Study of impurity C transport and plasma rotation in negative triangularity on the TCV tokamak

Carbon impurity transport is studied in the TCV tokamak using a charge exchange recombination diagnostic. TCVs flexible shaping capabilities were exploited to extend previous impurity transport studies to negative triangularity (δ < 0). A practical way of studying light impurity transport (like C, TCVs main impurity species due to graphite tiled walls) is to investigate the correlations between the impurity ion gradients that, in this study, highlighted significant differences between positive (PT) and negative δ (NT) plasma configurations. δ scans ( −0.6<δ<+0.6 ) were performed in limited configurations, but displayed little correlation between C temperature, rotation and density gradients for positive δ. This stiff response for δ > 0 changes for negative δ, where the evolution of ∇vtor was accompanied by variations of ∇nC over a range of negative δ, showing that transport, in NT, is affected by velocity gradients. Similar δ scans were performed with additional NBH (Neutral Beam Heating), with power steps ranging from 0.25 MW to 1.25 MW, highlighting increased momentum confinement in negative δ. Finally, the evolution of intrinsic plasma toroidal rotation across linear to saturated ohmic confinement regime (LOC/SOC) transitions was explored at δ < 0, expanding previous studies performed in TCV for δ> 0 (Bagnato et al 2023 Nucl. Fusion 63 056006). Toroidal rotation reversal was not observed for δ < 0, despite clear LOC/SOC transitions, confirming that these two phenomena occur concomitantly only in a restricted number of cases and under specific conditions.


Introduction
Intrinsic impurities are unavoidable in tokamak plasmas.The strength of their sources (such as the plasma facing components) and transport mechanisms determine their core plasma components concentration profiles.While their accumulation has detrimental effects, reducing confinement and diluting the fuel, their presence, if kept under control, can also be beneficial.Seeding impurities into hot plasmas has even been observed to improve core confinement [1].Moreover, in a fusion reactor, their presence at the plasma periphery is considered necessary to increase radiative emission and, thus, the radiated power fraction, that helps in decreasing the heat load to the divertor targets to tolerable levels [2].
Impurity transport also presents an interesting subject for physics research, as it is concomitantly driven by both collisional and turbulent mechanisms.Plasma conditions, together with impurity charge and mass, determine the relative strengths of these mechanisms.In particular, light impurity (Z ⩽ 10) transport is universally accepted to be driven by turbulent mechanisms [3,4].
This work focused on the study of carbon transport in the TCV tokamak.Carbon is the ideal candidate for turbulent transport studies, as it is a light impurity (Z = 6) and naturally present in TCV due to plasma edge interaction with its near fully tiled graphite vessel walls.Moreover, its kinetic profiles (T, v, n) are readily measurable, with little perturbation to the diagnosed plasma, using TCVs diagnostic-beam based charge exchange recombination spectroscopy (CXRS) diagnostic [5].
TCVs flexible shaping capabilities [6] were exploited to cover a large range of poloidal triangularity shapes, including extremely positive to extremely negative configurations.This possibility is unique to TCV and exploits its open vacuum chamber and generous poloidal field coil array, providing the capacity to generate extremes of plasma shaping while naturally accommodating a range of divertor geometries.
This paper is structured as follows: the first section presents results from an experimental investigation of C transport in negative triangularity configurations performed through δ scans of Ohmically heated discharges operated in limited configurations.This δ scan in limited configuration was then repeated together with additional external heating to investigate how particle and momentum transport differs with strong neutral beam injected power (employing TCVs 1.3 MW neutral beam injector, hereby simply called NBI, but often labelled NBI-1 [7] to distinguish it from the more recently installed second NBI [8]) between positive and negative triangularity.These results are presented in the second section.
The following section describes the analysis of energy confinement and intrinsic plasma rotation in negative triangularity configurations during ohmic density ramps.In particular, the linear to saturated ohmic confinement regime (LOC/SOC) transition, together with its possible relation with the rotation reversal phenomenon, was investigated.These experiments expand previously reported scenarios that were restricted to positive δ [9][10][11].The paper concludes with a discussion and conclusions.

Impurity transport in negative triangularity
One of TCVs initial and continued objectives is to study the effects of plasma shape on confinement and plasma stability.Experiments conducted in TCV in the 1990s pioneered the investigation of negative triangularity, showing that plasmas operated with an inverse D-shape displayed an increased energy confinement that were concluded to result from reduced transport with respect to near symmetric positive δ counterparts.Since those early results, record performance were obtained for L-mode confinement regimes ( [12][13][14]) with auxiliary heating directed to both the electrons (using ECRH [15]) and majority ions (using TCVs more recently installed NBH [7,8]).Global confinement was found to approach H-mode levels although the plasma state clearly remained in L-mode [12].One of the major challenges for future machines is the control or, possibly, the suppression of edge localised modes (ELM) [16], as they could lead to large and uncontrolled heat fluxes to the tokamak walls, making this plasma configuration very promising for a future fusion reactor operating in a high confinement ELMfree regime [17][18][19][20][21]. Fluctuation measurements revealed that this enhanced confinement was accompanied by (or quite possibly the result of) turbulence reduction [22][23][24], with gyrokinetic simulations providing initial insights into the physics of this phenomenon [25,26].More recently, results from DIII-D [13,14,27] and ASDEX Upgrade [28] have confirmed TCVs findings, albeit with additional compromises required on the range of δ accessible from their local device specifications.
The goal of the experiments presented in this work was to expand previous studies of light impurity transport to strongly negative triangularity configurations.It is widely accepted that impurity transport in magnetic confinement devices is affected by neoclassical (collisional and curvature) mechanisms [29].However, measured light impurity transport levels are often found to greatly exceed neoclassical predictions, indicating that additional mechanisms are at play.This additional transport, termed 'anomalous', is widely accepted to stem from plasma turbulence resulting from instabilities that develop on microscopic scale lengths (microinstabilities), i.e. within the gyro-radius [30].
In addition, heavy and light impurity transport are often affected by a range of mechanisms.In particular, it has been shown that high-Z impurity transport is easily dominated by neoclassical processes, whereas light impurities (like C or B), of interest in this work, are more strongly affected by the effects of turbulence [30].
A general expression for impurity transport can be derived from a quasilinear approximation of gyrokinetic theory [3].Equation ( 1) is a diffusion-convection equation which represents a model for turbulent particle flux: where R is the major radius, n is the particle density, L g = −( ∂ln(g) ∂ρ ) −1 the normalised logarithmic density gradient, with ρ the normalised poloidal flux [31], defined as 2π is the stream function at the considered surface (with ψ pol the poloidal flux), and ψ 0 and ψ LCFS the stream functions at the magnetic axis and at the last closed flux surface (LCFS), respectively.
is the gradient of the Mach number [32], here employed to ease comparison between machines [33,34] and in TCV discharges operated in different scenarios.D nZ R LnZ is a diffusive term.The second and third terms, one proportional to the logarithmic temperature gradient and the other to the gradient of toroidal velocity (scaled to the Mach number), are traditionally termed thermo and roto-diffusion, respectively, despite being convective terms.This is an appropriate physical decomposition, but not a linearised description.Consequently, it is not simple to separate convective and diffusive terms [35].
The density profile is strongly affected by changes in the temperature and toroidal velocity gradients that, in turn, also affect each other.Therefore, a pragmatic way of studying how the off-diagonal (non-orthogonal) terms L TZ and u ′ affect transport is to look for correlations between these terms and L nZ .
The following sections report on triangularity scans performed in Ohmic and NBI heated discharges, operated in limited configurations.Radial impurity profiles (T C , v C , n C ) were measured with TCVs CXRS diagnostic, comprising 4 systems with lines of sight covering the entire vessel section (2 toroidal systems, covering the Low and High Field Sides, 2 poloidal LFS, of which one covering the plasma edge with enhanced spatial resolution [5]).
It is important to mention that TCVs CXRS employs a nonperturbative diagnostic NBI (DNBI) as a source of neutral particles for the CX reaction with plasma ions, often C, naturally present in TCV due to its graphite-tiled walls.The DNBI is a low power beam, optimised, in terms of energy of injected particles, for the observation of a C emission line at 529.1 nm.
Its injection geometry was designed to maximise the beam penetration while minimising the applied toroidal torque.As a non-perturbative beam, it provides an optimal environment for the investigation of low-torque scenarios and intrinsic rotation studies [36].

Triangularity scan in limited configurations
A continuous triangularity scan in limited configuration between δ ∼ −0.6 and δ ∼ +0.6 was performed (figure 1) to investigate the evolution of C ion density, temperature and velocity profiles.Each plasma discharge was performed trying to keep a constant value of δ and similar electron density profiles (figure 2).
Figure 3 shows a comparison between positive (blue) and negative (red) triangularity n C profiles.The plot on the left displays the δ = ±0.3discharges' profiles, while the plot on the right displays those for δ = ±0.5.
It is important to remind that sawtooth (ST) activity can alter impurity kinetic profiles inside the inversion radius (r inv , indicated by a dashed line in the plots), for instance flattening n C profiles after a ST crash [37,38].As TCVs CXRS systems are routinely operated with an integration time of 8 ms, that can easily be larger than the ST frequency, measured impurity kinetic profiles are averaged over multiple ST crashes, meaning that any peak or depression in an n C profiles can be the result of ST activity.Moreover, previous studies in TCV ([39]) showed a dependence of ST period (T ST ) on δ, with T ST reaching a minimum for δ ∼ −0.26.Nevertheless, the scan in limited configuration here presented allowed for a detailed comparison between positive and negative δ discharges, highlighting strong differences.
Positive δ plasmas show a flat C density profile in the core region, with no major difference between the δ = +0.3 and δ = +0.5.Negative δ discharges also display flat C density profiles in the core region, but with steeper gradient and higher n C .Although the n C profiles behaviour could be ascribed to ST activity in the inner plasma region 0.1 < ρ < 0.4 [40],  negative δ discharges display consistently higher C densities with respect to their positive triangularity counterparts.This could, of course, be due to the wall conditioning state, so a scan within a single discharge was developed (discharge #67817, from δ = −0.45 to δ = +0.5, figure 4), showing the reproducibility of the results for the kinetic profiles and impurity content changes.
There was no significant difference from the above to these positive and negative δ ion temperature profiles, that also displayed similar gradients, although T i is higher in the δ = −0.5 discharge (figures 5(a) and (b)).Electron temperature profiles are also similar, with slightly higher T e in the δ = −0.5 discharge compared to its positive δ counterpart (figures 5(c) and (d)).
For the rotation profiles, toroidal velocity and Mach number gradients differ between positive and negative triangularity discharges, with the differences increasing in the more strongly shaped cases δ = ±0.5 (figure 6).v Tor profiles are hollow in the core region (ρ < 0.3) for positive δ.At midradius (ρ ∼ 0.5), this profile becomes peaked and finally tends, after a strong gradient region, to an edge region slowly rotating in the co-current direction.The negative δ discharge also features a peaked profile at mid-radius but with a reduced gradient and with an edge rotation now slightly positive (counter-current direction).A similar behaviour is observed for higher δ (±0.6).Here, the gradient is steeper for the δ > 0 discharge, while its δ < 0 counterpart displays a reduced peak at mid-radius with a different curvature in the gradient region.Here, again, the profile behaviour within the ST inversion radius can be strongly affected by ST activity [38,41].Therefore, the analysis focused on the gradient region (ρ > 0.6) throughout the rest of the section.
Previous experiments in TCV showed a reduction in energy transport for negative δ, with discharges at δ = −0.4displaying electron diffusivities (χ e ) a factor of two lower than their positive triangularity counterparts (δ = +0.4)[42].As described in the introduction, this reduction in χ e was attributed to reduced TEM strength directly resulting from the reversed D shape.This hypothesis has been further strengthened by experimental observations [23] and theoretical investigations [26,43].In particular, recent results from DIII-D confirmed these trends [13], showing reduced χ e in the confinement region (0.4 < ρ < 0.8) and, although gyrokinetic simulations are still being discussed, theoretical works indicate that the transport reduction stems from a decrease of turbulent amplitude that is caused by the shape change [26,44,45], although, since triangularity does not penetrate far into the core plasma, understanding why the transport is  reduced across the complete core remains incomplete and is still under investigation [46].
While δ > 0 discharges display flat core C density profiles, regardless of the absolute value of δ, n C profiles in negative triangularity show an accumulation, together with a steeper gradient, that strengthens with increasingly negative δ. Similar observations were reported from past campaigns (2006, [47], 2018, [48]).To bolster this observation, figure 7 plots the ratio nC ne over ρ for δ = ±0.3 and δ = ±0.5 discharges showing, again, a higher C content with δ < 0.
It is important to recall that absolute ion density measurements are notoriously difficult and depend heavily upon a reliable absolute calibration.Herein, such calibrations must be performed close to the time of measurement due to uncertainties in changes to the vacuum window transmission that is part of the CXRS optical chain.Therefore, comparisons between n C profiles in positive and negative triangularity discharges performed during non-contiguous experimental campaigns should be made with particular care, ensuring that the calibration did not evolve significantly due to possible changes  in elements in the complete optical chain (mirrors, lenses, fibers, etc).
As previously described, light impurity transport is deemed to be driven by turbulence.Equation (1) showed that the turbulent flux can be expressed as a combination of diffusive and convective terms.The diffusive terms, in particular, depend upon the impurity ion temperature, density and toroidal rotation gradients, factors that can all be obtained from the kinetic profiles measured by the CXRS diagnostic.To avoid the influence of ST, these gradients were evaluated at ρ > 0.7, i.e. outside the inversion radius and the q = 1 surface.
Figure 8 plots the normalised logarithmic temperature (top left) and C ion density (top right) gradients, along with the Mach number (bottom left) and its gradient (bottom right) as a function of δ.The blue dots correspond to the time frames acquired during the continuous δ scan already shown in figure 3.As previously mentioned, each plasma discharge was performed trying to keep a constant value of δ and similar electron density profiles (see, again, figure 2).The control system kept the δ variations within a ±0.01 range, except for the δ = −0.5 plasma, that displayed stronger variations (visible in the larger horizontal spread of blue dots around δ = −0.5 in figure 8).Discharge #67156 (δ = −0.6),although belonging to the same set of discharges, is plotted in green, to distinguish it from #67154 (δ = −0.5).The red dots correspond to the profiles acquired within a single discharge (#67817), where a δ scan from −0.5 to +0.5 was performed.There was a δ scan from t = 0.5 s to t = 1.5 s in this discharge.42 CXRS time frames were acquired with a 16 ms exposure time, separated by 8 ms, during which the background light was acquired to perform a passive signal subtraction.
Mach number and C ion density profile gradients display strong variations with δ < 0, whereas no marked change was observed in n C , T i and v tor profiles from zero to the highest positive triangularity, similarly to the majority of legacy TCV discharges that rarely explored negative triangularity.In particular, R Ln C increases when δ decreases, reaching a maximum at δ ∼ −0.3 and decreasing for lower values.Similarly, although the data points corresponding to the same discharge tend to accumulate vertically and, therefore, u ′ profiles at different δ can display similar values, the gradient of the Mach number u', on average, decreases after δ ∼ −0.3.Also the Mach number u displays a non-monotonic trend across the δ scan that, however, is not as clear as in the other plots due to the relatively large scattering of the data points.These observations suggest that transport in negative δ plasmas, when the contribution from ST crashes can be excluded, i.e. outside r inv , is strongly affected by variations of the toroidal velocity profile, in particular its gradient.It appears reasonable to speculate that this trend would continue for lower values of δ (δ < −0.6).Here, δ was kept constant (the control system kept δ variations within a ±0.01 range, apart from the discharge at the lowest δ), and a profile was acquired for each of the 42 CXRS time frames during the current flat-top; in green, a discharge performed at extreme negative δ (−0.6).Again, it was more challenging to maintain the value of δ constant and the data points are more scattered compared to the blue dots; in red, a δ scan performed within a single discharge, from negative (−0.5) to positive (0.5) δ.This discharge, due to the rapid δ variation, shows relatively high scatter in the data points that, nevertheless, follow the trends of the other discharges.

External torque injection through neutral beam
The scan in triangularity for a limited plasma configurations was repeated with the addition of high power NBH injection.The goal here was to explore how external torque injection affects carbon ions' kinetic profiles in positive and negative triangularity inspired by the differences described above.
The beam power injection scheme is shown in figure 9, along with the electron and ion temperatures trace of a δ > 0 (blue) and δ < 0 (red) discharge, showing consistently higher T e and T i at δ < 0. Five NBH pulses of 100 ms duration were applied during the scan.The pulses were separated by a 100 ms beam OFF-phase, with injected power increasing at each step by 0.25 MW.It has to be mentioned that, as TCVs beam energy increases with power (ranging from 7 keV to 28 keV  ).An increase in the emitted neutral signal below 23 keV is visible in both positive and negative δ discharges.This is the signature of a gradual slowing-down within the plasma, consistent with fast-ion confinement.
at maximum power, see [8]), also the torque deposition profile evolves during such a power scan.DNBI CXRS measurements covered the shot time window between 0.5 s and 1.5 s, allowing for non-perturbative C kinetic profiles measurements during both the ON and OFF NBH phases.All discharges were performed in the unfavorable B T configuration to avoid Hmode access and any ensuing ELMs that would compromise the CXRS data quality.
Unfortunately, neutron emission rate measurements were not yet available for these discharges.However, neutral emission spectra were recorded by a compact neutral particle analyser (CNPA) [49] to probe the fast ion behaviour and, thus, the effectiveness of the beam deposition.Figure 10 shows the neutral emission spectra recorded during the injection of a 1.0 MW NBH pulse in a positive and a negative δ discharge.The spectra are normalised to their values at 23 keV, that is the energy of the closest NPA energy channel to the NBH energy (25 keV).The emitted neutral signal increases below 23 keV in both positive and negative δ, displaying a gradual slowingdown within the plasma, consistent with fast-ion confinement [50].
The effect of neutral beam heating is also visible in figures 11 and 12(a) and (b), that show, respectively, the increase of energy confinement time τ E and plasma β time traces during NBH injection for positive and negative δ discharges.β N , termed normalised β, is defined as β N = β aBT IP , with β the ratio of plasma to magnetic pressure, a the minor radius, B T the toroidal field and I P the plasma current.All these values were calculated with TRANSP simulations [51].As mentioned at the beginning of this section, plasmas operated at δ < 0 display consistently higher values of τ E and β N , as routinely observed in TCV [12].
Figure 13(a) shows T i Te consistently higher or equal to 1, compatible with NB-heating, with similar values for positive and negative discharges, except for the P NBI = 1MW case, in which the δ < 0 plasma displays higher T i Te .No significant difference between δ > 0 and δ < 0 is observed in the R LT i and R LT e plots (figures 13(b) and (d)), whereas R Ln C is higher at negative δ during the first three beam pulses ([0.25, 0.5, 0.75] MW, figure 13(c)).
Positive and negative triangularity discharges are further compared in figure 14, where two C ions density profiles are   shown: on the left (a, c, e), δ = −0.5 discharges, on the right (b, d, f), δ = +0.5.The red profile corresponds to an Ohmic discharge in limited configuration, and the profile in blue a discharge repeat with the addition of NBH following the injection pattern described above.Here, the absolute value of n C is not directly indicative of a change in transport, as the electron density suffered moderate variations with beam injection (figures 14(c) and (d)).However, the n C gradient was seen to change dramatically with NBH, with n C consistently higher, as shown by the nC ne profiles (figures 14(d) and (f)).In the absence of NBH, the C ion density profiles tend to remain fairly flat in the core region, before developing a gradient after ρ = 0.4.With NBH (0.5 MW, as shown in figure 14(a), n C now peaks in the core with a consequent strong gradient region curvature of the profile at mid-radius, where the gradient relaxes compared to its ohmic counterpart.
The same discharge (limited configuration + NBH) at positive triangularity (figures 14(b), (d) and (f)) displayed a different behaviour.Interestingly, here, NB injection's effect on the n C profile shape is much weaker.The n C profiles are even flatter with profile steepness decreasing for ρ > 0.5.In contrast, the absolute value of carbon density decreases strongly from n C ∼ 1.6 × 10 18 m −3 at ρ = 0.1 without the NBH to n C ∼ 0.5 × 10 18 m −3 with 0.5 MW of NBH.As observed in the previous section, δ < 0 discharges displayed a higher C concentration, as visible comparing figures 14(e) and (f).
Figure 15(a) compares n C profiles during the 0.75 MW NB injection.Temporarily leaving the absolute C ion density aside, the δ = −0.5 discharge has a peaked core profile with a steep gradient until ρ ∼ 0.6, where the profile gradient relaxes.Increasing NBI power strengthens these changes, enhancing the n C peaking and profile steepness.Conversely, not only does NBI have an opposite effect for positive δ by flattening n C profiles, but increasing NBI power appears to engender little further change in the absolute values of the C density nor its gradients.Similar to the C impurity ion density profiles, the n e profiles are peaked in the negative triangularity discharge and flat for positive δ (figure 15(b)).Although the shape of the n C and n e profiles for negative triangularity are similar, the C ion density profile is more peaked for negative triangularity than n e , with a steeper gradient at mid-radius (figure 15(c)).Restricting the analysis outside the q = 1 surface (located at ρ ∼ 0.5 in discharge #68037, δ < 0), the C ion concentration remains higher in δ < 0 discharges compared to their positive counterpart.
The higher impurity content observed in TCV for negative triangularity discharges is in disagreement with DIII-D TRANSP simulation results previously [13] that showed a higher C concentration in δ > 0 plasmas, that explained a lower measured neutron rate through D dilution.Moreover, values of Z eff ∼ 1.5 were measured in recent δ < 0 discharges in DIII-D, that are remarkably low when compared to DIII-D δ > 0 discharges with comparable heat confinement (H-mode) that exhibited Z eff ∼ 2.5, as reported in [52].Nevertheless, as shown in this section and reported in previous works where matching positive and negative δ scenarios were compared [44,47,48], the C concentration is consistently higher for δ < 0 in TCV, both in Ohmic and NB-heated discharges.Interestingly, in DIII-D, peaked n C profiles were observed for δ > 0 NB heated discharges, whereas the n C profiles at δ < 0 were hollow [52].Conversely, when NBH is injected into TCV, strongly peaked n C profiles are observed at δ < 0, whereas n C profiles in matching δ > 0 discharges remain flat (see, again, figures 14(a), (b) and 15(a)).It is important to remind here that the discharges reported in this work were operated in limited configuration.Recent TCV highperformance diverted discharges, instead, did not display high values of Z eff .Therefore, further experimental investigations are needed to confirm these results, possibly by performing δ scans with matching scenarios between positive and negative δ discharges on different tokamaks.
Although the absolute value of the carbon ion density cannot be taken as directly indicative of a strong change in impurity transport, especially when the plasma density varies between positive and negative δ discharges, the impurity content is crucial in simulations to retrieve a robust estimate of the transport level, as shown in [53] and [26].An increase in the effective charge Z eff (and, thus, in collisionality ν * ∝ neZ eff T 2 e ) causes a reduction of ion and electron fluxes by ion dilution and collisional stabilisation of trapped electron modes (TEMs) [26,44].Ion dilution, in agreement with our experimental observations, increases with decreasing negative δ.Therefore, ion temperature gradient (ITG), that usually become stronger than TEM effects when ion dilution decreases, remain stable.Recent theoretical works further explored the beneficial effects of plasma shape on confinement and turbulence suppression, confirming that negative triangularity has a stabilising effect on both TEM and ITG modes [54][55][56].Consequently, in the δ < 0 scenarios explored in this work, TEMs remain the dominant turbulence and, thus, transport determining modes, in agreement with other publications [25,26].Conversely, when strong NBI heating is applied, in particular when T i > T e , the dominant turbulence regime in TCV was found to be a mixture of TEM and ITG modes, as shown by linear gyrokinetic simulations reported in [23].
Electron density profiles, and other ion kinetic parameters (T i , v tor ), were probed to see whether the changes observed in n C between positive and negative triangularity plasmas are reflected in other quantities.As expected, T i profiles become peaked during beam injection in both positive and negative δ discharges, with the core temperature increasing with power (direct ion heating).Ion temperature profiles also tend to be steeper, and T i higher for negative triangularity discharges.
Significant differences were also observed in the rotation profiles.Before NBH, negative δ toroidal velocity profiles are hollow in the core and slightly peaked at mid-radius.A similar profile of v Tor is seen for positive triangularity.During the Ohmic phase, the plasma rotates in the counter-current direction for both negative and positive δ plasma discharges.During NBH injection, v Tor evolves towards negative values, with a strong plasma rotation in the co-current direction, i.e. the direction of momentum drive from NBH (figure 16).Toroidal velocity progressively increases with power in line with the additional toroidal torque applied by the beam.
The negative δ discharge with NBH injection (#68037) is now compared to its positive δ counterpart (#68038).Figure 17 shows the evolution of toroidal rotation profiles before, during, and after the injection of a 0. As before, both positive and negative δ toroidal velocity profiles become hollow in the co-current direction, as would be expected by the dominant effect of momentum injection from the beam, with δ < 0 plasmas displaying similar or slightly higher rotation velocity.After beam injection ends, the rotation profiles relax and flatten.However, negative δ plasmas maintain a strong rotation in the co-current direction for considerably longer after beam termination, indicating higher momentum confinement with negative triangularity.
The δ > 0 plasma continues to rotate in the co-current direction after beam injection ceases, but quickly slows, before, finally, retrieving pre-injection rotation levels, i.e.v Tor > 0, within t ∼ 100 ms (see figure 18).Conversely, the δ < 0 plasma does not have the time to retrieve pre-injection rotation levels before the next beam pulse occurs.Looking at figure 18, that shows the central toroidal velocity as a function of time for discharges #68037 (δ < 0, red) and #68038 (δ > 0, blue), it can be estimated that the δ < 0 discharge retrieves pre-injection rotation levels within t ≲ 200 ms.
The data points during the Ohmic phase following beam termination were fitted with an exponential decay function y = ae − t T i .The time constant in table 1 shows, again, the higher momentum confinement in plasmas operated at δ < 0.
The behaviour of toroidal rotation profiles and plasma confinement at δ < 0 is further investigated in the following section.

Intrinsic toroidal rotation and plasma confinement in negative triangularity
Plasma rotation can be influenced by a large number of factors, including plasma shape and configuration, turbulent transport and MHD activity [38,47,57].
The following section reports on the effect of negative triangularity on intrinsic toroidal rotation and, in particular, the rotation reversal phenomenon and its correlation with the LOC/SOC transition.As reported in [10,58], deuterium plasmas operated in positive triangularity and diverted configuration are often observed to rotate in the co-current direction at low density in the LOC regime.Rotation reversal was initially defined as a relatively rapid change in rotation direction at a certain density threshold that, in some cases, appears to coincide with the critical density associated with the LOC/SOC transition [10,59].This n e threshold was found to depend upon the plasma current and machine size [10].A toroidal rotation reversal was reported for the first time at the Tokamak Chauffage Alfvén tokamak in 1992 [60], but it was only in 2006 that it was extensively studied in TCV [47,[61][62][63].Since then, it has been reproduced in several other devices (like Alcator C-Mod [64][65][66], AUG [11], MAST [67], KSTAR  Central toroidal velocity, here multiplied by −1 to display positive values, as a function of time for a negative (red) and a positive (blue) triangularity discharge with neutral beam injection.During the fourth and fifth beam pulses (1.0 MW and 1.25 MW, respectively), the CXRS signal of the δ > 0 discharge was strongly perturbed as the plasma briefly entered an ELMy H-mode phase, explaining why a few data points are missing.[68], JET [69], ADITYA [70]), a thorough explanation this phenomenon is still missing.Curiously, TCV charges operated in limited configuration rotate in the countercurrent direction at low density, with a consequent reversal occurring in the co-current direction (see [61]), i.e. opposite to that usually observed in other machines that often operate with diverted configurations.As shown in [5,9], this causal relation between rotation reversal and LOC/SOC transition was not maintained in H and He majority plasmas.However, a strong correlation between the rotation profiles and the evolution of the density gradient was seen, as previously suggested by the AUG team [71][72][73].used to fit the central toroidal velocity data points during the Ohmic phase that followed beam termination (figure 18).[t 1 , t 2 , t 3 ] correspond, respectively, to the Ohmic phases following the [0.25, 0.5, 0.75] MW beam phases.The two Ohmic phases following the 1.0 MW and 1.25 MW beam pulses were not analysed due to the lack of data points.As shown in figures 19(a) and (c), the LOC/SOC transition and the rotation reversal occur at the same density in limited configurations.The rotation profiles evolve from counter to co-current direction until n e ∼ 6.6 × 10 19 m −3 and the sign of their gradients reverses across the LOC/SOC transition.When TCV density ramps were operated for a diverted configuration, the toroidal velocity radial profiles evolved from the co to the counter-current direction, i.e. in agreement with other machines.Here, however, no correlation with the LOC/SOC transition was observed, as the v tor profiles continued to evolve 'rigidly' towards the counter-current direction, as shown in figures 19(b) and (d), i.e. without saturating or changing rotation direction at the LOC/SOC transition density threshold.

Plasma
These observations demonstrated how plasma shape and configuration can strongly affect the shape of plasma rotation profiles and their behaviour.However, they also make a causal relation between the LOC/SOC transition and the rotation reversal controversial, showing that using the change of toroidal rotation direction or its saturation to define rotation reversal can lead to misleading interpretations.As defined in [9], a more general indicator of rotation reversal is a change in the sign of the gradient of the toroidal velocity profile (figure 19(c)).Consequently, a 'rigid' displacement of the rotation profiles (figure 19(d)), despite the change of rotation direction, will not be considered as a rotation reversal.

Ohmic density ramps in negative triangularity
Ohmic density ramps were performed in negative triangularity and limited configurations in TCV to investigate the LOC/SOC transition and the evolution of rotation profiles by this plasma configuration, expanding the experimental scenarios previously reported in TCV that were limited to δ > 0. Previous works reported a possible rotation reversal with δ < 0 but no extensive conclusion could be drawn [47].
Figure 20 shows the evolution of the energy confinement time and toroidal velocity at mid-radius in a negative triangularity deuterium discharge (here, again, operated in limited configuration), where a colourbar indicates the logarithmic density gradient.As noted in the introduction, it has been speculated that the variations of toroidal observed during Ohmic density ramps could be strong variations of density profiles (especially their second derivative that, unfortunately, is hard to probe experimentally) [71].This is supported by recent experiments in TCV that highlighted a strong correlation between n e gradients and rotation reversal in D Ohmic density ramps performed at high current (I P = 340 kA) in limited configurations [5] (also reported from AUG [72]).This correlation is usually accompanied by changes in the underlying turbulent mechanisms, often, but not always, seen in gyrokinetic simulations as a TEM/ITG domination bifurcation across the rotation reversal (supported, experimentally, by Phase Contrast Imaging in Alcator C-Mod [59]).
For negative triangularity, the LOC/SOC transition occurs at higher density than for positive triangularity (n e ∼ 8.4 × 10 19 m −3 at δ < 0, n e ∼ 6.5 × 10 19 m −3 at δ > 0).Despite the changes of the density gradients (here measured with the normalised logarithmic density gradient), no rotation reversal is observed, although a decrease in the absolute value of v tor was seen.
Figure 21 shows toroidal velocity profiles at three different times during a density ramp with δ < 0. The plasma rotates in the co-current direction, with edge rotation close to zero or slightly in the counter-current direction in the early stage of the density ramp.As the density increases, the rotation profiles evolve in the co-current direction without showing significant changes in their shape.In particular, the gradient of the rotation profile does not change across the density scan, showing no rotation reversal.
To further investigate the effect of shape, both the absolute values of δ and κ were varied, but none of these discharges displayed a clear change in sign in the gradient of the rotation profiles, despite nearly the strongest variations in the electron density peaking currently available, as shown in figure 22. Here, a density ramp with constant negative δ of −0.34 (#69306) was performed.Although the absolute value of the central velocity saturates at a relatively low density (n e ∼ 4.8 × 10 19 m −3 ), no correlation with the LOC/SOC change (here occurring at n e ∼ 7 × 10 19 m −3 ) and no rotation reversal was observed (figure 22(b)).
To resume, the experimental toroidal rotation profile variations all resembled a rigid displacement of the entire rotation profile and/or variations of the sole absolute value of v tor .If strong variations of turbulence are needed to induce the changes in n e (and its derivatives) that, in turn, lead to the observation of an intrinsic rotation reversal, a resilience to a transition from TEM to ITG dominance, displayed by negative triangularity plasmas, could explain why only mild variations of v tor are observed during density ramps for δ < 0.
To complete the investigation of δ effects on plasma rotation and confinement, the analysis of the δ scan presented in section 2 (from δ = −0.6 to δ = +0.6) is here complemented with a plot of β N as a function of δ (figure 23(a)), along with v tor measured in the edge region (ρ ∼ 0.9) of discharge #67817 (continuous δ scan from δ = −0.5 to δ = +0.5),figure 23(b).
Comparing figures 23(a), (b) and 23(a), 8(c) (u measured at ρ = 0.75, same set of discharges), no correlation between the strong increase of β N at δ < 0 and the absolute value of toroidal velocity at mid-radius, nor in the edge region (here plotted only for plasma discharge #67817 to ease visualisation),  can be concluded.u ′ , plotted in figure 8(d), is the only parameter, among those analysed, that varies monotonically with negative δ.However, such clear variations are observed only for δ < −0.2, whereas β N displays a sharp increase with the onset of negative δ.Therefore, no correlation between β N and the gradient of toroidal velocity profiles can be concluded either.
As described for the previous discharges, small variations of δ induce changes in v tor that, although not always large, are well outside the diagnostic uncertainties.As the ST period changes with δ, reaching a minimum at δ = −0.26(see, again, [39]), v tor profiles in the core region can be affected by ST crashes and, therefore, are not plotted.

Discussion and conclusions
This work focused on the investigation of impurity transport and momentum and energy confinement in plasmas operated at negative triangularity.During the δ scan reported in this work, an increase of the C concentration was observed for increasingly negative values of δ, while no strong variation was observed in their positive δ counterparts.The higher impurity content for δ < 0 can contribute in explaining a stabilisation of TEMs and the reduction in ITG's dominance: such an increase in Z eff causes a reduction of ion and electron heat fluxes following the consequentially increased ion dilution and increased collisional stabilisation of TEMs [26].As the ion    8, blue dots represent separate discharges performed at different δ and maintaining other plasma parameters constant.beta N from plasma discharge #67156 (δ = −0.6) is plotted in green to distinguish it from the discharge at δ = −0.5.Red dots correspond to a continuous δ scan from −0.5 to +0.5.(b) Toroidal velocity in the edge region (ρ ∼ 0.9), here plotted for plasma discharge #67817 to ease visualisation.dilution increases with more negative δ, ITGs remain stable and TEMs dominant.The opposite effect was observed during D density ramps with positive triangularity (see [5]), where the increase in collisionality (higher plasma density) was accompanied by a decrease of Z eff (often observed during density ramps), further destabilising ITGs due to a lower ion dilution.This change in the C concentration (and in density gradients) would explain why a significant variation of u ′ was observed only during the negative δ scan (figure 8(d), where u ′ is plotted as a function of R Ln ) and not in positive triangularity discharges, where only mild changes were observed when varying δ > 0.
As shown in section 3, a LOC/SOC transition, regularly observed in ohmic density ramps performed at δ > 0, was observed also at δ < 0 in TCV, albeit at higher densities.It had been speculated that a causal correlation between the LOC/SOC transition, the rotation reversal and the TEM/ITG bifurcation exists [10,59].However, the results herein reported showed that these LOC/SOC transitions were not accompanied by any rotation reversal in δ < 0 ohmic plasma density ramps.Recent experiments performed at TCV and reported in [9] confirm these observations, showing that LOC/SOC transitions are not necessarily accompanied by a reversal of rotation direction and/or a change of sign in the gradient of rotation profiles, nor a clear transition from a TEM to an ITG dominated plasma regimes, consistent with what was also observed and simulated for ASDEX Upgrade [74].Nevertheless, the turbulence suppression displayed by δ < 0 plasmas [26,[44][45][46] and, thus, their resilience to transition from TEM to ITG dominance (as modelled by gyrokinetic simulations [26] and experimental measurements [13]), could help explaining the absence of a rotation reversal.Studies of particle transport, in fact, showed that the behaviour of the n e profile, and the type of turbulence dominating the plasma, are strongly linked [75].
The changes in the nature of the turbulence (that, eventually, lead to a TEM/ITG bifurcation in D density ramps at δ > 0) could then contribute to the changes in the density gradient, that are thought to be the main actuator for the changes in plasma toroidal velocity [9,76].
The δ scans with NBH injection herein presented also showed increased momentum confinement at < 0, not necessarily accompanied by a significantly higher rotation.A comparison between rotation profiles, their gradients and β N within a δ scan did not highlight any correlation, showing that the improved plasma performance at δ < 0 cannot be ascribed solely to plasma rotation.
In TCV, TEM/ITG bifurcations during density ramps were only studied with linear gyrokinetic simulations at positive δ (as reported in [9]).Therefore, experiments would be required to further explore turbulence and toroidal velocity variations during LOC/SOC transitions, especially at negative δ.This may soon be facilitated on TCV using a TPCI (Tangential Phase Contrast Imaging) diagnostic, that can measure radial and temporally resolved profiles of turbulent fluctuations, possibly revealing TEM/ITG bifurcations during Ohmic density ramps.

Figure 4 .
Figure 4. (a) Carbon ion density profiles in positive (blue) and negative (red) triangularity during a δ scan from −0.45 to +0.5 (discharge #67817); (b) δ time trace during the same discharge.The profiles shown on the left correspond to the red and blue circles, at the beginning and at the end of the δ scan, respectively.

Figure 8
Figure 8. R LT i (a), R Ln C (b), u (c) (Mach number), u ′ (d) (gradient of the Mach number), R LT e (e) as a function of δ at ρ = 0.75 and T i /Te (f) at ρ = 0.05.Three sets of discharges are plotted: in blue, a delta scan performed with separate discharges at δ = [−0.5,−0.3, 0, 0.3, 0.5].Here, δ was kept constant (the control system kept δ variations within a ±0.01 range, apart from the discharge at the lowest δ), and a profile was acquired for each of the 42 CXRS time frames during the current flat-top; in green, a discharge performed at extreme negative δ (−0.6).Again, it was more challenging to maintain the value of δ constant and the data points are more scattered compared to the blue dots; in red, a δ scan performed within a single discharge, from negative (−0.5) to positive (0.5) δ.This discharge, due to the rapid δ variation, shows relatively high scatter in the data points that, nevertheless, follow the trends of the other discharges.

Figure 9 .
Figure 9. Electron (a) and ion (b) temperature traces of a δ > 0 (blue) and δ < 0 (red) discharge overlaid to the neutral beam power injection.Plot (b) is zoomed over the time window covered by the DNBI CXRS system ([0.5-1.5](s), whereas the Thomson Scattering diagnostic acquired during the whole discharge and, therefore, the entire traces are shown in plot (a).

Figure 10 .
Figure 10.Neutral emission spectra of a positive (blue, discharge #68038) and a negative (red, discharge #68037) triangularity discharge.Both spectra were recorded by a CNPA diagnostic during the injection of a 1.0 MW NBH pulse.Here, the signals are normalised to their values at 23 keV, the energy of the closest NPA energy channel to the neutral beam energy (25 keV).An increase in the emitted neutral signal below 23 keV is visible in both positive and negative δ discharges.This is the signature of a gradual slowing-down within the plasma, consistent with fast-ion confinement.

Figure 11 .
Figure 11.Energy confinement time trace for a negative (red) and a positive (blue) triangularity discharge with neutral beam injection.

Figure 13 .
Figure 13.T i Te (a) R LT i (b) R Ln C (c) and R LT e (d) as a function of NBI power calculated at ρ = 0.75 for a negative (red) and a positive (blue) triangularity discharge.

Figure 14 .
Figure 14.n C , ne and nC ne profiles in negative (left) and positive (right) triangularity discharges.In red without NBH, in blue with the addition of 0.5 MW NBH.

Figure 15 .
Figure 15.(a) Comparison between C density profiles in positive (blue) and negative (red) triangularity.Both profiles were acquired during the injection of a 0.75 MW NBH pulse.(b) ne profiles.(c) nC ne profiles.

Figure 16 .
Figure 16.Toroidal velocity profiles before (red) and during the injection of a 0.5 MW NBI pulse (blue), at negative (left) and positive triangularity (right).

Figure 17 .
Figure 17.Evolution of toroidal rotation profiles during and after beam injection ([10-20] ms after the end of the beam pulse).Negative (red) and positive (blue) triangularity discharges compared.

Figure 18 .
Figure18.Central toroidal velocity, here multiplied by −1 to display positive values, as a function of time for a negative (red) and a positive (blue) triangularity discharge with neutral beam injection.During the fourth and fifth beam pulses (1.0 MW and 1.25 MW, respectively), the CXRS signal of the δ > 0 discharge was strongly perturbed as the plasma briefly entered an ELMy H-mode phase, explaining why a few data points are missing.

Figure 20 .
Figure 20.D discharge #69284, negative triangularity, I P = 330kA, B T = 1.4T.(a) Energy confinement time as a function of density; (b) Toroidal velocity as a function of density.The colourbar represents the logarithmic density gradient.Despite a clear LOC/SOC transition, no rotation reversal is observed.

Figure 22 .
Figure 22.(a) Toroidal velocity at ρ ∼ 0.4 as a function of increasing density; (b) toroidal velocity (blue) and energy confinement time (red) plotted as a function of density.The LOC/SOC transition occurs, again, at a higher density compared to plasma discharges operated with positive triangularity.This, however, is not accompanied by a rotation reversal.

Figure 23 .
Figure 23.(a) β N as a function of δ different sets of discharges: as in figure8, blue dots represent separate discharges performed at different δ and maintaining other plasma parameters constant.beta N from plasma discharge #67156 (δ = −0.6) is plotted in green to distinguish it from the discharge at δ = −0.5.Red dots correspond to a continuous δ scan from −0.5 to +0.5.(b) Toroidal velocity in the edge region (ρ ∼ 0.9), here plotted for plasma discharge #67817 to ease visualisation.

Table 1 .
Time constant of the exponential decay function y = ae