Ti/Te effects on transport in EAST low q95 plasmas

Enhanced confinement is observed in EAST low q95 ( q95<3.5 ) plasmas with the temperature ratio ( Ti/Te ) increasing. A statistically significant positive correlation between H98y2 and Ti/Te has been established. Increased Ti triggerd by Neutral Beam Injection in experiments maintaining constant Te leads initially to an improved Ti/Te ratio, which subsequently mitigates heat transport in the ion channel. The Trapped Gyro–Landau Fluid transport model was applied to analyse the dependence of the turbulent transport on Ti/Te . Simulation results demonstrate that the Ion Temperature Gradient mode is stabilized in high Ti/Te plasma, with ion flux results from predictive modelling further validating this effect. These findings corroborate the Weiland model and complement one another. This study contributes to a deeper understanding of how the dimensionless parameter Ti/Te influences plasma transport, and helps demonstrate the feasibility of operations under the low q95 condition required for the ITER-inductive scenario in the new Ti/Te regime.


Introduction
It is universally acknowledged that understanding plasma transport, which directly determines plasma performance and confinement, is crucial for the success of magnetic confinement fusion.Previous experiments have indicated that plasma confinement is impacted by the ion to electron temperature ratio (T i /T e ) through anomalous transport [1].In reactor-like tokamaks, the ion temperature is expected to approach the electron temperature as the energy confinement time will be Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.long enough to achieve thermal equilibration.For the future fusion machine ITER, the condition on q 95 (q 95 ∼ 3) is the basis of its scientific goal (Q = 10).Therefore, the impact of the dimensionless temperature ratio on plasma confinement and transport in the q 95 ∼ 3 condition requires thorough investigation.
Previous theoretical investigations have established foundational understanding of the effects of T i /T e ratios.Guo et al analytically derives the threshold ofη i (η i ≡ dlnT i /dlnN i ) mode as a function of T i /T e ratio.They also noted that the stability properties of the η i mode vary across different ranges of T i /T e [2].Additionally, the T i /T e impact on η ic exhibits different characteristic when density profile changes [3].Moreover, T i /T e effects can interact with plasma beta to influence ITG instability [4].These theoretical studies provide qualitative predictions that increasing T i /T e ratio can stabilize the ITG mode, which motivates our work to validate the theories against experiments, especially under conditions of low q 95 discharge, which are scant in previous publications.To date, explorations on the temperature ratio effects have been conducted in several tokamaks (e.g.JT-60U, Alcator C-Mod, DIII-D, JET, AUG, KSTAR [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].Experimental evidences have shown improved plasma performances when T i /T e increased [5,10].Negative central shear (NCS) and weak shear (WS) have been found to mitigate the confinement degradation typically observed with a decrease in T i /T e through electron cyclotron resonance heating (ECRH) application [22,23].The heat transport in the ion channel will be enhanced if T i /T e approaches unity with the application of electron cyclotron heating [11,13,16,17].However, these results are usually in relatively high q 95 condition.There are still no comprehensive and thorough understanding of the temperature ratio effects on plasma transport due to the incompleteness of the q 95 range.In low q 95 plasmas (q 95 ∼ 3), the safety factor profile is usually monotonic so that the magnetic shear is positive.The suppression of turbulence may be more difficult for lack of the effects of NCS or WS, due to the limited modulation of magnetic shear in absence of ECRH [23] in low magnetic field.The limitations of turbulence control (e.g.magnetic shear effect) in low q 95 regime also motivate us to research the further confinement improvement with the temperature ratio effect.
Besides, as we know, an important practical objective for future tokamaks is to enhance the production of thermonuclear power beyond the input heating power, thereby achieving a higher Q factor, as described by the following equations [24]: (n = plasma density, ⟨σv⟩ = reaction rate, E = energy released per reaction, V = volume, P H = heating power, T = temperature, τ E = energy confinement time, E α = reaction energy carried by the α particles).To augment the Q factor, it is essential to extend the energy confinement time τ E .According to the scaling laws [25], τ ELMy E,th = 0.0562I 0.93 B 0.15 P −0.69 n 0.41 ×M 0.19 R 1.97 ε 0.58 κ 0.78 (I = plasma current in MA, B = toroidal magnetic field in T, P = loss power in MW, n = density in 10 19 m −3 , M = average ion mass in AMU, R = major radius in m, ε = inverse aspect ratio, κ = plasma elongation), τ E is in proportion to I, implying that a longer τ E require a higher I, which corresponds to a lower q 95 , the safety factor at the 95% flux surface [26]: Combined with the limitations of the magnetic field coil capacity, to achieve Q ∼ 10, ITER inductive scenario designs q 95 to be ∼3 as fundamental to its scientific objectives.
Consequently, the T i /T e effects on transport in this condition are pivotal, and addressing the existing gaps in understanding these effects is crucial for advancing tokamak performance.
In this paper, we will assess the impact of the temperature ratio on confinement scaling in EAST low q 95 discharges, which is the first fully-superconducting device with metal walls and a tungsten diverter.In section 2 we introduce a database of low q 95 plasmas and describe the main experimental observations; in section 3, simulation tools are introduced and T i /T e effects are analysed and validated further through modelling; in section 4, other equilibrium factors are discussed.Finally, the conclusion and discussion are presented in section 5.

Experimental observations
In this section, a database built to explore the feature of the low q 95 range is presented.All the plasmas in the database meet the criteria of q 95 < 3.5.These plasmas were chosen with parameters at the current flat top.18 shots (1-5 time slices per discharges) with a total number of 40 cases are used to construct the database.The main parameters of these plasmas are reported in table 1.Here, R represents the major radius from current centroid core, a is the minor radius, κ is the elongation at plasma boundary, B is the toroidal magnetic field at magnetic axis, I is the plasma current, n is the line-averaged electron density and P is the total heating power.These cases are all H-modes, primarily heated by NBI, with Lower Hybrid (LH) waves utilized solely for maintaining plasma current.
Figure 1 illustrates variation of the normalized confinement factor (H 98y2 ) with respect to the temperature ratio T i /T e for the stationary discharges in the database.Here, H 98y2 is defined as the energy confinement time normalized by the IPB98(y,2) scaling ∝ P −0.69 [27].The temperature ratio is a volume-averaged value in the range of normalized radius from 0 to 0.55 due to the measurement limitation of Tangential xray Crystal Spectrometer (TXCS).The uncertainties of H 98y2 mainly come from the calculation of power absorption of NBI and LHW, which had been evaluted in EAST, and the error ultimately transmitted by P abs and W th is about 13.6% [28,29].And the evaluation of T e and T i in EAST can be referred in [30,31].As shown in the figure 1(a), H 98y2 shows an evident increase from 0.65 to 1.03 with the increase of T i /T e .Linear regression analysis indicates that 60% of the variation in H 98y2 can be attributed to the temperature ratio T i /T e (R 2 = 0.60).It appears that T i /T e does play an important role in the variation of H 98y2 .It should be noted that all plasmas in this database are heated by three or four neutral beams, which introduce torques.As elaborated in [32], the rotation induced by torque injection from NBI is considered one of the most important sources of the change in plasma confinement.However, data from Charge eXchange Recombination Spectroscopy (CXRS), covering the same radial range (ρ ∈ [0, 0.4]), reveal no remarkable correlation of H 98y2 with Mach number (R 2 = 0.09) as shown in figure 1(b), This finding is consistent with observations from other tokamaks such as AUG, JET and JT-60U [32].
In other words, T i /T e appears to significantly impact plasma confinement and the key feature of positive correlation between H 98y2 and T i /T e is shown.Experimentally, the typical turbulence data in EAST T i /T e campaign of shots 123239 and shot 123246 have shown lower intensity of ion scale turbulence in shot with higher T i /T e .We will try to determine the mechanism on how T i /T e influences plasma confinement and transport in the following content.Most importantly, those results will help to form the physical basis for model validation in low q 95 plasmas.
For detailed investigation, three time slices from discharge #115 584 in the database were selected.Figure 2 shows the three time slices at 3.7, 3.91, and 4.31 s in #115584, indicated by red, blue, and black dashed lines, respectively.The confinement factors of #115584 @3.70 s, @3.91 s and @4.31 s are 1.02, 0.98 and 0.71 respectively.LH are used solely for driving the plasma current during the ramp-up phase.In these three cases, there is no LH heating, and only NBI is used for ion heating.The electron density at 3.7 and 3.91 s is similar, while it is slightly lower at 4.31 s.The profiles of n e , T e and T i are shown in figure 3. The electron density is measured using 11-channel POlarimeter-INTferometer and density profile reflectometer.The electron temperature is determined from Thomson Scattering.The ion temperature is determined

Modeling tools and workflow
As we all know, the experimental cross-field transport generally exceeds the predicted neoclassical levels.Turbulence transport has been widely accepted as the main contributor.The fundamental gyrokinetic equation for the turbulence transport induced by drift-wave instabilites such as ITG modes, trapped electron modes (TEMs) and electron temperature gradient (ETG), is so complex that it requires too much computational resources even on modern computers for a full-radius tokamak plasma.Thus, reduced models for turbulent transport are necessary.The Trapped-Gyro-Landau-Fluid (TGLF) model represents a significant advancement in this area.Developed to offer a fast and accurate approximation to the linearly unstable eigenmodes for drift-wave instabilities (ITG, TEMs and ETG) [33], TGLF has refined the capabilities initially established by its predecessor, the GLF23 model.Compared to its predecessor GLF23, the enhanced TGLF model is more accurate and extended with comprehensive physics (dynamic electrons, deuterium and carbon ions, electron-ion collisions, shaped Miller geometry, and electromagnetic finite beta physics) and has been used to perform linear stability analysis of DIII-D discharges successfully [34].
The entire workflow is shown below: (1) experimental data including electron temperature profile, ion temperature profile, rotation profile and reconstructed equilibrium at t 0 , e.g.t 0 = 3.7s, are inputted.(2) Keeping the kinetic profiles and the plasma current Ip fixed, ONETWO [35] calculates the energy sources and sinks and evolves the plasma current density with the external current drive calculation by the RF codes if there is RF for time step τ from t 0 to t 0 + τ .Here τ is set to 20 ms that the temperature profiles will not change much within 20 ms in the integrated modeling.(3) Employ EFIT [36][37][38] to update the equilibrium with P ′ (pressure gradient) and FF (poloidal current gradient) from ONETWO output at the end of step (2).( 4) profiles_gens preprocess the data from ONETWO to standardize and improve geometry input e.g.increasing the density of the data grid [39,40].The SAT1 model of TGLF, which can be referred to [41], forms the saturation rule.There are three rates competing the saturation mechanism.The linear growth rate, zonal flow k xmixing rate and drift-wave mixing rate are comparable for low-k y .There is a clear separation for high-k y and only zonal flow mixing rate competes with the linear growth rate for high-k y .

Ion heat transport
For the three selected cases introduced in the previous section, we employed ONETWO code [35] coupled with NUBEAM for neutral beam calculation to analyse ion heat transport.In the simulations, the effective charge Z eff is fixed at 1.75 across the radial profiles for all three cases [42,43].There is no difference in the toroidal rotation profiles for all three cases.As presented in figure 4(a), except near the magnetic axis where results are considered unreliable due to mathematical treatment limitations, ion thermal diffusivity exhibits a regular distribution in the entire region of ρ ∈ (0, 0.4), indicating ion heat transport increases with time.Concurrently, figure 4. (b) provides the T i /T e radial profiles in this region.A converse relationship is observed: the T i /T e value at 3.70 s is greater than that at 3.91 s which in turn is greater than the value at 4.31 s.This implies a dependence of the ion thermal diffusivity on the temperature ratio, indicating the ion heat transport diminishes with T i /T e increasing.This observation aligns with findings reported in [10].Linear transport analysis of #115584@3.7 s, @3.91 s and @4.31 s by TGLF.ky ρs spans from 0.1 to 1.The real frequency ω < 0 (blue area), represents the drift waves propagating along the ion diamagnetic drift direction.γ is the growth rate, which is always positive.According to the space scale of different drift wave modes, there are two turbulence modes in the central region: TEM (red area) and ITG modes (blue area).

Micro-instabilities simulations
Further exploration into the evolution of micro-instabilities was conducted using the TGLF model that addresses the linear eigenmodes of turbulence.As shown in figure 5, k y ρ s (ρ s = c s /Ω s , k y = ρ s k θ , c s is ion sound speed, Ω s is ion gyrofrequency, ρ s is ion sound Larmor radius, k θ is poloidal wave number) spans from 0.1 to 1. γ is the growth rate, which is always positive.The red area corresponding to the real frequency ω > 0 represents the drift waves propagating in the electron diamagnetic drift direction, and the blue area corresponding to the real frequency ω < 0 represents the drift waves propagating in the ion diamagnetic drift direction.According to the space scale of different drift wave modes, there are mainly two drift-wave instabilities modes contributing to ion heat flux in the central region: TEM and ITG modes.The ITGdominated area expands towards the core from 3.7 to 4.31 s.This implies that the enhanced ion heat transport should stem from the destabilization of the ITG mode.
According to the reactive two-fluid Weiland drift wave model [44], the complete expression for the ITG threshold is as follows.
When the gradients of normalized density meet the criteria ( R Ln < 5), the gradually decreasing T i /T e should lower the gradient threshold for the onset of ITG mode.The calculation from the three cases, as shown in figure 6, demonstrate the validity of the Weiland drift wave model.In other words, the mechanism implied by the model accounts for the experimental and simulative consequence stated previously.
In order to validate the mechanism further, a predictive simulation has been conducted using TGLF-SCAN by scanning values of T i /T e .TGLF-SCAN is a module of TGLF used to scan a given quantity and detailed description can be referred to [39].We choose the case of #115584@4.31s and scan T i /T e from the experimental value 0.95-1.20 at ρ = 0.3.The relevant Physics controls involves: 1. Include transverse magnetic fluctuations [45][46][47] 2. Ignore pressure gradient contribution to curvature drift [48,49] As depicted in figure 7, the particle flux, heat flux, and momentum flux all decrease with increasing T i /T e .It is more clearly shown in the growth rate and frequency spectrum as presented in figure 8 that the results are due to the decrease in   the ITG growth rate with increasing T i /T e .However, the turbulence suppression effect of high T i /T e appears to wane with further increases in T i /T e .This observation calls for additional research to understand the mechanisms behind the decay in turbulence suppression effectiveness.
In a word, both experimental and simulation results presented in this study corroborate the influence of T i /T e on plasma confinement and transport, aligning with predictions from the Weiland drift wave model.This consistency underscores the model's relevance and utility in explaining key aspects of plasma behaviour in tokamak environments.

Discussion about other equilibrium quantities
In EAST low q 95 discharges with only NBI heating, the safety factor profile is usually monotonical so that the magnetic shear is positive.
Owing to high-power NBI, it is necessary to pay attention to the effects of fast ions on turbulence and confinement, e.g. the electromagnetic stabilization [50,51], wave-particle resonant effect [52], and the impact of zonal flow generation [50,53].We obtain the fast ion density profiles using the TRANSP code.As shown in figure 9, the fast ions are highly concentrated in the core in all three cases.NBI modulates the T i initially and does not induce a significant change of the fast ion density.
Besides, there are some density gradient differences between the three cases, even though limited.We assessed the impact of density gradient by scanning electron density scale length with 34% variation.The value of 100% corresponds to case@4.31s experimental values.As shown in figure 10, no  evident impact of density gradients is observed.The growth rate and frequency spectrums remain mostly unchanged as presented in figure 11.
Thus, to summarize, the impact of the factors which are most likely to cause trouble is limited and negligible enough for us, and the role of T i /T e dominants on confinement and turbulence.

Conclusion
An important feature discovered in the database established from the EAST low q 95 experimental campaign is that increasing the T i /T e ratio is beneficial for enhancing plasma confinement.Specifically, the confinement factor H 98y2 demonstrates a notable increase from 0.65 to 1.03 as T i /T e rises from 0.89 to 1.71.This improvement in confinement is consistently reflected in experimental profiles, as illustrated in the accompanying figures.Utilizing the ONETWO code, we observed a clear enhancement in heat transport within the ion channel correlated with increasing T i /T e .Further investigation into micro-instabilities via the quasi-linear transport model (TGLF) indicates that higher T i /T e ratio at low density gradient (i.e.R Ln < 5) is desirable for suppressing turbulence in the ITG mode.Predictive simulations confirm that particle flux, heat flux, and momentum flux are all reduced as T i /T e increases.The impact of other factors that are most likely to make sense is discussed and the dominant role of T i /T e remains, these results are consistent with the Weiland drift wave model and substantiates earlier theoretical studies.Increased T i triggerd by NBI in T e constant experiments leads to an initial improve of T i /T e , the increased T i /T e provokes an increase in the ITG threshold and this leads to the weakened ion heat transport, which further promote the increase of T i and T i /T e .Ultimately, this cycle contributes to significant improvements in both confinement and overall fusion performance.
The result in this study implies that for future device ITER increasing T i /T e up to a certain range could be beneficial to improve confinement and fusion performance.The q 95 of the plasmas investigated in this study is lower (q 95 < 3.5) than those earlier works, which yields more confidence of operating in low q 95 condition for ITER inductive scenarios (Q = 10, q 95 ∼ 3).However, the analysis in this article is rather qualitative, further dedicated experiments with turbulence diagnostics are planned to explore the best temperature ratio range.Owing to the limitation of TGLF, the fast ion pressure impact cannot be well treated and nonlinear gyrokinetic simulation is needed.The work of temperature ratio effects on other scale turbulence is continuing.

Figure 2 .
Figure 2. Time trace of the main plasma parameters (a)-(e) plasma current Ip, line averaged electron density ne, confinement enhancement factor H 98y2 , auxiliary heating power of LHW, auxiliary heating power of NBI.The red, blue and black lines indicate time slices @3.70 s, @3.91 s and @4.31 s, respectively.

( 5 )
TGLF mode (i.e.Get growth rate spectra and fluxes) is used to set up TGLF inputs.The key settings of TGLF are as follows: -Physics Controls: Include transverse magnetic fluctuations.-Numerical Controls: Use bisection search method to find width that maximizes growth rate; Compute quasilinear weights and mode amplitudes.-k y Grid Model: Standard k y spectrum for transport model.-Number of poloidal modes in the high-k spectrum of TGLF_TM: 12. -Physics Switches: Include parallel velocity shear for all species; Include ExB velocity shear for spectral shift model; Include the trapped/passing boundary electron-ion collision terms.Include the Debye length term.

Figure 4 .
Figure 4. (a) Radial profiles of the ion heat conductivity in#115584 in the range of normalized radius from 0 to 0.4.(b).Radial profiles of temperature ratio in#115584@3.70s, @3.91 s and @4.31 s in the range of normalized radius from 0 to 0.4.

Figure 5 .
Figure5.Linear transport analysis of #115584@3.7 s, @3.91 s and @4.31 s by TGLF.ky ρs spans from 0.1 to 1.The real frequency ω < 0 (blue area), represents the drift waves propagating along the ion diamagnetic drift direction.γ is the growth rate, which is always positive.According to the space scale of different drift wave modes, there are two turbulence modes in the central region: TEM (red area) and ITG modes (blue area).

Figure 11 .
Figure 11.Growth rate and frequency spectrum with electron density scale length scan at ρ = 0.3.

Table 1 .
The value range for plasma parameters in the database.
Contract Nos.12005262 and 11975274, the Users with Excellence Program of Hefei Science Center CAS under Grant No. 2021HSCUE018, and Science Foundation of Institute of Plasma Physics, Chinese Academy of Sciences, No. DSJJ-2021-04.