Electron ITB formation in EAST high poloidal beta plasmas under dominant electron heating

Plasma confinement and transport in tokamaks play a crucial role in the development of high poloidal beta steady-state operation scenarios. Therefore, it is very important to study the relevant mechanism of internal transport barriers (ITBs), which can help plasmas to obtain better confinement in order to achieve higher fusion gain. This paper mainly introduces the analysis of the characteristics of electron heat transport of discharges with ITB in high βP operation regime in Experimental Advanced Superconducting Tokamak (EAST). Based on the statistical analysis of stable discharges with βP > 1.5, it is found that there is an obvious bifurcation of the normalised electron temperature gradient (ETG) ( R/LTe ) in the range of βP = 2–2.2. Then the discharges of lower βP ( βP < 2, where the value of βP is below the bifurcation threshold) and of higher βP ( βP > 2.2, where the value of βP is above the threshold) were selected for analysis. The diagnostic data provided by Thomson scattering, x-ray crystal spectrometry and charge exchange recombination spectroscopy are used to provide reliable parameter profiles and then combined with the data of external magnetic probe measurements and the polarisation interferometer diagnosis system to fully reconstruct the balance. A relevant plasma current calculation model is used to calculate and analyse the current density profiles and power deposition, and then the transport analysis is carried out. Interestingly, in the higher βP discharges, it is found that the turbulence intensity provided by the CO2 laser collective scattering system gradually decreases and the normalised ETG R/LTe gradually increases. It is also found that the electron heat transport coefficient decreases in the discharge with higher βP and the growth rate of the electron-scale turbulence calculated by transport gyro-Landau fluid (TGLF) is significantly reduced. Meanwhile, similar conclusions are also obtained in the discharges when the βP is further increased.


Introduction
The high poloidal beta (β P ) regime was first proposed as a high bootstrap (BS) current scenario for a steady-state fusion pilot plant in the 1990s [1].Since then, many research devices, such as Doublet III -Divertor (DIII-D) and EAST have carried out a series of studies on this topic and made advances in theories, models, and experiments [2][3][4][5].Both experimental evidence and modelling analysis show that the high β P regime has great advantages in tokamak advanced operating scenarios, such as high-energy confinement quality at low rotation, excellent core-edge integration, high line-averaged density above the Greenwald limit, low disruption risk, and high BS current fraction for steady-state operations [6].
In fusion plasmas, the α particles produced by fusion will preferentially heat electrons, and thermal electrons must efficiently transfer energy to ions to maintain the burning of the plasma.Therefore, understanding electron heat transport characteristics and suppressing abnormal energy loss in the electron channel is one of the biggest challenges in fusion research.Additionally, ion heat transport is relatively well understood and, near the internal transport barrier (ITB) of some large devices, the loss of ion channel has been reduced to the level of the neoclassical transport [7].In general, however, electron heat transport is still known to be much higher than the neoclassical transport level.Therefore, electron heat transport is related to the self-sustaining burning of plasma in fusion devices and its effective understanding is a key issue in plasma confinement research.Thus, studying the characteristics of electron heat transport in EAST poloidal beta plasmas is an essential step to understand transport and confinement and to provide a basis for the development of International Thermonuclear Experimental Reactor (ITER)'s steady-state operation scenario [8,9].
As the world's first fully superconducting tokamak device, similar to ITER, EAST is currently the only international experimental platform capable of carrying out long-pulse high-confinement fusion plasma physics research on a time scale of more than 100 s [10].Understanding electron heat transport is crucial for EAST high β P plasmas where the electronic channel ITB (e-ITB) improves the energy confinement.Here, β P = P/ ( B 2 P /2µ 0 where P is the plasma thermal pressure and B P is the poloidal magnetic field strength.In this scenario, plasmas could obtain better confinement and higher fusion gains with a higher rate of BS.The energy and particle transport of the thermal plasmas is a critical concern for high β P experiments since the BS current is proportional to the pressure gradient.It has long been recognised that a higher Shafranov shift, which is proportional to β P , plays a crucial role in the suppression of turbulence and related transport.The higher value of the Shafranov shift induces a high pressure gradient leading to high values of the magnetohydrodynamic α parameter (α = −q 2 βR∇P/P, where R is the major radius, q is the safety factor, P is the pressure, ∇ is the radial gradient, and β is the ratio between kinetic and magnetic pressure).Similarly, for low or negative magnetic shears, high α reduces the curvature and ∇B drifts driving curvature-type microinstabilities.Therefore, high values of α can stabilise part of the microturbulence, which leads to a higher pressure gradient and to even higher α [11].Most of the devices such as DIII-D and JT-60U had many experiments to achieve the discharges with ITBs [7,12] and reported a variety of good results and conclusions.Multiple factors have been found to affect ITB formation and maintenance in those devices, which includes E × B shear flow, zonal flow, rational surface, minimum q at the rational surface, magnetic island, BS plasma current, and so on.In addition, in the DIII-D high β P experiment, by adjusting β N to modify β P and adjusting the current to modulate β P , it was found that there was a β P threshold to trigger e-ITB in this type of discharge in DIII-D and whenever β P > 1.9, e-ITB began to form [13].The purpose of this paper is to explore whether there is a similar β P threshold that forms the electron thermal channel ITB in EAST and to discuss the characteristics of electron heat transport of e-ITB discharges under different β P conditions.This paper mainly introduces the analysis of some experimental phenomena about the characteristics of electron heat transport of discharges with e-ITB in high β P operations on EAST.Significant progress has been made towards realising the relationship between the β P and ITB by statistical analysis and experimental data calculation of the stable discharge with β P > 1.5, and statistical results are shown in figure 1.The locations of the maximum normalised electron temperature gradient (ETG) R/L Te of these statistical discharges are in the range ρ = 0.2-0.25, and the R of R/L Te is the large radius of the tokamak.The R/L Te (Y-axis) is an important parameter to characterise the strength of e-ITB (weak or strong) [14].Figure 1 shows that the correlation between ETG and β P has clearly different trends on both sides of the β P = 2-2.2range.When β P is less than this range, the correlation between β P and R/L Te is not clear and the change of β P does not cause notable changes in R/L Te .On the other hand, when β P > 2.2, β P and R/L Te show a certain positive correlation that R/L Te increases with the increasing β P .So, we call the β P = 2-2.2range a 'turning point' in this study, which may indicate that the plasma electron temperature stiffness is broken when β P exceeds 2.2.It also indicates the formation of e-ITB when β P is greater than the 'turning point'.In other words, this may be the β P threshold for e-ITB formation in EAST plasmas.

Experimental and simulation settings
Typical discharges outside the β P = 2-2.2range are selected for detailed analysis.From the 2021 EAST campaign, discharges #101379(β P = 1.8) and #101449(β P = 2.5) have been chosen because they are on opposite sides of the turning point, which might give a hint of the physical processes and mechanisms involved in plasma transport and confinement under different β P levels.
Shot #101379 is heated by 4.  2. The two discharges have similar densities and heating conditions and the loop voltage is well controlled to be zero during the plasma flattop, which indicates a fully non-inductive current drive condition.The power deposition profiles (PDPs) for all the components of the external heating are presented in figure 3. The PDPs are calculated with one-dimensional transport code for plasma in a toroidal magnetic field (ONETWO) and TRANsport Simulation and Modeling Program (TRANSP), where electron cyclotron resonance heating (ECRH) uses GENeral Ray-tracing (GENRAY) [15], lower hybrid (LH) uses curvilinear quadratic lagrangian version 3D (CQL3D) [16], and ion cyclotron resonance heating (ICRH) uses Tokamak ORBIT Code (TORIC) [17].
In this work, the time slices at t = 6.0 s for #101379 and at t = 6.75 s for #101449 are selected for further analysis.The experimental plasma profiles are obtained by the following diagnostics: The reconstructed equilibrium is obtained by equilibrium fitting code (EFIT) [18]; the electron temperature (T e ) is measured by Thomson scattering diagnostics; the ion temperature (T i ) is measured by charge exchange recombination spectroscopy and tangential x-ray crystal spectrometer; and the electron density (n e ) is reconstructed by polarisation interferometer (POINT) [19] and reflectometers.Note that the turbulence intensity is given by the CO 2 laser collective scattering system [20].The safety factor (q) profile of EAST is obtained by using the method developed in [18], which is constrained by POINT and magnetic diagnostics.All the profiles are plotted in figure 4.
It can be seen that the electron temperature profiles of the two discharges show a very large difference as presented in figure 4(c).However, other profiles such as n e, T i , and q have slight differences only.The profiles of #101379 remain unchanged from 2 to 8 s, the T e profile and the R/L Te of #101449 gradually increased from 3 to 8 s.The time slices were selected for analysis at when the core electron temperatures and R/L Te of these two discharges have the biggest difference.
Figure 4(c) shows that discharge #101449 has higher ETG and the calculated result of normalised ETG (R/L Te ) at ρ = 0.2 is approximately 23, which is much higher than at other radial locations.This means that the stiffness of the ETG is broken and indicates the formation of e-ITB in #101 449.As mentioned in the literature [21,22], the T e profiles should clearly exhibit an almost constant R/L Te value before the stiffness is broken in the confinement region.Combined with the PDP in figure 3, there are only slight differences of total Q e that could be found in the core region, indicating that the difference in T e (ρ) profiles should come from the result of the formation of e-ITB.
The POINT diagnosis system and the moving Stark effect diagnosis system provide the data on the internal magnetic field constraint required for plasma kinetic equilibrium fitting.The thermal diffusivities of electrons and ions are calculated from a power balance analysis for the energy transport.It is found that the electron heat transport coefficient decreases at ρ < ITB foot region in #101 449 with the higher β P , as shown in figure 5, and the electron thermal diffusivities in the core are lower than the neoclassical diffusivity for the ions.The thermal diffusivities also suggest the formation of ITB in the discharge with higher β P .This seems to support that the confinement is significantly improved when poloidal beta (β P ) exceeds the threshold and an internal transport barrier of electrons (e-ITB) appears.

Turbulence analysis
The turbulence intensity data provided by the CO 2 laser collective scattering system and the simulation calculations are used to further explore the physical processes of these two discharges with different β P values.The turbulence-induced density fluctuations were measured by the CO 2 diagnostic system in the ρ = 0-0.4region with k θ = 12 cm −1 .Since the corresponding k θ ρ s of #101379 is ∼2.28 and that of #101449 is ∼2.64, combining with the simulation results, the measured turbulence may contain information about the trapped electron mode (TEM) and ETG mode.As shown in figure 6, the solid line shows the normalised turbulence intensity evolution of the two shots.In the lower β p discharge (101379), the turbulence intensity remains constant at a high level.On the other hand, in the higher β P discharge (101449), after reaching the high-level by power injection, the turbulence intensity gradually decreases with the formation of ITB.
The dotted line in figure 6 shows the evolution of R/L Te of the two discharges after power injection.It is found that both the turbulence intensity and the normalised ETG are maintained at a certain level and there is almost no notable change in #101379.However, the normalised ETG of #101449 gradually increases with the decrease in turbulence intensity, which also    The E × B shear flow appears near the foot point of ITB and it causes a reduction in the level of fluctuation (ω E×B shearing effect).As a result, the pressure gradient increases in the region where the E × B shear flow is large enough to reduce turbulence transport.The increase in the pressure gradient contributes to the further increase in the E × B shear flow.Therefore, either a slight increase in the E × B shearing rates or a slight decrease in the linear growth rate for a given temperature gradient can trigger this feedback process.The authors consider that, in high β P plasma discharges (in this paper, the high β P value is devoted to the high Shafranov shift, which refers to high α effect), higher power injection and β P increase the pressure gradient so that the pressure gradient balance in the positive feedback process is broken, consequently triggering a positive feedback loop.This loop explains the continuous decline of turbulence intensity and the gradual rise of normalised ETG after ITB formation.
Based on our current understanding, electron anomalous heat transport is closely related to electron mode turbulence, generally including TEM turbulence and ETG mode turbulence [23][24][25].Although some studies have shown that ion mode turbulence-ion temperature gradient mode (ITG) turbulence and microtearing mode that dominate the ion transport channel-also have some effects on electron transport, but it is generally believed that electron mode turbulence dominates abnormal electron heat transport.
In addition to large-scale ITG, abnormal heat transport of electrons is mainly attributed to the electron mode turbulence, including TEM and ETG, with slightly larger TEM mostly dominating the heat transport of electrons.However, as the temperature gradient of the electrons increases, smaller-scale ETG is considered to be the main cause of abnormal electron heat conduction.
Therefore, the TGLF code [26] was used to study the turbulence characteristics of the selected two shots and presented in figure 8(a) in order to explore the differences in their TEM and ETG turbulence.It is found that in the discharge of higher β P , the electron mode turbulence growth rate, TEM, and ETG modes at ρ = 0.2 are significantly reduced.This  indicates that after the formation of e-ITB the growth rate of electron turbulence of higher β P become lower, the electron abnormal transport decreases, and the electron thermal transport coefficient decreases.Thus, the confinement in the ITB region is significantly improved.Similarly, when β P is much higher than the one in #101449, as shown in figure 8(b), this phenomenon still exists.The electron mode turbulent growth rate of TEM and ETG for higher β P discharges have a certain decrease compared to the lower β P discharges.It is also confirmed that the turbulence is stabilised to a certain extent after the formation of ITB in the aforementioned positive feedback process in figure 7.

Conclusion
After the β P threshold of e-ITB formation on DIII-D has been discovered, this paper aims to explore whether a similar threshold exists on EAST to trigger e-ITBs.To this end, the authors statistically analyse the experimental data of high β P discharges on EAST, examining the correlation between poloidal beta β P and normalised temperature gradient R/L Te .Notably, a clear bifurcation of R/L Te emerges as β P rises beyond 2-2.2 range.In the discharges with β P > 2.2, poloidal beta β P and normalised temperature gradient R/L Te show a relatively clear positive correlation but no such correlation in discharges with β P < 2. Additional evidence suggests that the stiffness of the electron temperature profile of the discharges with β P > 2.2 is broken but not for those with β P < 2. Therefore, the authors propose the value of β P corresponding to the bifurcation of R/L Te as the threshold of ITB formation in EAST plasmas.
Then, in order to better explain the characteristics of electron thermal transport, the discharges on both sides of the bifurcation are simulated and analysed.It is found that the electron thermal transport coefficient is significantly reduced in the discharge on the higher β P side of the bifurcation, which is also an important feature of the formation of e-ITB.This turning point is likely to be the β P threshold of e-ITB formation on EAST.As this paper is based on statistical analysis, the suggested threshold is a range of β P rather than a specific value.Thus, the β P threshold for e-ITB formation is not specifically given as done in DIII-D but it will be further investigated in future experiments.
Combining the turbulence data and the simulation results, it is found that after the formation of e-ITB, there may exist a positive feedback mechanism among the β P effect, E × B shear flow, turbulence, and pressure gradient.When the heating power becomes larger and causes changes in β P and the pressure gradient, the balance of the plasma has been modified so that this positive feedback process works to modulate the plasma equilibrium, which consequently reduces the turbulence intensity and strengthens the e-ITB structure.The simulation results from TGLF show that the electron mood turbulence, ETG, and TEM have a greater impact on the abnormal transport of electrons, especially in higher β P discharges.
There are many other factors in tokamak plasmas that will affect electron heat transport, but this paper only finds the correlation between poloidal beta β P and the normalised ETG R/L Te through statistical methods and presents the basic kinetic analysis of discharges under different correlations.However, a more detailed analysis of electron heat transport characteristics, particularly the physical mechanism of the positive feedback process, remains a focus for future research.

Figure 1 .
Figure 1.The results of experimental data statistical analysis about correlation between the β P and the normalised electron temperature gradient R/L Te .

Figure 2 .
Figure 2. Time evolution of basic plasma parameters.

Figure 3 .
Figure 3. Power deposition profiles (PDPs) for all the components of the external heating, (a) is for LH heating power in electron heating, (b) is for ECRH in electron heating, (c) is for ICRH in electron and ion heating, and (d) is for total power in electron and ion heating.

Figure 4 .
Figure 4.The plasma parameters profile of #101379 and #101449, (a), (b) are the ne, q, T i profiles of #101379 and #101449; (c) is the Te profile of #101379 and #101449.

Figure 6 .
Figure 6.Normalised turbulence intensity (solid line) and the normalised electron temperature gradient (filled triangle) of EAST discharge #101379 (blue) and #101449 (red).The dotted lines are used as guide lines to present the change trend.

Figure 7 .
Figure 7. Feedback process among the E × B shear flow, turbulence, and pressure gradient in the barrier formation.

Figure 8 .
Figure 8.The calculated results by TGLF of turbulence growth rate and frequency of different β P discharges.