Experimental study of the core instability before and after internal transport barrier formation in EAST

In a reversed shear discharge in the Experimental Advanced Superconducting Tokamak (EAST), an internal transport barrier (ITB) was formed. For the first time, the turbulence in the plasma core before and after the formation of the ITB in EAST was investigated by microwave reflectometry. It was found that during the formation of the ITB, the turbulence inside the barrier was not completely suppressed. The density fluctuation level decreased in the early phase of ITB and significantly increased later. It was found that the density fluctuation level increased with the density gradient after the appearance of reversed shear Alfvén eigenmodes (RSAEs). The change in turbulence, measurable by the reflectometer, did not affect the rate of increase in core density. Through the measurement of RSAEs, it was found that the formation of this ITB may be related to the minimum q (q min). q min was close to 2.

Extensive experiments show the importance of the positions of rational surfaces [4,17] and the position of the minimum q (q min ) [5,7,20] in the formation of the ITB. Currently, it is generally accepted that E × B shear is a possible mechanism triggering the formation of the ITB [30][31][32][33][34]. The E × B shear can affect anomalous transport through a reduction in (and even a suppression of ) the amplitude of the turbulent fluctuations [19,[35][36][37] or the radial correlation lengths by breaking up the turbulent eddies [38,39]. In addition, in the early days of the ITB era in magnetic fusion research, Terry et al proposed a theory that most transport reduction due to E × B shear flow comes from the change in the phase relation between the fluctuating radial velocity (transporter) and the quantity that is transported (transportee) [40,41]. This allows significant transport reduction even if the fluctuations increase or decrease only slightly. Significant theoretical disagreements have emerged concerning this claim [42][43][44][45]. At present, amplitude reduction is favored as the primary mechanism for transport reduction. E × B shear can reduce plasma transport by reducing turbulence. The increase in the pressure gradient due to the reduction in transport subsequently contributes to the increase in E × B. This creates a positive feedback process in the formation and development of the ITB. Therefore, the turbulent behavior plays an important role in the formation of the ITB.
To date, there have been many reports on experimental studies of turbulent behavior during ITB formation. Suppression of the fluctuation level has been observed in most ITB experiments at the transition to enhanced core confinement [6,16,21,22]. However, a fluctuation level that remains unchanged [9,23] or increases [10] after transition has also been observed. Therefore, the relationship between fluctuation suppression and barrier formation is not fully understood. For example, in JET, Conway et al observed that the transport reduction within the internal transport barrier is associated with the suppression of density turbulence [6]. The suppression of long wavelength turbulence and short wavelength turbulence is related to the toroidal velocity and pressure gradient, respectively. This observation is consistent with the E × B shear positive feedback loop. In ASDEX Upgrade, Conway et al observed that the turbulence was only reduced but never completely suppressed during the ITB phase [16]. The turbulence reduction is localized spatially around the ITB gradient and the ITB-foot-point region. The radial extent and extent of the turbulence reduction are related to the strength of the ITB. In addition, the turbulence reduction seems to be related only to the formation of thermal barriers rather than a particle barrier. In JT-60U, Nazikian et al observed that the size of the turbulent structures decreases continuously with decreasing density scale length during the evolution of the ITB, while the fluctuation level is similar to the level before the formation of the ITB [9]. In DIII-D, Shafer et al found that long wavelength density turbulence was significantly reduced at q min = 2, while an enhanced shear flow was observed that transiently exceeded the turbulent decorrelation rate [21]. These effects are strongest near the q min = 2 surface and are found to track behind the q = 2 surface as it propagates radially outward. Since the mechanism of the formation of an ITB cannot be accurately explained thus far, more related research is needed.
Recently, ITB discharges have been achieved in EAST [24][25][26][27]. In this paper, the turbulence in the plasma core before and after ITB formation is investigated for the first time using multichannel poloidal correlation reflectometry (PCR) [46] and density profile reflectometry (DPR) [47][48][49][50] in EAST. The remaining sections in this paper are as follows. The EAST experimental setup and related diagnostics are introduced in section 2. Section 3 presents the experimental results. A discussion and summary are included in section 4.

Experimental setup
The experiment was carried out in the EAST tokamak (R = 1.85 m and a = 0.45 m). The plasma facing components are a molybdenum wall in the main chamber, a graphitic bottom divertor, and an ITER-like W/Cu top divertor. The experiment was performed with the upper single null (USN) divertor configuration. The auxiliary heating scheme was a lower hybrid wave (LHW) at 2.4 GHz, LHW at 4.6 GHz, and neutral-beam injection (NBI) (co-and counter-current directions) system was used. The NBI system had two beam injectors, and each injector was composed of two ion sources. Through the adjustment of the injection times of the four ion sources, a stepwise increase in the beam power could be achieved. The injected deuterium beam energies are 54 keV, 55 keV, 51 keV and 54 keV for the four ion sources, respectively.
Eleven-channel polarimeter-interferometer (POINT) diagnostics were used to measure the line-averaged densities. Charge exchange recombination spectroscopy diagnostics were used to measure the T i profiles and V t profiles. Due to the use of LHW, the true local temperature could not be obtained from electron cyclotron emission (ECE) data under the influence of superheated particles. Therefore, ECE diagnosis was used only in conjunction with magnetic probes to identify magnetohydrodynamic (MHD) instabilities.
Turbulence measurements were obtained using two PCR instruments. One of the PCR instruments had four probing frequencies (i.e. 42.4 GHz, 48 GHz, 52.6 GHz, and 57.2 GHz) in the U-band with O-mode launch from the low-field side (LFS) of the tokamak, while the other PCR had four probing frequencies (i.e. 79.2 GHz, 85.2 GHz, 91.8 GHz, and 96 GHz) in the W-band, with X-mode also launching from the LFS. The density profile was measured by a fast frequency-sweeping DPR, which was also used to locate the turbulence measured by PCR. The DPR had a horizontal view approximately 3 cm above the midplane. The two PCR instruments were located approximately 16 cm below the midplane with the line-of-sight perpendicular to the magnetic field. The sampling frequency of the PCR was 2 MHz [51]. I/Q detection technology was used, and in-phase (I) and quadrature (Q) signals could be measured. A complex signal (S) could be constructed from the I/Q signals; S = I + iQ. Some characteristics of turbulence could be acquired by carrying out an analysis of S. The fluctuation amplitude at a specific frequency range, such as 100 kHz-800 kHz, could be extracted as follows. A bandpass filter with a frequency range (100-800 kHz) is first applied to the I and Q signals, and two new signals, I [100−800] kHz and Q [100−800] kHz , can be obtained. Then, the fluctuation amplitude can be calculated by

Experimental results
An ITB was formed in a discharge during the EAST 2019 campaign, as shown in figure 1. The main plasma parameters are a plasma current (I p ) of 500 kA and a toroidal field (B t ) of 1.75 T. In the flattop phase (t = 5.5-6.5 s) with maximum heating power, the auxiliary heating power values are P LHW,2.4 GHz = 0.5 MW, P LHW,4.6 GHz = 1.5 MW, P co−NBI = 3.1 MW, and P counter−NBI = 2.8 MW. After 6.14 s, the core line-averaged density shows a continuous increase, while the edge line-averaged density hardly changes. Similar phenomena can be observed in the ion temperature (T i ) and toroidal rotational velocity (V t ). Simultaneously, the normalized beta (β N ) and the plasma diamagnetic energy (W dia ) increase. This result indicates that the increase in stored energy during this phase comes mainly from the core confinement improvement. Figures 2(a)-(c) shows the evolution of the normalized gradient lengths of the electron density (R/L ne , R/L ne = R·|∇n e /n e |), ion temperature (R/L Ti , R/L Ti = R·|∇T i /T i |) and toroidal rotational velocity (R·∇V t /V thi , where V thi is the ion thermal velocity) at different radial positions in the plasma core (ρ = 0.15, 0.2, 0.25, 0.3, and 0.4). As shown in figures 2(a)-( f ), after 6.14 s, the core n e continues to rise and expands to ρ = 0.3, and T i and V t for ρ < 0.4 also continue to rise. In addition, the n e profile at t = 6.39 s clearly shows that there is an n e barrier at the core, and R/L ne = 20 at ρ = 0.3. This suggests that the subsequent further improvement in core confinement is due to the formation of the ITB. There is a strong correlation between R/L Ti and R·∇V t /V thi at different positions in the period from t = 6.14-6.5 s, as shown in figure 2(g). The relationship between T i and V t during the formation of ITB in this discharge is similar to that in the normal H mode [52]. The start time of ITB formation is identified as t = 6.148 s (see below) and is indicated with a vertical dashed line in figure 1.
In the spectrograms of the PCR, the appearance of reversed shear Alfvén eigenmodes (RSAEs) indicates that this is a discharge with reversed shear configuration, and q min is near the corresponding cutoff layer. Figures 3(e) and ( f ) show the spectrograms of the fluctuation amplitudes for the 91.8 GHz and 96 GHz PCR channels, respectively. To show the RSAEs in each signal as clearly as possible, the 50-800 kHz amplitude signal is used for the 91.8 GHz channel, and the 100-800 kHz amplitude signal is used for the 96 GHz channel. The toroidal Alfvén eigenmodes (TAEs) at approximately 90 kHz and the RSAEs with upward sweeping frequency in the 50-80 kHz range are clearly seen, where the RSAEs are identified using the method described in [53]. The detailed determination process of the RSAEs is described later. The time evolution of each RSAE band in figures 3(b)-( f ) is selected and combined, as shown in figure 3(a). The figure shows that the identical bands measured by different diagnostics overlap very well. A detailed theoretical interpretation demonstrates that RSAEs can occur only when the condition m − n · q min (t) = 0 is satisfied as q min passes a rational magnetic surface [54]. RSAEs are localized near q min [55]. Therefore, the cutoff points of 91.8 GHz and 96 GHz are located near q min . Since the RSAE first appears in the 91.8 GHz channel (at t = 6.206 s) and then in the 96 GHz channel, the cutoff point of 91.8 GHz is closer to q min than that of 96 GHz.
The identification of RSAEs is achieved based on the measurement limits of the diagnostics. As shown in figure 4, for the band in the period from t = 6.32 s-6.36 s, the mode frequency increases from 53 kHz to 82 kHz. At this moment, the mode can be observed in the following signals: the ECE channel at ρ = 0.33, 91.8 GHz channel of PCR at ρ = 0.3, and 96 GHz channel of PCR at ρ = 0.22. For amplitude signals in the same frequency range of PCR, the mode is generally stronger and clearer in the 91.8 GHz channel than in the 96 GHz channel, so q min is always closer to the cutoff point of 91.8 GHz than that of 96 GHz. Therefore, it is estimated that q min is approximately ρ = 0.3 at t = 6.34 s. As shown in figures 4(a)-(d), in the period from t = 6.32-6.36 s, there is only a small change in plasma temperature, density, etc. Therefore, this excludes the possibility that the frequency sweeping is due to the change in the kinetic profile. Another well-known factor for the frequency sweeping of the core mode is toroidal rotation. This possibility can also be excluded, as explained below. Figure 4(c) shows that the change in the toroidal rotational velocity (ΔV t ) does not exceed 11 km s −1 , considering the and Dα signal, (c) edge line-averaged electron density ( n e1 ) and core line-averaged electron density ( n e5 ), (d) edge ion temperature (T i,edge ) and core ion temperature (T i,core ), (e) edge toroidal rotation velocity (V t,edge ) and core toroidal rotation velocity (V t,core ). change in rotation with time and the error bar. If the frequency change (Δ f ) of the mode is due to the toroidal rotation change, then Δ f = nΔV t /(2πR). For the present case, Δ f = 29 kHz, R = 1.85 m, ΔV t 11 km s −1 , and the toroidal mode number n should be larger than 30. Figure 4(e) shows the poloidal distribution of the magnetic field pitch angle at ρ = 0.3 (the position of q min ), which is calculated based on the EFIT reconstructed equilibrium. For a flute-like mode, k // ∼ 0, and for a mode with finite k // , e.g. TAEs, k // = n/2R [56], the poloidal distributions of k θ for the two kinds of modes with n = 30 are shown in figure 4( f ). As a result, the lowest k θ for the n = 30 mode for the present plasma is approximately 4.26 cm −1 , which much exceeds the upper limit of k θ resolution for POINT diagnostics (k θ 1.43 cm −1 ) and ECE diagnostics (k θ 0.5 cm −1 ) [53]. This clearly contradicts the observation that the mode can be observed in the ECE channel in the period from 6.32-6.36 s. Therefore, the mode frequency sweeping is not due to the rotation change. In summary, the mode frequency sweeping observed in this discharge cannot be explained either by a change in the dynamic profile or by a change in toroidal rotation. To our knowledge, only RSAEs could explain this observed frequency sweeping.
The value of q min is estimated by the varying TAE frequency in figure 3, and q min is close to 2. Considering the Doppler shift caused by the toroidal plasma rotation, the frequency measured in the laboratory frame for a TAE mode with toroidal mode number n is [54,57]: where f φ is the frequency of the plasma's toroidal rotation, . f T is the eigenfrequency of the TAE, which can be simply expressed as: where V A = B/ √ μ 0 n i M i is the Alfvén velocity, B is the modulus of the magnetic field, n i (≈n e ) is the ion density, M i is the major ion mass, q is the safety factor, and R is the tokamak major radius. As shown in figure 3, in the period from t = 6.122-6.22 s, there is a TAE visible only in the 91.8 GHz channel of the PCR but not in the 96 GHz channel. This In the above estimation, ΔV t may be overestimated due to the limited temporal resolution of V t , resulting in an underestimation of q and an overestimation of n for the TAE. However, for the TAE frequency equation used above, as mentioned in [57], the actual TAE frequency falls below this value as β increases. Therefore, the value of q may be overestimated from this point of view. Since q min q TAE , q min is close to 2 in the period from 6.22-6.4 s.
Changes in turbulence occur only within the ITB during the formation of the ITB. Figures 5(a)-(d) show the spectrograms of the reflected signal measured by PCR, three from the X-mode reflectometry channel (79.2 GHz, 91.8 GHz, 96 GHz) and one from the O-mode reflectometry channel (57.2 GHz). The signals from the other channels are not shown because their cutoff layers are located in the pedestal (42.4 GHz,48 GHz, 52.6 GHz, O-mode) or absorbed by the plasma (85.2 GHz, X-mode). Figure 5(e) shows the characteristic plasma frequencies calculated from the electron density profile measured by DPR at t = 6.12 s, 6.18 s and 6.39 s and the cutoff point positions for each reflectometry channel. Notably, in the period from 6.1-6.18 s, 91.8 GHz is absorbed by the plasma due to the low core density, as seen in figure 5(e). Therefore, there is no turbulence information in the 91.8 GHz spectrum in the period from 6.1-6.18 s. After the ITB is formed (t = 6.39 s), the 91.8 GHz and 96 GHz cutoff points are located inside the ITB, and the 57.2 GHz and 79.2 GHz cutoff points are located outside the ITB. It is obvious that during the formation of the ITB, only the turbulence inside the ITB changes significantly, while the turbulence outside the ITB changes little, as shown in figures 5(a)-(d). This localization of the turbulence changes during the transition to enhanced core confinement is similar to that in other devices [6,9,16,22].  During the formation of n e -ITB, the ITB foot and q min move outward, and the density fluctuation level within ITB increased after a brief decrease. Figures 6(a) and (b) show the time-space evolution of R/L ne and the fluctuation level (ñ e /n e ), respectively. The fluctuation levels are estimated by a one-dimensional model [58] using the signals from the PCR described above (figures 5(a)-(d)). As shown in figures 1 and 6(a), after t = 6.148 s, the core density gradient starts to increase, and the region of the steep density gradient expands radially outward. At the same time, the density gradient at ρ > 0.4 does not change, and the energy storage further increases. Therefore, t = 6.148 s is chosen as the ITB start time [24]. In the period from t = 6.148-6.5 s, the density profile changes due to the formation of ITB and the burst of an edgelocalized mode (ELM), which results in the movement of the probing wave cutoff points, as shown in figure 6(b). Nonetheless, during the formation of the ITB, both the 91.8 GHz and 96 GHz cutoff points are within the ITB, and the 91.8 GHz cutoff point is closer to the ITB foot than the 96 GHz cutoff point. In addition, as mentioned above, there is a similar relationship between the 91.8 GHz and 96 GHz cutoff points and q min , which suggests that q min is also near the ITB foot. As shown in figures 3(e) and ( f ), the RSAEs are consistently visible in the 91.6 GHz and 96 GHz channels as the 91.8 GHz and 96 GHz cutoff positions move outward with increasing core density. Furthermore, in ECE diagnosis, the RSAE is first observed at ρ = 0.28, and then the RSAE is observed at ρ = 0.32, as shown in figures 3(c) and (d). These results all suggest that as the core density increases, q min and the ITB foot move outward. As shown in figure 6(a), clearly, ITB formation is divided into two processes: the radial expansion of the barrier (t = 6.148-6.19 and t = 6.23-6.27 s) and the enhancement of the barrier gradient (t = 6.27-6.5 s). Finally, the ITB foot is located at approximately ρ = 0.4. During the formation of the ITB, the change in core turbulence can also be divided into two phases: a low fluctuation level phase (before RSAEs appear) and a high fluctuation level phase (after RSAEs appear). In the low fluctuation level phase, the core density perturbation decreases during the initial phase of ITB formation, as shown in figure 6(b). To demonstrate this process more clearly, figure 6(c) shows the profiles of the density fluctuation level at two moments before (t = 6.125 s) and after (t = 6.16 s) ITB formation. Note that the 91.8 GHz microwave was absorbed by the plasma before 6.18 s, so the density fluctuation level shown in figure 6(c) is only for three radial positions. The density fluctuation level within the ITB gradually increases after the decrease. After the appearance of RSAEs, according to the localization of RSAEs, the core fluctuations around q min are the strongest, which is similar to the results from the TFTR [10]. During the phase, the level of fluctuations within the ITB is enhanced as the density gradient increases. The relationship between q min and the ITB foot, as well as changes in turbulence near q min , seem to imply that q min may play a role in the formation of this ITB.

Discussion and summary
The turbulence changes within the ITB measured by PCR seem to not affect the increase in core density. The broadband turbulence within the ITB is variable during the formation of the ITB, as shown in figures 4(c) and (d). Figures 7(b) and (c) show the time window from 6.24 s to 6.32 s in more detail. As an example, figures 7(d) and (e) displays the spectra of the signals measured from the 91.8 GHz and 96 GHz channels of the PCR during 1 and 2 , respectively. Figure 7( f ) shows the density profiles at these two moments and the corresponding cutoff points for the two probing waves. Significantly, although the suppression of low-frequency turbulence and the burst of high-frequency turbulence occur intermittently within the ITB, these changes do not affect the rate of increase in the core density. That is, the main driving force for the formation of ITB in this discharge is not from the change in turbulence measured by PCR.
The characteristics of the turbulence within ITB cannot be obtained from the experiment. Attempts to measure the radial and poloidal correlation lengths of the turbulence around the ITB in this discharge were precluded by technical problems with the reflectometer. Therefore, turbulence cannot be specifically classified as a certain type of instability. Since both density gradients and ion temperature gradients in the plasma core are enhanced during ITB formation, ion temperature gradient (ITG)-type turbulence and trapped electron mode (TEM)-type turbulence may exist. Electron temperature gradient (ETG)-type turbulence is beyond the measurement capabilities of PCR. These changes in turbulence may be due to the transition between ITG and TEM.
The formation of ITB is accompanied by the disappearance of a 2/1 tearing mode (TM). As shown in figure 1(c), there is an oscillation can be seen in the core channels of the POINT. According to analysis, this oscillation is induced by a 2/1 TM at ρ = 0.1-0.2. The TM disappears at t = 6.165 s. It is well known that the presence of the TM can limit plasma confinement [59]. As shown in figures 1(b) and (c), the energy storage increased slightly between 6.13-6.148 s, which may be related to the weakening of the TM. A comparison of R/L Ti and R·∇V t /V thi at t = 6.14 s (during the TM phase) and t = 6.19 s (after the TM disappears) shows that R/L Ti and R·∇V t /V thi are synchronously enhanced at different positions within ρ < 0.4. Figures 2(e) and ( f ) show the T i profile and V t profile at these two moments, respectively. Considering the position of the TM and the radial variation range of V t , it is likely that the enhancement of V t and ∇V t within ρ < 0.4 stabilizes the TM at ρ = 0.1-0.2. However, other factors that may stabilize the TM are not excluded due to the complexity of the plasma. The stabilizing effects of V t and ∇V t on TM have been studied in references [60][61][62].
In summary, a discharge with the ITB operating in a reversed shear configuration was analyzed. For the first time, we observe the changes in the core turbulence during the formation of ITB through the microwave reflectometry on EAST. The locality of turbulence changes during the formation of ITB is consistent with the experimental results on other devices. Generally, it is believed that the formation of ITB is associated with the suppression of turbulence. However, it is observed in the experiment that the density fluctuation level within ITB decreases in the early phase of ITB and significantly increases later. This phenomenon implies that during the formation of the turbulence, there is a competition between the turbulence suppression caused by E × B and the turbulence enhancement caused by the temperature gradient. Analysis of this density fluctuation, it is found that the density fluctuation increases with the density gradient after the appearance of RSAEs. The core density fluctuation around q min is the strongest. Although the suppression of low-frequency turbulence and the burst of high-frequency turbulence occurred intermittently within the ITB, this change did not affect the rate of increase in the core density. Through the localization of RSAEs, it was found that q min may have played a role in the formation of the ITB, where q min was close to 2. During the formation of the ITB, there may have been a feedback process among the pressure gradient, bootstrap current and q min inside the ITB. Ultimately, the ITB was radially expanded to ρ = 0.4. We believe that the present results will be beneficial to understanding the formation of ITB.
In view of the lack of diagnostic capabilities, the PCR system will be upgraded in the future to improve its radial and poloidal spatial resolution in order to analyze the characteristics and propagation directions of each turbulent flow during the formation of the ITB and their specific impacts on particle transport and energy transport.