Study of correlations between LOC/SOC transition, intrinsic toroidal rotation reversal and TEM/ITG bifurcation with different working gases in TCV

The effects of different working gases on the transition from linear ohmic confinement (LOC) regime to saturated ohmic confinement (SOC) regime and its relation to the intrinsic toroidal rotation reversal phenomenon were explored in the TCV tokamak. The energy confinement saturation was studied across D, H and He density ramps, and a range of ECRH injection power and through variations of ohmic plasma current. The occurrence of rotation reversal, concomitantly with the LOC–SOC transition, was observed only for certain cases, making us formally exclude a causal relation between the two phenomena. A strong correlation between the evolution of toroidal rotation profiles and electron density gradients was, however, observed, in agreement with previous works (Lebschy et al 2017 Nucl. Fusion 58 026013; Hornsby et al 2018 Nucl. Fusion 58 056008). Linear gyrokinetic simulations were performed to probe the turbulent regime of these discharges, showing a dominance of trapped electron mode (TEM) during the LOC phase and a mixture of TEM and ion temperature gradient (ITG) following the transition to SOC regime in D. Such a TEM/ITG bifurcation was less pronounced in H and He. MHD activity was monitored throughout the discharges and possible correlations between sawteeth instability activity, energy confinement time saturation and rotation reversal are highlighted.


Introduction
Since the early 1970s the global energy confinement time τ E in tokamak plasmas was observed to scale linearly with the electron density n e until a saturation threshold [1]. A critical density divides the plasma energy confinement into two regimes named linear ohmic confinement (LOC) and saturated ohmic confinement (SOC) [2,3]. Figure 1 shows an example of LOC-SOC transition observed during an ohmically heated D density ramp in TCV with a limited configuration and positive triangularity (see also figure 2). The dotted lines highlight the region in density where τ E saturates. The energy confinement time τ E is calculated by a combination of Thomson scattering (TS) and Charge Exchange Recombination Spectroscopy (CXRS) data: where V is the plasma volume, P in the input power, W the plasma stored energy, n e , T e and n i , T i the electron and ion density and temperature, respectively. The dW dt term is small during the plasma current flat-top phase and, thus, usually neglected.
A theoretical explanation of the LOC/SOC transition observed during density ramps is conventionally linked to changes in the plasma's turbulent state [5]. A transition of the dominant turbulent transport from trapped electron mode (TEM) to ion temperature gradient (ITG) mode is often concluded during density ramps. Ions and electrons are weakly thermally coupled at low density, where the collisionality is low, and TEMs are particularly virulent, leading to the poor confinement observed in the early phases of the discharge. As the density increases, the coupling between ions and electrons grows from the increasing collisionality, which also serves to decrease the growth rate of TEMs through collisional detrapping of electrons [6]. The growth rate of the dissipative TEMs can be written as [7]: with ϵ = r R , ω * n = cTe eB k ⊥ | ∇n n |, ω * T = ω * n dln(T) dln (n) and ν e−i the electron-ion collision frequency, indicating that increasing collisions between ions and electrons lead to a reduction in the TEM growth rate (see also [8] for a comprehensive description of these terms).
The higher collisionality is also accompanied by a decrease in the impurity content, that reduces the ion dilution by 1 − nD ne (where n D and n e are the deuterium and the electron densities, respectively). This strongly affects the ITG stability. At low collisionality, the relatively high effective ion charge (Z eff = ∑ i ni Z 2 i ne ) and ion dilution are universally observed to stabilize ITG modes. Conversely, as ν e−i increases, decreasing ion dilution leads to an increase in the ITG growth rate [9,10]. After the LOC/SOC transition, the thermal diffusivity of electrons and ions becomes independent of the electron density and ITG now dominates over TEM in the confinement scaling [11]. The stiff thermal transport associated with ITG modes explains why increasing ohmic heating cannot raise the temperature gradients or the stored energy [12,13], contributing, in part, to the confinement saturation [6].
Another phenomenon often observed during ohmically heated density ramps is that of spontaneous toroidal intrinsic rotation reversal. Intrinsic rotation in tokamak plasmas, i.e. not induced by external torque input such as neutral beam injection, presents a rich and complex phenomenology. TCV's Ohmically heated plasmas operated in limited configuration at positive triangularity are often observed to rotate in the counter-current direction, with rotation at the edge close to zero. Rotation reversal consists in a relatively sudden change of toroidal rotation direction at a highly repeatable threshold density (n e ∼ 6.7 × 10 19 m −3 in TCV's 2006 shots). This density depends upon plasma current, magnetic field, machine size and plasma shape [14]. Although initial observations reported a near complete reversal (magnitude and sign) of the rotation profile, a more general indicator of rotation reversal is a change in the sign of the gradient of the toroidal velocity profile. Using only a change in the toroidal rotation direction can, in fact, lead to misleading interpretations, as v tor profiles that evolve from co to counter-current direction without changing their concavity were often observed in TCV's diverted discharges, as shown in figure 3, where toroidal rotation profiles of a limited and a diverted discharge are compared across the LOC and the SOC phases. In this case, although the value of v tor (or part of the rotation profile) changes sign, the gradient of the toroidal rotation profile remains unchanged. These v tor profiles often show a slow, rigid displacement towards the counter-current direction, but no change in the gradients is  (2.9). This feature, along with its 16 individually controllable poloidal field coils, allows for unique shaping capabilities [4]. (a) Toroidal velocity profiles during the LOC and the SOC phases (red and blue, respectively), D discharge #68408 operated in limited configuration and positive plasma current (Ip = 340 kA). The plasma rotates in the counter-current direction at low density in the LOC regime. The post-reversal toroidal rotation profiles still displays edge rotation close to zero, but now the plasma core rotates in the co-current direction and the gradient at mid-radius is flipped; (b) Toroidal velocity profiles during the LOC and the SOC phases (red and blue, respectively), D discharge #68272 operated in diverted configuration and negative plasma current (Ip = −320 kA). The vtor profiles evolve from co to counter-current (opposite to the limited case). However, the gradient of the rotation profile does not change sign and a rigid displacement of the vtor profile towards the counter-current direction is observed. observed, where, herein, we do not consider this evolution as a rotation reversal.
Toroidal velocity, along with ion temperature and density, is measured with a Charge Exchange Recombination Spectroscopy (CXRS) diagnostic in TCV. TCV's CXRS comprises 6 spectrometers, with lines of sight intersecting TCV's main heating beams (called, respectively, NBI-1 and NBI-2 [15]), as well as a Diagnostic Neutral Beam Injector (DNBI), i.e. a low power beam that provides neutrals for the CX reaction without perturbing the plasma [16]. The DNBI, due to its non-perturbative nature, is particularly suited for intrinsic rotation measurements in Ohmic discharges. Figure 4 shows the lines of sight of the two systems employed to measure the toroidal ion velocity profiles herein presented.
A rotation reversal was first reported at the TCA (Tokamak Chauffage Alfvén) tokamak in 1992 [17], but it was only in 2006 that it was extensively studied [14,[18][19][20], and has, since then, been reproduced in several other devices [3,[21][22][23]. Figure 3(a) shows, again, the toroidal velocity profiles before (blue) and after (red) such a reversal on TCV during a D Ohmic discharge operated in limited configuration at positive triangularity. The edge rotation remains close to zero, while the core rotation evolves from ∼ −30 km s to ∼ +20 km s , i.e. from counter-current to co-current direction. The reversal consists in inverting the profiles derivative at mid-radius, which then evolves from positive (hollow) to negative (peaked).
Rotation reversal has often been reported to occur in the same parameter range of the LOC/SOC transition. Figure 5(a) shows the central toroidal velocity (blue dots) and the energy confinement time (red dots) evolution as a function of plasma density in a deuterium discharge with a limited configuration and positive triangularity (see, again, figure 2) performed in TCV. It became tempting to suggest that a causal relation between the two phenomena exists, implying that rotation reversal can be used as a precise measurement to monitor the less distinct confinement time saturation onset [6,24].
However, cases of toroidal velocity reversal not occurring at the LOC/SOC transition density were also documented [25,26], making such a relation between the two phenomena controversial. These works reported a strong correlation between the variations of toroidal rotation profiles and electron density gradients, motivating the investigation of such a relation in TCV discharges.
Since turbulence is deemed to be responsible for most of the heat, particle and momentum transport in tokamaks, it was conjectured that the TEM/ITG bifurcation could unify the LOC/SOC transition and rotation reversal [6]. Gyrokinetic simulations performed at AUG [25,27] suggest that the LOC/SOC transition is, however, not determined by a change from TEM to ITG. The τ E saturation is rather explained by stronger ion energy transport at higher densities caused by the decreasing plasma dilution. Such a TEM/ITG bifurcation, moreover, cannot occur simultaneously across the whole confined plasma profile (or, in this case, at one universal density threshold). Following the argument above, as the plasma density increases, the change develops at the plasma periphery and moves inward towards the core [28]. Experimental and modeling works performed in AUG [27] and Alcator-C Mod [29] suggest that such a transition may only exist in the edge region, with the plasma core remaining dominated by ITG (within ρ < 0.8) [25]. A TEM to ITG transition was still, however, necessary to explain the observation of the electron density peaking in the parameter regime of the LOC to SOC bifurcation. In that case, as shown in [25], a change in v TOR was not necessarily expected to occur concomitantly with the LOC-SOC transition, but rather after the maximum peaking of the electron density profile, in agreement with other turbulent transport studies [30,31]. These works also suggested an even stronger correlation between variations of toroidal rotation gradients and density profile curvature (second derivative) that, however, are harder to investigate experimentally.
Although a working hypothesis to explain the LOC/SOC transition now exists, the rotation reversal phenomenon remains unclear. The experiments presented in this work were conducted in TCV to investigate the relation between the LOC/SOC transition and the rotation reversal through a wide range of parameters, including plasma current and toroidal magnetic field in order to modify the safety factor profile. This study was particularly focused on the effect of different working gases, including isotopes, on confinement and rotation, with plasma discharges performed in deuterium, hydrogen and helium. TCV's flexible shaping capabilities were also exploited to vary plasma shape and configuration (limited and diverted [4]) to provide a wide range of conditions over which to compare both phenomena.
If residual stress is an important player in the rotation reversal, it could be expected that the electron density and temperature gradients, together with the ions kinetic profiles gradients, have a strong impact upon the rotation profiles. By taking care to monitor the rotation profiles, with a view to a causal relationship between their evolution and the measured plasma gradients, we can probe this possibility. Furthermore, by performing the same experiments over several working gases, including isotopes (and all of them will be used at some stage in ITER), we hope to distinguish any fortuitous correlation to better identify the underlying physics.
This work is structured as follows: the first section describes the working gas effect on plasma confinement and intrinsic toroidal rotation reversal. This section also presents results from linear gyrokinetic simulations performed to explore the turbulent modes that dominate across the LOC/SOC transition and an in-depth experimental investigation of correlations between the rotation reversal and density peaking. The second section focuses on the study of LOC/SOC transition and rotation reversal on plasmas operated in diverted configurations. Finally, a section is dedicated to the study of the effect of q variations on rotation profiles. This is followed by some further discussion and conclusions.

Effect of different working gases, including isotopes, on LOC-SOC transition and rotation reversal
The following section reports on the effect of different working gases (including isotopes), intrinsic toroidal rotation reversal and their correlation with the LOC/SOC transition. Effects of sawtooth (ST) instability crashes, plasma shape and plasma configuration are also considered.

LOC/SOC transition in majority D, H and He plasma discharges
A deuterium reference discharge (#68408: I p = 340 kA, B T = 1.4 T) was developed in a limited configuration with positive triangularity (figure 2). A density ramp was commenced at n e ∼ 3 × 10 19 m −3 to probe the LOC and SOC phases. The electron density was increased until main plasma disruption, where it attained a maximum value of n e ∼ 9 × 10 19 m −3 .
The same discharge program was replicated with H and He working gas. The LOC/SOC transition occurred at different densities for all three working gases. Figure 6 shows the locus of the energy confinement times τ E as a function of electron density.
The LOC/SOC transition, here highlighted by opaque bands, is clearly different between discharges. The highest transition density was obtained in He, preceded by D and H (n sat e (H) < n sat e (D) < n sat e (He)). while the LOC/SOC transition occurs at lower density, and for lower τ E , in H, the value of the energy confinement saturation in D and He is similar, albeit slightly higher in He, thus following the same order as the saturation density: τ sat E (H) < τ sat E (D) < τ sat E (He). This result is supported by experimental observations from other machines (JET [32], AUG [33], LHD [34]). The ion mass (m i ) dependence appearing in the e − i heat transfer p e−i may explain the reduced confinement in hydrogen [33]: where t e,coll is the collision time for electrons, n the plasma density, Z i the ion charge number and T e , n e and T i , n i the temperature and density of electrons and ions, respectively. When comparing the three different majority species discharges, the decrease of T e − T i with increasing density is also an indicator of stronger e − i coupling. Figure 7 shows the electron-ion heat exchange p e−i before and after the LOC/SOC transition in D, H and He. The reduced energy confinement observed in H could also be explained by a decrease in electron temperature that is not fully compensated by an increase in ion temperature. A similar trend is observed in the early phase of the density ramp, where the H ion temperature is comparable to D. At the LOC/SOC transition, however, the D and He core ion temperatures are similar, while H is lower, again in line with the more similar energy confinement times of D and He. This is reflected in the p e−i plot in figure 7 (as p He e−i over most of the radius, i.e. the e − i coupling is lowest for H, compared to D and He, in both the LOC and SOC phases.
It should be emphasized that these observations were exclusively obtained in the L-mode confinement regime. Recent works have shown that the isotope effect is weak in L-mode regimes and mostly depends upon the e − i energy exchange or the external heating scheme and less on changes in transport caused by the different isotope mass. A stronger confinement dependence on the isotope mass appears, however, in H-mode [32,33,35]. Moreover He, being doubly charged, could present different properties compared to hydrogen isotopes. Nevertheless, it was employed during the experiments presented in this work to explore the effects of different working gases on plasma confinement and probe a possible correlation with toroidal rotation reversal in these different scenarios.

Intrinsic toroidal rotation reversal in majority D, H and He plasma discharges
Plasma rotation (in the absence of an explicit external source, such as a Neutral Beam) can be influenced by a large number of factors, including plasma shape and configuration, turbulent transport and MHD activity [18,36,37]. Plasma rotation was studied in the majority D, H and He plasma discharges presented in the previous section. The evolution of toroidal velocity profiles was monitored, with a particular focus on their gradients, to probe a possible correlation with the LOC/SOC transition.
Deuterium discharge #68408 showed a clear LOC/SOC transition accompanied by a reversal of the toroidal rotation profiles for similar plasma density values (figures 3(a) and 5(a)).
The same behavior was not observed in hydrogen discharge #68428, where the LOC/SOC transition occurred at a lower density, with respect to the deuterium discharge, but was not accompanied by a rotation reversal (figure 5(b)). Although a general trend in the v tor trace can be seen (despite a large scatter between the data points), no evident causal correlation between the two phenomena can be inferred.
The same discharge was repeated in He (#68536). Here, the toroidal rotation reversal occurred before the LOC/SOC transition (figure 5(c)) and the two phenomena are better separated with respect to their D and H counterparts. Therefore, this result suggests that the correlation observed for D was circumstantial and restricted to a particular number of situations. Figure 8 shows the toroidal velocity profiles in the He discharge at the start of the density ramp (blue, counter-current direction) and following rotation reversal (red, co-current). Interestingly, here, the shape of the v tor profile is different from the D case. The rotation at the edge remains, again, close to zero. However, the reversal is not symmetrical about the axis as for D. The gradient changes sign at mid-radius but the postreversal profile (red) is now flat in the core. These profiles continued to evolve in the co-current direction as the density increases further, together with v Tor data scatter. H and He plasmas displayed larger error bars at high density compared to D (figures 5(b) and (c) compared to (a)). This is not due to the nature of the gas, but rather to unfavorable measurement conditions. Here (H and He), in fact, the density was increased until its limit, where CXRS measurements are often noisier, whereas, in D, n e was increased more gently and the discharge naturally disrupted without reaching the density limit.

Linear gyrokinetic simulations across the LOC-SOC transition
Linear gyrokinetic simulations were performed for several radial positions with the local version of the GENE (Gyrokinetic Electromagnetic Numerical Experiment [38]) code to probe the most unstable mode and explore the TEM/ITG dominance across the LOC/SOC transition and the rotation reversals for the experiments reported herein. The local approximation implies that no radial variation of profiles and their gradients, as well as magnetic geometric coefficients, are taken into account. Magnetic geometry was reconstructed from experiments using the MHD code CHEASE (Cubic Hermite Element Axisymmetric Static Equilibrium [39]).
The most unstable mode of the form e (γ+i ω)t was computed for each wave number κ y ∼ κ θ , with γ the mode's growth rate and ω its (real) frequency. The ω shown herein corresponds to the κ y mode. Figure 9 shows the frequency of the most unstable mode (the contribution of sub-dominant modes was not explored) as a function of ρ for D discharge #68408. Its evolution across the LOC/SOC transition was monitored by performing the calculation at conditions corresponding to several shot times (t = [0.9, 1.2, 1.3] s), including collisions and impurities in the simulation.
The central region of the plasma appears clearly dominated by ITG (ω > 0) for all three time frames. However, moving towards the plasma edge, where the ion temperature profiles develop a gradient, a significant difference appears. The plasma is dominated by TEM (ω < 0) for ρ > 0.6 in the LOC phase. As the density increases, an ITG-like mode develops with ω > 0 at ρ > 0.6 (figure 9(a)) and TEMs are gradually stabilized ( figure 9(b)). Now, after t = 1.2 s, i.e. after the LOC/SOC transition, ITGs dominate also at ρ ⩽ 0.7. Although it is hard to observe a precise transition from TEM to ITG dominance with time, it is clear from the simulations that a change in turbulence regime occurs in the region of the LOC/SOC transition parameters. These simulations, although only local and, therefore, unable to reproduce any global effect correctly, were performed at multiple radial locations, providing support to the argument that the TEM/ITG bifurcation is local within the plasma radius [25] and, as argued in the introduction, cannot occur over the entire plasma profile simultaneously.
A similar analysis was performed for H discharge #68428, where the LOC/SOC transition occurred at a lower density compared to the D discharge, but where no rotation reversal was observed (figure 10). The development of an ion-directed mode across the LOC/SOC transition is less pronounced here. The transition is only localized to a small area, with no difference observed outside ρ = 0.65, probably not impacting the global transport profile. Therefore, it is not possible to infer the presence of a clear TEM/ITG transition in this H discharge.
Finally, the He discharge #68536 analysis yielded a similar outcome. Figure 11 shows just a minor change in the frequency of the most unstable mode across the LOC/SOC transition and negligible change across the rotation reversal parameters.
Similar simulations were performed for the D and H density scans operated in diverted configurations. Preliminary calculations showed that, here, both the majority D and H plasmas remained dominated by TEM at ρ = 0.6 and ρ = 0.8.
It is pertinent to recall that experiments and simulations reported in [40] suggested that a TEM/ITG bifurcation is, however, responsible for both the toroidal rotation reversal and a simultaneous LOC/SOC transition. Those experiments, performed in Alcator C-Mod, employed a turbulence suppression technique to show that co and counter-current toroidal rotation, as well as LOC and SOC like energy confinement times, can be observed in plasmas with near identical density and temperature profiles. The experiments performed in TCV, that employed high resolution diagnostics to explore a much wider range of scenarios, did not reveal any such similar relation. Consequently, the authors conclude that the existence of a causal relation between the TEM/ITG bifurcation and the rotation reversal (and the LOC/SOC transition, too) is not justified but may be further documented, for example exploring the correlation between the changes in turbulent regimes and the plasma density gradient suggested in [31]. This may become possible in the near future when TCV's TPCI (Tangential Phase Contrast Imaging) diagnostic becomes available. The TPCI can measure radially and temporally resolved profiles of turbulent density fluctuations, possibly indicating whether TEM/ITG bifurcations really occur during Ohmic density ramps.
Putting these results together, no evident TEM/ITG bifurcation was found in H and He discharges operated in limited configuration. After the LOC/SOC transition, D plasmas showed that ITGs overtake the region 0.6 < ρ < 0.75, previously dominated by TEMs during the LOC phase. No such difference was observed in H and He, with the core region (ρ < 0.6) dominated by ITG and the edge (ρ > 0.6) by TEM during both the LOC and the SOC phases.
Within the constraints of local models that were available to the authors, there is no indication that such a radial redistribution of turbulence regimes covers the range of the LOC/SOC simultaneously with the rotation reversal change. Therefore, a transition between dominant turbulent modes must be excluded as the fundamental cause for either the τ E Figure 9. Frequency (a) and growth rate (b) of the most unstable mode across the LOC/SOC transition, D discharge #68408. During the LOC phase (blue dots) the plasma was dominated by ITG for ρ < 0.6 and TEM towards the edge. During the transition from a LOC to a SOC confinement phase, the region 0.6 < ρ < 0.75 became dominated by ITG mode (propagating in the ion diamagnetic direction). saturation or the rotation reversal. This agrees with AUG's findings [25] that suggested that the LOC/SOC transition is not directly related to a TEM/ITG bifurcation, but rather a stronger ion energy transport at higher densities, caused by the decreased plasma dilution, leading to a τ E saturation. A strong correlation between density peaking and profiles steepness, also reported herein, instead, supports the hypothesis that it is rather the change in n e (and its gradient) that drives the rotation reversal rather than something directly connected to LOC/SOC [30].

Density peaking and toroidal rotation reversal
As suggested in the previous section, recent developments in modeling of intrinsic rotation in ohmic discharges of AUG suggest that changes in the curvature (i.e. the second derivative) of density profiles can strongly alter the residual stress and that this could be the cause of the rotation reversal [30]. Furthermore, a strong correlation between the toroidal rotation reversal and density peaking was observed in AUG discharges. In particular, it was shown that a core toroidal rotation reversal occurred after the LOC/SOC transition and was concomitant with peaking of the electron density [25,26,31]. Other studies performed in KSTAR reported a dependence of the gradient of the rotation profiles upon the plasma collisionality, although a correlation with the normalized density and temperature gradient could not be investigated [41].
These results already appear to rule out a causal correlation between the LOC/SOC transition and the rotation reversal. Following these works' methodology, the density peaking  was calculated for all TCV discharges used herein and its evolution compared to the toroidal velocity and its gradient. Density profiles were measured with TCV's Thomson diagnostic. Figure 12 shows an example of the evolution of such profiles across the LOC/SOC transition in D discharge #68408. Figure 13 shows D discharge #68408 energy confinement time and toroidal velocity as a function of density. , here measured at ρ ∼ 0.7, where the density profiles tend to display a steeper gradient. The logarithmic density gradient was calculated from the density profiles measured by the Thomson diagnostic. The relative uncertainties resulted from the propagation of the uncertainties of the density and its gradient, as L ne = dln(ne) dr −1 = ne ∇ne , with a maximum value, at ρ = 0.7 (where the gradients were evaluated), of ±0.06, i.e. within the variations shown in the following plots.
The velocity profiles start to reverse at n e ∼ 5 × 10 19 m −3 , as − R Ln e reaches its maximum. Although the LOC/SOC transition and the rotation reversal occur in the same parameter range in this shot, figure 13(b) suggests that the rotation reversal occurs slightly after the energy confinement time saturation, concomitantly with the minimum of the − R Ln e , that, itself, corresponds to the maximum steepness of the electron density profiles.
A better indicator of a rotation reversal, as described above, is a sharp change in sign of the gradient of the toroidal velocity, here normalized by the thermal ion Mach number, defined as and Ω = vtor R [42], chosen to facilitate comparisons between TCV's different scenarios and with other machines' results. Figure 14 shows the evolution of the gradient of the Mach number in D discharge #68408. The gradient is not evaluated in the centre, where the profiles tend to be flatter, but, again, at ρ ∼ 0.6, where the profiles tend to display their maximum steepness. The change in sign, now considered as the onset of a rotation reversal, starts after a central n e ∼ 5.5 × 10 19 m −3 and, from figure 14(a), occurs slightly before the LOC/SOC transition, but still within the same parameters range.
The relation between the gradient of the Mach number and the density peaking is highlighted in figure 14(b) , with a linear regression plotted in red.
He discharge #68536, which presented a well separated LOC/SOC transition and rotation reversal, also shows a similar correlation with density gradients ( figure 15). The gradient of the Mach number, shown in figure 16(a), follows the same trend previously observed in D, changing sign at the maximum steepness of the density profile. The LOC/SOC transition, as shown earlier, occurred at a higher density for He compared to D and clearly after the rotation reversal, as highlighted in    Figure 16(b) shows, again, a linear relation between the gradient of the Mach number and the density peaking.
The same analysis was performed for H discharge #68428, where no rotation reversal was observed, even though a clear saturation of the energy confinement time is visible in the Here, the two phenomena were well separated, with rotation reversal occurring before the LOC/SOC transition. A correlation between the rotational and the density gradients is, again, observed. To further probe a possible effect of peaking, additional X2 ECRH was applied and deposited close to the q = 1 surface with the double objective of displacing this surface outwards and increasing the density peaking, possibly leading to a rotation reversal (similar to what was reported in [43]). This discharge was performed at the same plasma current of #68428 (I p = 340 kA), whereas the average density was kept roughly constant (n e ∼ 3 × 10 19 m −3 , see also figure 21) to avoid the X2 ECRH density cut-off, which is relatively low for TCV's ∼1.4 T toroidal magnetic field. Three 300 ms pulses were injected with increasing launch power (0.17 MW, 0.5 MW and 0.6 MW), where CXRS temporal coverage was ensured to also include the Ohmic phase before ECH injection. As discharge #69898 did not employ a density ramp, the evolution of the toroidal velocity is shown as a function of time in figure 18, with the ECRH injected power scheme overlaid on the time axis. Figure 19 shows the evolution of the gradient of the Mach number with time. Here, the logarithmic density gradient increases similarly to the density ramp discharges in the other gases. Toroidal velocity profiles start to reverse as the first ECRH power pulse is applied. A complete reversal from counter to co-current direction occurs with the second 0.5 MW ECRH pulse, with no further visible change observed with the injection of the final 0.6 MW pulse. Interestingly, the q = 1 surface was, as expected, displaced from ρ = 0.25 at t = 0.4 s to ρ = 0.35 at t = 0.6 s, i.e. before the full reversal, whereas the ST inversion radius remained constant. Consequently, this reversal is also unlikely to be explained by changes in ST activity.  A similar evolution, compared to the D and He density ramps where a rotation reversal was observed, is retrieved here. u ′ changes sign, i.e. the vtor profile reverses, displaying a similar correlation with the density gradient.
The discharge was repeated in D with a similar outcome: the toroidal rotation profile reversed concomitantly with the maximum density peaking but, importantly here, without a density ramp. In this discharge, the reversal occurred at the very start of ECRH injection (0.17 MW), with no meaningful change seen between the three injection phases. Figure 20 shows the gradient of the Mach number as a function of the logarithmic density gradient for the H + ECRH discharge (left) and D + ECRH (right). The previous linear relation is recovered in these cases too.
A clear difference between the D, H, He ohmic density ramps and the H + ECRH discharge is in the shape of the density profiles. Figure 21 shows the n e profiles between the LOC and the SOC phase in the D, H and He ohmic density ramps and compares them to the density profiles of the H + ECRH discharge. The D and He discharges, where both the LOC/SOC transition and the rotation reversal occurred, show flat profiles before and after the transition. Interestingly, the H discharge, where LOC/SOC transition was not accompanied by a rotation reversal, displays a slightly peaked profile at mid radius. The H + ECRH plot shows that electron cyclotron heating not only increases density peaking, but flattens the density profile. Again, rotation reversal was observed to occur concomitantly with the maximum steepness of the n e profile, similarly to the D and He ohmic density ramps.
As ECRH injection strongly affects temperature profiles and their gradients, the Te Ti ratio was monitored to assess possible correlations with the evolution of toroidal velocity profiles. Figures 22(a) and (b) show the Te Ti trace measured at ρ = 0.55 of discharges #69898 (H + ECRH) and #69980 (D + ECRH), respectively. The bottom plots (figures 22(c) and (d)) show the gradient of the Mach number u ′ and the density peaking (here measured as the ratio of the plasma density at ρ = 0.3 and ρ = 0.8) for the same discharges. All these data are plotted over time as these discharges were performed at constant density to avoid the ECRH cut-off. As expected due to the ECRH injection, Te Ti increases, oppositely to what is observed in Ohmic density ramps ( figure 23(a)   remains the common factor in these Ohmic and ECRH heated discharges that displayed a rotation reversal.
These observations suggest that, where the change in v Tor can be clearly separated from the ST activity, the gradient and the peaking of the density profiles are the main actuators for the rotation reversals in this plasma configuration (limited, positive triangularity) operated in TCV.

Discussion
The stabilization (or destabilization) of turbulent modes most probably plays a major role in understanding rotation reversal in plasmas between different majority species. Investigations on isotope effects reported in [44] (TEXTOR) showed that increasing the isotope mass reduced transport ascribed to a  decrease in the step size of collisional transport and turbulent structures with the ion gyroradius ρ s , consistently with [45] and [46], where the improved confinement in D (compared to H) was suggested to result from higher zonal flow levels. Further studies, based upon analytic calculations, suggested that TEM turbulence is also directly influenced by the isotope mass [47]. An extensive study of the isotope effects of TEMs [48], which also included the presence of impurities, showed that the maximum growth rate of the TEM scales as γ max ∝ M −0. the charge concentration of impurity ions. This implies that TEMs are more unstable in H than D and He. A similar scaling was reported for ITG [49][50][51].
As described in previous sections, these TCV plasmas tend to be dominated by virulent TEMs at the lower densities of the early phases of density ramps, where the plasma is characterized by low collisionality and a higher impurity content. If the growth rate of TEMs scales with mass as γ ∝ 1 √ Mi , it is likely that any stabilization of TEMs by collisional detrapping is less effective in H than in D and He, thus reducing the effects on density profiles and their gradients that, as speculated in the past (see, again, [31]), may induce variations in plasma toroidal rotation and, eventually, lead to a rotation reversal.
Nevertheless, such a correlation cannot be concluded based on the present analysis that showed, for instance, no evident TEM/ITG bifurcation in He, despite the clear LOC/SOC transition and toroidal rotation reversal. This may be further explored in the future employing, as explained in the previous sections, a TPCI diagnostic in TCV, that can measure radially and temporally resolved profiles of turbulent density fluctuations, possibly probing a TEM/ITG bifurcation associated with density and toroidal velocity variations.

Effect of q variations on toroidal velocity profiles
The impact of ST instability on toroidal velocity profiles has been extensively studied in TCV [14,18,37]. Previous works showed that the core rotation is relatively constant for high q (low current) discharges until q reaches values ∼3 and below which the whole rotation profile changes significantly [19]. ST crashes not only alter the magnitude of the v Tor profiles inside the ST inversion radius (position of the q = 1 surface), but also their gradients. The details of these studies can be found in [18,37].
As the impact of the ST crashes on rotation profiles is not negligible, the ST activity was monitored in all the discharges presented in the previous sections. ST frequency and inversion radius were extracted from soft x-rays diagnostic measurements to assess, respectively, possible correlations with the density variations, energy confinement time and changes of the v Tor profiles inside the q = 1 surface. In particular, the evolution of rotation profiles was monitored making sure that the measurements were made well outside the ST inversion radius.
A plasma current ramp was performed in a limited configuration of positive triangularity at a density lower than, but close to, the rotation reversal threshold of the high current D reference discharge. The goal was to monitor changes in the core velocity across q variations. Figure 24(b) shows the core rotation evolution during a plasma current ramp. Negligible variations are observed in the v Tor trace until 0.7 s, when the edge safety factor decreases to below ∼4.4. After t ∼ 0.7 s, the core toroidal velocity accelerates in the co-current direction, in agreement with previous findings [14]. It is well known that the density threshold for the observation of a LOC/SOC transition and rotation reversal scales with plasma current [14,24]. This discharge encouraged the exploration of possible correlations between the energy confinement time saturation and the toroidal rotation reversal at low current and high q.
A density ramp, similar to #68408, was replicated at lower plasma current, where the q value always remained above ∼4.4. Figure 25 shows the toroidal velocity and energy confinement time as a function of density. The DNBI injection (and, therefore, the acquisition of CXRS active signal) started earlier in discharge #68793 compared to #68408, that explains why the density scales are different between the two plots despite being a replica of the same density ramp. A LOC/SOC transition occurred at n e ∼ 7 × 10 19 m −3 , similarly to the high current discharge. However, no toroidal rotation reversal was observed with the rotation profiles remaining peaked in the counter-current direction. Here, again, no evident correlation between the LOC/SOC transition and the rotation reversal was concluded in this parameter (I p , B T , n e ) range.
To further explore the possible correlations between rotation reversal and LOC/SOC transition at high q, density ramps should be performed at low plasma current with the support of fluctuation measurements to investigate the variations of the underlying turbulent mechanisms. This, however, was beyond the scope of this work, where we limited our investigation of ST activity to its main parameters (frequency, inversion radius) to make sure that our measurements were not altered by ST crashes.

LOC/SOC transition and rotation reversal in diverted configurations
The LOC/SOC transition and its relation to the rotation reversal was also investigated for diverted configurations. Legacy experiments showed that diverted plasmas in TCV mostly rotate in the co-current direction and that any rotation reversal occurs in the counter-current direction in these cases [14,23], in agreement with observations reported from other machines [24,26]. To be clear, and as shown in the previous sections, this is the opposite for TCV plasmas operated in limited configuration, where the plasma rotates in the counter-current direction at low density in the LOC regime and co-current direction at higher density in the SOC regime. This highlights the importance of plasma shape and configuration when analyzing plasma rotation and tends to question the concept that the intrinsic rotation direction is driven by a particular dominant turbulence regime that ought to be relatively similar at the start of the density ramps of both configurations. Figure 26 shows the energy confinement time and the central toroidal velocity evolution as a function of density in a deuterium discharge with negative plasma current (I p = −320 kA) and a diverted configuration with positive triangularity (δ ∼ 0.23). As a reminder, the plasma current in the plasma discharges performed in limited configuration was positive. Therefore, a negative value of v Tor corresponds to co-current rotation in these diverted discharges with I p < 0, while v Tor > 0 corresponds to counter-current rotation.   A LOC/SOC transition occurs at a higher density compared to the similar limited discharge. However, the central toroidal velocity continuously evolves toward the counter-current direction without displaying a reversal.   Toroidal velocity profiles before and after the rotation reversal, diverted D discharge #73426. Here, the inner divertor leg was shorter (compared to plasma discharge #68272 in figures 26 and 27, where rotation reversal was not observed) and the plasma shape approached that of a limited configuration with positive triangularity (note the proximity of the last closed flux surface to the inner machine wall). density ramp. Despite relatively big errorbars, mostly resulting from the rapid variation of n e on the CXRS measurements, there is no change in sign of the gradient at any ρ. The slow change towards the counter-current direction is more of a rigid displacement of the entire profile than a profile reversal, differently from previous reports, where a clear reversal in diverted configuration was observed [19]. There, however, the plasma configuration was highly elongated, close to being inner wall limited and with shorter divertor legs compared to #68272 (see figure 26). As shown in [14], the plasma shape parameters (elongation, triangularity) and, possibly, the wall gaps (since they appear to provide an edge v = 0 that is approached by some diverted regimes), appear to be crucial for the observation of rotation reversals.
Based on these results, a density ramp in diverted configuration was performed with an adjusted shape, i.e. higher elongation and shorter inner divertor leg (and, therefore, higher δ ∼ 0.41) to reduce the wall gap and, possibly, replicate the results obtained in the aforementioned discharge performed in TCV in 2007 [19]. Here, with this optimized configuration, a rotation reversal was observed ( figure 28). Interestingly, a LOC/SOC transition also occurs at n e ∼ 6 × 10 19 m −3 and t ∼ 0.8 s, but the rotation reversal was only observed at t ∼ 1.2 s and n e ∼ 6.9 × 10 19 m −3 .

Toroidal rotation in D and H plasma discharges operated at different density in diverted configuration
To further explore plasma rotation and LOC/SOC transition with different working gases, measurements were performed in piggyback experiments aimed at studying the effect of isotopes for varying dominant turbulent modes. These discharges, although not directly related to the study of plasma rotation, allowed for a further exploration of toroidal velocity profiles' behavior in plasmas of majority D and H. If it is true that plasmas are TEM dominated at low density in the LOC phase and ITG dominated at high density in the SOC, a simple method to explore the isotope effect on transport in different turbulent regimes would be to replicate a similar discharge at different density, monitoring the plasma confinement to locate a LOC/SOC transition and, possibly, a TEM/ITG bifurcation. Based on this assumption, a series of discharges was performed with increasing density in D and H. All the discharges were operated in diverted configuration with δ ∼ 0.3 (see figure 29(a)), I p = −200 kA and B T = −1.4 T. The toroidal velocity at fixed ρ ( = 0.1) was calculated from each discharge and drawn as a function of central electron density (figure 29). The energy confinement time is shown as a function of density in figure 30.
The linear increase in v tor , previously observed in a D density ramp (#68272, figures 26 and 27), is again retrieved in H ( figure 29). This series of D and H discharges was performed with I p = −200, whereas the Ohmic D density ramp in diverted configuration presented in the previous section (#68272) was performed with I p = −320 kA.
The different value of I p affected the value of the density at the LOC/SOC transition threshold. As expected [14], the density at the LOC/SOC transition threshold was higher for the higher current and, as for limited configurations, occurred at a lower value in H compared to D. No rotation reversal was observed but, again, a slow, rigid displacement of the toroidal velocity profiles towards the counter-current direction with little change in their gradients.

Effect of plasma shape and configuration on the evolution of rotation profiles
Curiously, the evolution of rotation profiles in this series of plasma discharges operated in diverted configuration (with the exception of the highly elongated #73426) was similar to that of δ = 0 plasmas operated in limited configurations. To make a comparison, figure 31 shows the energy confinement time and central toroidal velocity as a function of density of discharge #73204, consisting in a density ramp operated in limited configuration, δ = 0 and I P = −230 kA. The LOC/SOC Here, again, no rotation reversal was observed but rather a rigid displacement of the rotation profiles towards the counter-current direction that, as argued in the text, should not be considered a rotation reversal. transition occurred at n e ∼ 7.1 × 10 19 m −3 , in the same parameter range of discharge #68408 (D plasma, limited configuration, δ > 0). This, however, was not accompanied by a rotation reversal but, again, a rigid displacement of the v tor profiles towards the counter-current direction, curiously similar to some of the diverted cases. Despite the different shape of v tor profiles between this limited discharge operated at δ = 0 (#73204) and diverted discharges operated at δ > 0 (#68272, for instance), both cases displayed a similar evolution of v tor during density ramps ( figure 31(b)) and no correlation between the gradient of the rotation profiles and the logarithmic density gradient. The highly elongated diverted discharge (#73426), instead, resembles a limited configuration with a clearly pronounced positive triangularity and, therefore, a deeper penetration of the triangular shape within the flux surfaces. All the other diverted discharges presented here show a less pronounced triangularity, more similar to a δ = 0 plasma operated Table 1. Summary of LOC/SOC transition and toroidal rotation reversal characteristics for different working gases discharges operated in different configurations (limited or diverted) and plasma current. The plasma discharge number is indicated in the first column, except for the two density scans in D and H that are composed of multiple discharges, along with the majority plasma species and the plasma configuration. The second column indicates the plasma current. The third and the fourth columns indicate the density threshold for the LOC/SOC transition and the toroidal rotation reversal, respectively. The cases where the LOC/SOC transition was not followed or preceded by any rotation reversal are indicated as 'no v TOR rev.'.

Discharge
I P (kA) a Discharge #73204 was a density ramp in limited configuration with δ = 0. b Discharge #73426 was a density ramp in diverted configuration performed with an adjusted shape. Here, the inner divertor leg was shorter (compared to plasma discharge #68272 in Figures 26 and 27, where a rotation reversal was not observed) and the plasma shape was close to that of a limited configuration with positive triangularity.
in limited configuration. This shows, again, the importance of plasma shape when studying plasma rotation. Table 1 shows a recap of the discharges operated with different working gases presented in the previous sections. Their characteristics are reported (majority species, plasma configuration and current), along with the density threshold for the LOC/SOC transition and the toroidal rotation reversal, where present.

Recap and conclusions
This work presents results on different working gases' (D, H and He) effects on plasma confinement and rotation obtained in TCV. The main objective of the study was to explore the previously suggested existence of a relationship between the LOC/SOC transition and the rotation reversal phenomena observed during plasma density ramps. The two phenomena were reported to occur in the same parameters range (n e , B T , I p ) at least in high current D discharges and a causal relation was suggested between the two phenomena. Furthermore, a commonly accepted explanation for the saturation of the energy confinement time above a density threshold was a change in the plasma turbulent state, with the ohmically plasma transport dominated by TEM at low density in the LOC regime and ITG at higher density in the SOC regime. Should such a relation exist, it must occur for all plasma discharges, albeit for different plasma parameters. Since the turbulent nature is known to depend upon the majority plasma component, similar experiments were performed in D, H and He majority plasmas, that would probe different nuclear masses and mass to charge ratios to seek evidence of such commonality.
No causal relation between the saturation of the energy confinement time and the rotation reversal could be concluded from the experiments reported herein. Detailed analysis of the gradient of the toroidal velocity profiles highlighted a clear separation between the two phenomena with rotation reversals occurred before the LOC/SOC transition in both D and He discharges.
Linear gyrokinetic calculations were performed to investigate the dominance of turbulent modes across the region of the observed LOC/SOC transition and rotation reversals. An ion-directed mode indeed developed in the outer plasma region across the LOC/SOC transition for the D discharge. This observation agrees with previous findings that suggested that the TEM/ITG bifurcation cannot occur globally but would first occur at the plasma edge and then propagate towards the core for increasing density. No evident transition from TEM to ITG was, however, observed for H and He discharges where only slight changes in mode frequencies and growth rates were obtained.
TCV's experiments indicate that, when changes in toroidal velocity profiles can be clearly separated from ST activity, the changes in the gradient of the density profiles are well correlated with the changes in toroidal rotation observed in these plasma configurations (limited, positive triangularity). In particular, as reported in [30], curvature variations of the density profiles can strongly affect the residual stress and, although they cannot be considered the only pertinent parameter, for these results, this is consistent with an important role in driving changes in the rotation profiles, possibly including reversals.
The updated definition of rotation reversal, i.e. not only a change of toroidal rotation direction, but also a change of the sign of toroidal velocity profiles' gradients, can be applied to both the diverted and limited discharges. Moreover, plasmas operated in limited and diverted configurations appear to rotate in opposite directions, implying that the boundary conditions change the balance.
These results motivate further exploration of the correlation between plasma rotation and variations of the density profile, in particular with respect to first and second order profile derivatives that the authors hope may be soon augmented by direct turbulence core and edge profile measurements in preparation for TCV.