 MW of alpha power.Some of the power including alpha heating is deposited on the ions resulting in a mix of 30% of the total power (external and fusion power) on the ions and 70% on the electrons.In this case, it is found that the central T i /T e is close to 0.75 consistently with the increased energy confinement time with respect to the electron-ion collision heat exchange time and the additional ion heating.Here volume averaged temperatures are used from ρ = 0 to ρ = 0.2 to compare WEST and the ITERlike case while having different heat deposition profiles.The modelling results suggest that dominant electron heating is not a problem regarding a possible saturation of the central ion temperature, and thus fusion performance, as long as the electron to ion collisional heat exchange time is sufficiently smaller than the energy confinement time.This is further shown in figure 16 where electron heating only (provided by a centrally peaked Gaussian deposition profile) is increased on this ITERlike case and the alpha heating has been artificially removed.This shows an ion temperature saturation at around 20 keV in the unfavorable case of strictly zero external ion heating.Additionally, up to 10 keV T i and T e are strongly coupled.When adding alpha heating, Q ∼ 8 can also be achieved with 40 MW of electron heating.

Conclusions
The ion temperature saturation observed in plasmas with dominant electron heating (e.g.[2]) can be captured by flux driven integrated modeling combining equipartition and the computation of a realistic turbulent heat transport model.In the present work, the integrated modeling code METIS together with the turbulent transport computations with the neural network version of the gyrokinetic code QuaLiKiz have been used for steady state simulations.The full radial domain up to ρ = 1 is modeled for heat transport while the density is fixed to experimental values.This framework has been applied to WEST electron heated plasmas (LHCD only) where such saturation is observed.The reasons for the observed T i saturation on WEST, is, as on AUG and W7X (heated by ECRH), due to the reduction of the equipartition term as T e increases, with a dependency in T −3/2 e , together with decreased confinement times (with increasing power).Modifying the T i /T e dependence on the turbulent heat fluxes does not impact our results significantly in our case (unlike what is observed in W7X [2] and NBI+ECRH AUG plasmas [30]) as long as core Electron Temperature Gradient modes are not significantly destabilized.
The T i saturation is captured by the competition between the global energy confinement time (τ E ) and the volume averaged electron-ion collisional heat exchange time (τ ei ).If the heat exchange time is reduced for example by increased density, the saturation of T i will be weaker.And if the confinement time increases, the saturation of the ion temperature will also be weaker.It is shown that QLKNN-10D reproduces quantitatively the global energy confinement time and in particular the power degradation of τ E consistently with scaling laws and experimental data within 20%, allowing quantitative predictions of the ion to electron temperature ratio with respect to τ ei /τ E .It has to be mentioned that this global trend involving the global energy confinement time could be modified if a local transport barrier develops in the central region (thus contributing less to the global τ E ).This situation was not investigated in this work.Moreover, direct ion heating is very efficient to move away from this trend of τ ei /τ E and to obtain higher T i /T e , as the ion heating is not dominated anymore by collisional heat exchange.
When projecting ourselves towards ITER and reactors, two effects are in favor of larger T i /T e , (i) as shown in section 3, larger volume at constant ratio of power over the surface and constant edge safety factor allowing the increase of the energy confinement time compared to the electron-ion collisional heat exchange time scale, leading to higher T i /T e ratios (together with higher T e and T i ), (ii) alpha heating will dominantly produce electron heating, but it will also produce direct ion heating which is very efficient in increasing the T i /T e ratio.These two mechanisms explain why in modeling of ITER and DEMO (e.g.[8][9][10]12]) scenarios, no strong decorrelation between electrons and ions was reported unlike what occurs in our smaller electron heated devices (W7X, AUG and WEST).

A.1. Insights on ion temperature saturation key physics: analytical model derivation
To highlight the main dependence for T i /T e in dominant electron heated plasmas, we develop an analytical model with the following assumptions: • Cylindrical geometry with elongation for the plasma • Time independent problem • Flat and constant electron density profile n e • Only two species of ions (main ion and one impurity) • The heat source is confined in small region of the core plasma • T e and T i are constant in the region where there is additional power • Constant ratio µ = T i /T e in gradient region and constant T e gradient • T e = T i = 0 at the LCFS • The ratio between electron and ion heat transport coefficient is fixed to a constant (can be a function of T e /T i ) Using these hypothesis, we define the radial coordinate: x = r/a, where a is the minor radius and we read the plasma volume inside x as V(x) = C v x 2 and the volume element is , where R is the major radius and κ the elongation.Choosing the charge effective to be constant, using the definition of Z eff and the electroneutrality equation: ) with Z main < Z eff < Z imp , where Z main is the number of charges of main ions and Z imp the number of charges of impurities ions, we get n main = C main n e , n imp = C imp n e and n i = n main + n imp = C i n e with The additional heating power is assumed to be deposited inside x ⩽ x 1 ≪ 1.We set the ion heat source Q i = δQ and the electron heat source Q i = (1 − δ)Q where δ is the fraction of heat that goes to the ions and Q = Q 0 for x ⩽ x 1 ≪ 1 and 0 elsewhere.We define the additional power P = ´1 0 2C v Qx dx.
In the gradient region (x 1 < x ⩽ 1) with above hypothesis, temperature profiles are T i = µT e and T e = T(1 − x)/(1 − x 1 ), if x ⩾ x 1 otherwise T e = T. Introducing a scaling for confinement energy, we can compute T: with τ = βP −α where β is a constant depending on engineer parameters other than P and α the exponent of P. We have W = τ P from the scaling law and by integrating the pressure on the plasma volume: W = 3/2 ´1 0 q e (n e T e + n i T i )V ′ (x)dx with q e the charge of electron.From the flat density hypothesis and the relation between T e and T i we get W = 3q e C v n e (1 + µC i ) ´1 0 T e x dx.Using the prescribed shape of T e , one arrives at: ) . (A.6) To evaluate µ one has to consider the time independent transport equation in cylindrical geometry: where Q ei is the energy exchange by collisions between electrons and ions (i.e the equipartition term).Assuming χ i = ηχ e , one gets in the gradient region x 1 < x ⩽ 1: The equipartition term is defined as [35,36]: .11)with The A ei term depends strongly on the plasma composition and weakly on plasma kinetic profiles via the Coulomb logarithm.Computing the integral in the gradient region This illustrates the main dependencies that one should expect, that is (i) a decrease of the collisional energy exchange with an increasing electron temperature, (ii) an increase with increasing density at given electron temperature, (iii) an increase with increasing plasma volume.Further specification on the shape of the transport coefficient has to be taken into account.In the following Bohm or gyro-Bohm transport is considered: Substituting T e one gets: Replacing these expressions for the heat diffusivity and the definition of the equipartion term in equations (A.9) and (A.10), one obtains the two following equations for the ion and electron temperature gradients: . (A.17) As the electron temperature shape is known, on can compute γ using: It follows: (A.20) Substituting in equation (A.16): At this point, using equation (A.6) one can find the numerical solutions for µ by integrating the equation for ∂T i /∂x.The results shown in section A.2 are derived from the previous equations in the limit of electron heated plasmas only (δ = 0) and using specified values of the parameter η.
To go further with analytical solutions, We assume some x 2 with x 1 < x 2 < 1 that verifies: And replacing T with equation (A.6), one gets: Results from the analytical model described in appendix A for WEST parameters.Here a scan in the external input power on the electrons has been performed from 0 to 7 MW for a given line averaged density of 4 × 10 19 m −3 (left panel).The ratio of the electron-ion heat exchange time over the energy confinement time is shown for different assumptions on the ratio of the ion to electron heat diffusivities for the same power scan (right panel).

. Insights on ion temperature saturation key physics: analytical model results
In the following, the reduced analytical model is used to reproduce qualitatively the central ion temperature and also to characterize the competition between collisional equipartition and global transport.The latter is given by the ITER L-mode scaling law [37] and given below: With I p the plasma current in MA, B T the toroidal magnetic field in T, P the power loss in MW, n the line averaged density in 10 19 m −3 , M the average ion mass in AMU, ϵ the inverse aspect ratio and κ the plasma elongation.It has been shown that WEST L-mode plasmas follow this scaling with a dispersion associated to cold and hot branches (see [16,28] for more details).
Furthermore, in this reduced model, the transport can be parameterized and the profiles normalized using scaling laws for the global energy confinement time.Then a consistent solution can be found for T e and T i in the simplest case where all the external power is given to the electrons.Using the L-mode scaling law from equation (A.22) with WEST-like parameters, the relation between the predicted T i and T e is shown for varying external input power in figure A1 left panel.The injected power ranges from 0 to 7 MW while the density is kept at 4 × 10 19 m −3 .
The central ion temperature is found to saturate and even decrease for sufficiently large electron temperatures.This is also qualitatively consistent with WEST experimental data, though the rollover is not observed in the experimental range of central electron temperature obtained.It is also shown that the decrease of T i with increasing T e is sensitive to the heat diffusivities ratio between electrons and ions.
Since this is a competition between transport and the ion heat source the parameter τ ei /τ E , the ratio of the volume averaged equipartition time to the energy confinement time is used to characterize this saturation as suggested in [2] with:  from ECE measurements for the reference WEST case.It is found that QLKNN-10D predictions are in good agreement with the experimental T e , as already discussed in the main text, but also with predictions of QuaLiKiz (within 15%) with similar central ion temperature (within 5%).Then the two codes have been compared for 3 values of the LHCD injected power (ranging from 1 to 3.8 MW).This allows to test the main results obtained in this paper, that is, the central ion temperature saturation in WEST and the ion to electron temperature ratio dependency with the ratio of the electron-ion heat exchange time over the global energy confinement time.These results using QuaLiKiz v2.8.4 simulations instead of the neural network are shown in figures C2 right panel and C3 respectively.
It is shown that the central ion temperature saturation is robustly reproduced with the two models with an overestimation of the central electron temperature with QuaLiKiz v2.8.4 for the 1 and 2.8 MW cases.This sensitivity on the kinetic profiles remains in acceptable ranges and comparable to differences between the QLKNN-10D and the older QuaLiKiz version on which it was trained v2.4.0 [4].Additionally, the main dependency of the ion to electron temperature ratio is well reproduced with QuaLiKiz v2.8.4 (figure C3).
Finally, the transport parameters from a steady state simulation of the ITER-like scenario presented in section 3.7 are shown and compared to the limits of the training domain for QLKNN-10D in figure C4.It is found that QLKNN-10D stays within its training domain up to the pedestal top which is also the domain on which it has been applied, the pedestal pressure being constrained by scaling laws [34].

Appendix D. Ion temperature evaluation in Tore Supra
To show the quantitative relevance of the central ion temperature evaluated from the measured D-D neutron rate, comparisons with other ion temperature diagnostics are shown for the Tore Supra tokamak.It has to be noted that the calibration of the fission chambers were only performed for Tore Supra and not in the current machine configuration (WEST).
Two diagnostics are used for the comparisons, i.e.X-ray line broadening [38] (denoted Bragg in figure D1) and charge exchange spectroscopy.For the latter, published data for ion temperature radial profiles are used in figure D2 and are taken from [39].
In figure D1, time traces of the central ion temperature for two Tore Supra discharges are shown.Discharge 28 205 (left panel) also features data from CXRS around 5 s when the neutral beams were switched on.A phase of constant LHCD heating power of 2.6 MW between 8 and 15 s is followed by an ICRH heated phase up to around 20 s, resulting in much higher central ion temperature.Discharge 31 149 (right panel), on the other hand, is an ohmic plasma.For these two discharges, the ion temperature has been reconstructed from measured D-D neutron rate using the same methodology described in section 2 and compared to other diagnostics previously described.A good quantitative agreement is found among all evaluations of the central ion temperature which validates the reliability of the neutron detectors calibration and the methodology used.
Regarding the strong assumption that is made on the ion temperature profile shape (since the neutron rate is an integrated quantity), radial profiles of the ion temperature measured from CXRS and published in [39] are compared to the hypothesis of T i = α √ n e T e , α being tuned to match the neutron rate.This is shown in figure D2 for two discharges at different plasma current.Discharge 39 648 is an ohmic plasma while in 39 598, 0.6 MW of ICRH has been added.It is found that the shape we prescribe for the central T i evaluation from neutron rate is in relatively good agreement with CXRS radial profiles and more importantly yields very similar central T i .

Figure 1 .
Figure 1.(left) Measured D-D neutron rate against central electron temperature from ECE.The database corresponds to the C4 and C5 WEST campaigns altogether with injected power above 1 MW (LHCD heating only) and for a plasma current of 0.5 MA, a magnetic field of 3.7 T and D only plasmas.(right) Corresponding central ion temperature inferred from the D-D neutron rate.

Figure 2 .
Figure 2. LHCD power scan based on discharge 55 025 at 8.5 s.Electron and ion temperature profiles obtained at steady state using METIS and QLKZNN-10D.The measured electron temperature profile from ECE is shown up to ρ = 0.5 due to pollution from fast electrons in more outward channels.

Figure 3 .
Figure 3. (left) Energy confinement time degradation with injected power computed from METIS with QLKZNN-10D compared to the L-mode scaling law and the WEST database.(right) D-D neutron rate versus central electron temperature obtained from METIS steady state simulations and compared to the WEST reduced database.

Figure 4 .
Figure 4. (left) Inferred central ion temperature against measured central electron temperature from the WEST database.Results from METIS+QLKNN-10D simulations are also shown for the LHCD power scan.(right) Ratio of the electron-ion heat exchange time over the energy confinement time for the WEST database and METIS+QLKNN-10D modeling.

3 / 2 e
) together with the increase in turbulent transport (τ E decreases) and is consistent with the reduced analytical model results shown in figure A1 left panel.

Figure 5 .
Figure 5. (left) Steady state electron and ion temperature profiles for different values of T i /Te used as inputs for QLKNN-10D.(right) Corresponding electron and ion heat diffusivities.

Figure 6 .
Figure 6.(left) Central ion temperature versus central electron temperature obtained from METIS+QLKNN-10D steady state simulations with constrained electron to ion temperature ratios.(right) Corresponding ratios of the electron-ion collision time over the energy confinement time against the electron to ion temperature ratio.

Figure 7 .
Figure 7. (left) Steady state temperature profiles for constrained and unconstrained electron to ion temperature ratio.The contributions of ETG on the total electron heat flux has been removed.(right) Corresponding Electron and ion heat diffusivities.

Figure 8 .
Figure 8. Cases without ETG contribution to the electron heat flux for:(left) central ion temperature versus central electron temperature obtained from METIS+QLKNN-10D steady state simulations with constrained electron to ion temperature ratio, (right) corresponding ratios of the electron-ion collision time over the energy confinement time against the electron to ion temperature ratio.

Figure 9 .
Figure 9. (left) Central ion temperature versus central electron temperature obtained from METIS+QLKNN-10D steady state simulations from power and electron density scans.(right) Ratio of the electron-ion heat exchange time over the energy confinement time for the WEST database and METIS+QLKNN-10D simulations.

Figure 11 .
Figure 11.(left) Central ion and electron temperatures from steady state simulations with additional ion heating compared to WEST data.(right) Energy confinement time power degradation with additional ion or electron heating.

Figure 12 .
Figure 12.Temperature profiles in simulations with increasing major radius at constant injected power (top left panel), power to plasma surface ratio (top right panel) and power to plasma volume ratio (bottom left panel).The corresponding increase in the bulk radiated power fraction is also shown (bottom right panel).

Figure 13 .
Figure 13.(left) Ratio of ion to electron central temperature for the 3 major radius scans at constant P, P/S and P/V.(right) Corresponding energy confinement time increase with the plasma major radius from METIS-QLKNN simulations (full lines) and L-mode scaling law (dashed lines).

Figure 14 .
Figure 14.(left) Variations of the electron-ion heat exchange time with increasing plasma major radius for the 3 cases with constant P, P/S and P/V.(right) Corresponding ratio of the electron-ion heat exchange time over the energy confinement time .(right) Corresponding variations of the electron-ion heat exchange time with T i /Te.

Figure 15 .
Figure 15.All results of the different scans performed in section 3 are reported in this figure showing the ratio of the collisional equipartition rate over the global energy confinement time versus the ratio of central ion to electron temperature.An ITER-like case is also highlighted and described in the text.

Figure 16 .
Figure 16.Power scan (central electron heating only) for the ITER-like scenario.The alpha power has been artificially removed.(left) Corresponding electron and ion temperature profiles.(right) Central ion temperature against the central electron temperature for increasing electron heating.

Figure C1 .
Figure C1.Input parameters of the QuaLiKiz 10D neural network for the WEST reference case after reaching a steady state (discharge #55025 at 8.5 s).The limits of the training set (hypercube) are shown with dashed lines.

Figure C2 .
Figure C2.Reference case based on discharge 55 025 at 8.5 s. (left) Electron and ion temperature profiles obtained at steady state using QLKZNN-10D and QuaLiKiz v2.8.4.The measured electron temperature profile from ECE is shown up to ρ = 0.5 due to pollution from fast electrons in more outward channels.(right) Measured central ion and electron temperature from figure 1. Results from the power scan modelling with QLKNN-10D and QuaLiKiz v2.8.4 are also shown.

Figure C3 .
Figure C3.Main dependency of the central ion to electron temperature ratio reproduced from figure 15. Results obtained with QuaLiKiz v2.8.4 are shown in red.

Figure C4 .
Figure C4.Input parameters of the QuaLiKiz 10D neural network for the ITER-like case.The limits of the training set (hypercube) are shown with dashed lines.

Figure D1 .
Figure D1.Central ion temperature evaluated using neutron rate and the methodology described in the main text (section 2), compared to spectral lines broadening in the x-ray range (Bragg) and from CXRS when available.

Figure D2 .
Figure D2.Ion temperature radial profiles evaluated from the D-D neutron rate and an imposed radial shape (∝ neTe) compared to CXRS measurements from[39].