Experimental and simulation analysis of Weakly Coherent Modes in I-mode discharges on EAST

This paper reports the recent observation of a weakly coherent mode (WCM) within a conventional reflectometer on EAST and successfully determines its poloidal wavenumber range. During the transition from the L-mode to I-mode, the line-averaged density remains nearly unchanged while a significant change is observed in the electron cyclotron emission (ECE) signals at the boundary. The difference between the signals for the two channels at the edge increased, coinciding with the appearance of the WCM and a simultaneous rise in the boundary electron temperature. Further investigation unveiled the modulating role of edge temperature ring oscillation (ETRO) (Liu et al 2020 Nucl. Fusion 60 126016) on high-frequency density fluctuations. Statistical results unveil an inverse relationship between the centeral frequency of the WCM and q 95. Simulation results provide additional insights, demonstrating that the simulated ‘WCM’ in the density fluctuations aligns with experimental data in terms of center frequency. Additionally, the radial distribution of the simulated ‘WCM’ closely corresponds to regions with the strongest electron temperature gradients. Finally, through a cross-correlation analysis of the simulated fluctuations, the following phase relationship for the wavenumber range of ‘WCM’ was observed: αT~e>αn~i∼αϕ~>αT~i .


Introduction
The I-mode is an enhanced confinement regime in the tokamak.It exhibits characteristics akin to both the H-mode 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.
with its temperature edge barrier and the L-mode featuring a low particle edge barrier [1].In the I-mode, the plasma achieves high energy confinement while maintaining low particle confinement, effectively preventing the accumulation of impurities.One notable advantage of the I-mode is its stability to edge-localized modes (ELMs) as its pressure gradient does not reach the unstable range of peeling-ballooning modes [2].The I-mode has been observed since the late 1990s [3,4] and has been studied across a wide range of parameters in various tokamaks, including ASDEX-Upgrade [5], Alcator C-Mod [6], DIII-D [7], EAST [8] and HL-2A [9].Typically, the I-mode phase is achieved with an ion B×∇B drifting away from the active X-point, which is the unfavorable direction.Additionally, a higher magnetic field is beneficial in expanding the operation space of the I-mode [10].In the I-mode statistics of EAST, the L-I threshold power is directly proportional to B 0.26 [11], and the power required for the I-mode transition to H-mode increases rapidly with the B T , thereby significantly broadening the power range of the I-mode as the magnetic field enhances.
In general, one characteristic associated with the I-mode phase is a broad-spectrum structure, with a frequency spectrum width typically reaching 50% of the center frequency.During the transition from the L-mode to the I-mode, the low-frequency fluctuations weaken while the high-frequency fluctuations strengthen, thus a broadband structure is formed, known as the weakly coherent mode (WCM) [6,[12][13][14].Usually, the WCM is used as one of the criteria for identifying the transition into the I-mode.Otherwise, this transition is accompanied by a significant decrease in the boundary thermal transport coefficient [15].The WCM can be observed in fluctuation signals of various physical quantities and exhibits a radial localized nature, primarily concentrated in the pedestal region.Soft x-rays (radiation measurements), electron cyclotron emission (electron temperature measurements), and reflectometry (density fluctuation measurements) can be observed through various boundary diagnostics, including Mirnov coils (magnetic field fluctuation measurements).Notably, WCM in density fluctuations has a much higher relative strength compared to that in temperature fluctuations.Due to its radial localized nature and the pronounced relative strength in density fluctuations, the WCM is considered an important channel for particle transport in the I-mode, contributing significantly to the maintenance of the density-temperature decoupling pedestal structure in this regime.In both C-Mod and AUG, the geodesic acoustic mode (GAM) was found to be nonlinear coupled with the WCM and was believed to be responsible for its broad frequency spectrum [13,14].However, this phenomenon is different in EAST.Similar to the phenomenon observed in C-Mod and AUG, a low-frequency toroidal symmetric mode, edge temperature oscillation (ETRO) [16], is present in the I-mode on EAST and has been observed in 90% of the discharges [17].However, it has been confirmed that ETRO is not GAM [17].
Manz et al [18] conducted simulation of the I-mode using the global three-dimensional gyrofluid electromagnetic turbulence code GEMR.These simulations suggest that the WCM exhibits characteristics resembling a drift-wave.However, due to the nonadiabaticity induced by the electron thermal conductivity α φ, Te > α φ,ñe remains finite.The associated perpendicular heat transport drives the WCM.Furthermore, a simulation study using a two-fluid six-field model, incorporating Braginskii equations on the BOUT++ framework, was conducted based on experimental data from EAST [19] and C-Mod [20].Linear simulations reveal that the instability of the I-mode pedestal is primarily attributed to the drift Alfven wave (DAW).Nonlinear simulations repeat a broad frequency structure in density fluctuations.Notably, the absence of DAW in nonlinear simulations results in the invisibility of the WCM, indicating that DAW is the physical effect driving the WCM [19].The DAW enhances both particle and heat transport, with particle transport being notably influenced.These observations align with the characteristic of the I-mode that decoupling of particles and heat confinement.SymPIC simulations using EAST experimental data similarly demonstrated a broad frequency structure (~67 kHz) [19].
This paper predominantly focuses on examining the behavior of WCM within the I-mode discharges on EAST.The paper is organized as follows: in section 2, the experimental observations and analyses were presented.The experimental conditions and diagnostics employed are illustrated.To begin with, an overview of the characteristics for the WCM is provided.The center frequencies of the WCM were statistically analyzed, and their variations were compared with changes in several plasma parameters.Subsequently, the first observation of the WCM in a poloidal correlation reflectometer (PCR) was introduced, revealing the presence of the poloidal wavenumber range in the WCM.The modulation role of ETRO in high-frequency density fluctuations was also demonstrated.In section 3, a simulation study using equilibrium files generated from the discussed experimental discharge #126760 was conducted.The radial distribution of the 'WCM' in density fluctuations and the phase relationships of several fluctuations are discussed.Finally, the impact of resistivity and q 95 is discussed using linear simulation analysis.

Experimental setup
All the experimental data presented in this study originate from the EAST [21][22][23], a superconducting tokamak characterized by a major radius R of 1.85 m, a minor radius of 0.45 m, and equipped with a molybdenum first wall and tungsten divertors.The I-mode discharges discussed in this paper are employed with various heating methods, including LHW (4 MW at 2.45 GHz and 6 MW at 4.6 GHz), NBI (2 MW-4 MW), ECRH (4 MW at 140 GHz) and ICRH.The key plasma parameters relevant to the experiments are summarized in figure 1.The normalized parameters are as follows: Plasma current I p : 1 MA Toroidal magnetic field B T : 3 T Line-averaged density ne : 4 × 10 19 m −1 Edge safety factor q 95 : 7 Stored energy W MHD : 200 kJ There are a total of 201 shots, with a data point taken every 0.1 s, leading to multiple points for some stable I-mode discharges, amounting to a total of 3157 data points.Among these discharges, there are 1532 points with NBI heating, 3105 with LHW heating, 590 with ECRH heating, and 859 with ICRH heating.All discharges discussed in this paper are with ion B ×∇ B drift away from the active X-point and plasma current in counterclockwise seen from the top.Additionally, figure 2 offers a poloidal view of the diagnostics utilized in this research.We derive the electron temperature profile using ECE [24] and Thomson scattering (TS), while the lineaveraged density is obtained from the far-infrared laser-based POlarimeter-INTerferometer (POINT) [25], and the density profile is measured using the density profile reflectometer (DPR) [26].Furthermore, the presence of the WCM is detected through both the Doppler reflectometer (DR) [27] and PCR [28].The O-mode polarized O-band (20.4,24.8, 33, 40 GHz) multi-channel correlation reflectometer in the PCR system has diagnosed the WCM recently.
The WCM detected in the DR system primarily stems from perpendicular velocity fluctuations, whereas those observed in the PCR are attributed to density fluctuations.Both systems capture signals as the in-phase (I = Acosϕ) and quadrature (Q = Asinϕ) of the I/Q mixer, the complex signal written as A iϕ = I + iQ.Specifically, the perpendicular velocity fluctuations are derived from the time derivative of the phase angle, which is the dϕ/dt.Given that the WCM is observed in two distinct poloidal channels within the PCR system, we are now equipped to calculate the poloidal wavenumber k θ associated with the WCM.

Statistical study of the WCM in I-mode plasma on EAST
A weakening of the WCM was observed as the line-averaged density increased [19].This observation led to speculation that the behavior of the WCM might be correlated with certain plasma parameters, prompting a statistical analysis of the WCM.Gaussian fitting was utilized to determine its center frequency.The frequency range of the WCM was selected, and Gaussian fitting was applied to obtain the center frequency denoted as f WCM in figure 3.
For the statistical analysis, we considered various plasma parameters, including plasma current I p , toroidal magnetic field B t , safety factor q 95 , line-averaged density n e , stored energy W MHD , absorbed power P loss , and injected power from ICRH, ECRH, LHW and NBI.It has been established that a higher magnetic field can enhance the I-mode performance, suggesting that B t plays a crucial role in influencing WCM behavior.However, the magnetic field range available in the EAST experimental is relatively limited.For most of the discharges, the magnetic field is between 2.45-2.67T, which can almost certainly be considered as being under the same magnetic field conditions, hence the magnetic field was not included in the regression statistical analysis.The regression analysis results are as follows: e,ped q −1.16±0.17In the regression analysis regarding f WCM , it can be seen that the two parameters with the largest proportions are the pedestal density n e,ped and the safety factor q 95 .The f WCM is inversely proportional to the pedestal density, which aligns with our predictions; meanwhile, the safety factor plays a dominant role among the parameters affecting f WCM , although the reason remains unclear.

WCM visible in PCR
In previous I-mode discharges on EAST discussed below, the WCM was only visible in DR and some ECE signals.Recently, WCM was observed in the conventional reflectometer (PCR on EAST), as shown in figure 4. In both discharges, the L-I transition occurs without additional injection power, and the plasma energy increased by about 13%.The edge electron temperature and its gradient also rose.The main difference between the control conditions is the application of RMP, which began at 2.95 s in #126760.It can be observed that, under the same control as other conditions, the plasma was delayed from entering the I-mode after the application of RMP, and the I-H transition was not realized.However, after the RMP was removed, the plasma remained in the I-mode phase for about 1.6 s.Thus, there is doubt regarding whether the maintenance of the I-mode is sustained by the RMP.By comparing the electron temperature of the ECE channels at the boundary, the difference between the channels located at ρ ∼ 0.83, 0.96 can be observed as a reflection of the gradient of the boundary electron temperature.The increase in the temperature difference between the two occurred almost simultaneously with the occurrence of the WCM.Additionally, the density profile of the pedestal remained almost unchanged during the I-mode phase in both discharges, suggesting that the WCM appeared to be triggered by the electron temperature gradient.
The WCM observed in the PCR differs from the previous reports from C-Mod [1] and AUG [14].In earlier studies, the WCM observed in conventional reflectometers indicated a reduction of low-frequency fluctuations and an increase in the WCM frequency band.However, in recent experimental results on EAST, the density fluctuations from the PCR only displayed a decrease in the low-frequency band.The intensity of density fluctuations in the WCM frequency band remained almost the same.This may be attributed to a weak increase in energy from the L-mode to the I-mode, with only a 13% increase in energy and a 21% increase in edge electron temperature (from 78 eV to 95 eV).
With the WCM visible in the two poloidal channels of the PCR, the wavenumber can be calculated through a two-point correlation analysis [29].The main concept behind the twopoint correlation analysis is the assumption that each state has a history, making it an algorithm that exchanges time for space.During the 4-6 s interval in discharge #126760, the plasma parameters remained nearly constant.Therefore, this time period was selected for the calculation of the two-point correlation analysis, and the results are presented in figure 5.The poloidal wavenumber of the WCM was observed to be approximately 0.3-1.1 cm −1 .
Additionally, the modulation of high frequencies by the ETRO was observed in the density fluctuations.The envelope of density fluctuations is determined by Envelope 100 kHz+ (t) = I 2 100 kHz+ + Q 2 100 kHz+ , where the subscript '100 kHz+' denotes 100 kHz high-pass filtering.A mode with a characteristic frequency of approximately 5 Hz is evident in the timefrequency spectrum of the envelope, indicating its modulation of high-frequency density fluctuations.Simultaneously, this mode is observed in other signals, including ECE in the edge (ρ ∼ 0.9), divertor LP, DR, SXR, AXUV, and Mirnov coils [17].Based on these features, it is identified as the ETRO.
In the field of scientific computing, there are many statistical tools that can be used to analyze random signals.
In signal processing, first-and second-order statistics are crucial, but many signals cannot be used using first-and second-order statistics describing nonlinear processes, so in the 60s of the last century higher-order statistical methods were developed.High order spectrum (HOS, also known as polyspectra) analysis is an important tool for analyzing non-Gaussian linear systems.The bispectrum is the most important part of the higher-order spectrum.For plasma analysis, Kim et al [30] focused on the plasma's medium-turbulent signal characteristics, leading to the development of a set of bispectrum algorithms for the analysis of physical signals.The bispectrum is a third-order correlation spectrum, and in frequency space, it is defined as The bispectrum can reflect the interaction of three waves, and the bispectrum coefficient corresponds to their coupling strength, with a larger coefficient indicating a higher coupling strength.
In figure 6(a), where X and Z represent density fluctuations and Y represents the Envelope mentioned earlier, a strong coupling between the WCM and background turbulence appears.In the inset at the lower left of figure 6(a), the low-frequency part of f 2 has been magnified.We can see   the portion with f 1 ∼ 3 kHz and f 2 in the frequency band of WCM is brightened, which is distinct from the ETRO at 5 kHz.As ETRO modulates high-frequency density fluctuations, we calculated the cross-bispectrum correlation between density fluctuations and envelope.We show that, in figure 6(b) that there is a strong coupling between ETRO and high frequencies, consistent with the observed modulation of ETRO for high-frequency density fluctuations.

The 'WCM' in ECE
A 'WCM'-like structure was also observed in the ECE signals, but its frequency band did not correspond to the time when the WCM appeared in other signals.However, the time at which the 'WCM' appeared in ECE roughly aligned with the appearance of a lower frequency broad-spectrum structure in the DR signal.It seems that the frequencies are more similar, as depicted in figure 7. The power spectrums of 3-3.5 s were presented in figures 7(d)-(f ).It is evident that the frequency bands do not match, indicating that they should be different.At around 2.3 s, ECRH with approximately 0.4 MW was injected, and the broad frequency spectrum might be attributed to this injection.At 3.5 s, the measurement position for the PCR 33G channel is at ρ ∼ 0.984, for DR it is at ρ ∼ 0.997, and for ECE, it is near the separatrix.It is evident that at this time, the DR measurement position is closer to that of ECE.After the L-I transition, the measurement position for the PCR 33G channel is at ρ ∼ 0.947, for DR it is at rho ~0.980, and for ECE, it moves a little outward to ρ ∼ 1.04, now the WCM is observable in both the PCR and DR.The electron temperature fluctuations increased, but there was no significant increase in high frequencies, primarily in low frequencies.This may be related to the formation of ETRO, while the WCM, on the other hand, did not manifest in electron temperature fluctuations.

Physics model and simulation setup
In this section, the nonlinear process of the edge pedestal for I-mode discharge #126760 on EAST was simulated using the two-fluid model within the tokamak configuration under the BOUT++ framework [31].The model is based on the Braginskii equations, adopting flute reduction and quasineutral conditions and expanded in the drift wave ordering [32].The evolving variables include vorticity ϖ, ion density n i , normalized parallel vector potential ψ, ion temperature T i and electron temperature T e , which are writen as: ) The variables in these equations are defined as In this model, all variables can be written as f = f 1 + f 0 , where f 0 represents the equilibrium part of the variable, and f 1 is the fluctuations part.The normalized parallel vector potential ψ = A ∥ /B 0 has no equilibrium quantity, only a perturbation part.ψ is the variable used in the model to calculate the magnetic field perturbation, the unit vector of the total magnetic field b = b0 + ∇A ∥ × b0 /B, and the field-line curvature vector κ0 = b0 • ∇ b0 .η SP is defined as the parallel Spitzer resistivity.As described below, the simulation of 4.2 s of discharge #126760 was conducted.The radial profiles of electron density, electron temperature, and ion temperature were utilized to calculate the kinetic EFIT file, as depicted in figure 8.The blue lines represent the fitting lines of experimental data, serving as the input data for the kinetic EFIT equilibrium calculation.To investigate the edge pedestal behavior of the plasma, the simulation domain is the region between the two green curves, ranging from the normalized magnetic flux Ψ p = 0.85 to Ψ p = 1.03, covering the pedestal and SOL region.The spatial resolution of the mesh is 260 in the radial direction (denoted as X) and 64 in the poloidal direction (denoted as Y), with 64 in the toroidal direction (denoted as Z) for the nonlinear simulation and 16 in the toroidal direction for the linear simulation.Figures 8(b)-(d) also display the profiles used in generating the mesh.The red lines represent the smoothed results and serve as the original profiles for the mesh.

Nonlinear results
The nonlinear process has three phases: linear, nonlinear, and saturation.The saturation phase was used for analysis.Figure 9 displays the evolution of ion density fluctuations and electron temperature fluctuations.It can be seen that the linear phase lasts approximately until 1200τ A , followed by the nonlinear phase around 1200τ A to 1500τ A , and the fluctuations became saturated after 1500τ A .Therefore, a time slice from 1600τ A to 2000τ A was chosen for further analysis.In this case, the normalized parameter of time τ A = 1.63 × 10 −7 s.
Compared to the experimental observation of WCM, a spectrum analysis for n i from t = 1600τ A to t = 2000τ A was performed, as depicted in figure 10.A broadband frequency band structure was evident, localized at Ψ p ∼ 0.975.Although the frequency band is shorter than the WCM observed in the experiment, as shown in figure 10(b), the center frequencies of both are around 70 kHz.For the sake of illustration, the broadband structure in the simulation is temporarily referred to as the 'WCM'.
A root mean square (rms) calculation of density fluctuations was carried out in the toroidal direction, revealing that the radial position with the strongest density fluctuations is approximately at Ψ p = 0.982.This position closely aligns  with the radial location exhibiting the strongest density gradient.However, it is evident that it does not coincide with the radial position where the 'WCM' appeared.The strongest electron temperature gradient is located at Ψ p = 0.974, while that of the ion temperature gradient is at Ψ p = 0.955.The closest one to the position of the 'WCM' is the electron temperature, which is just slightly outside of the 'WCM.'Therefore, it is natural to assume that the driven source of the 'WCM' is the gradient of the electron temperature.In accordance with the central localization of the 'WCM' appearance position, identified at Ψ p = 0.975 on the outer midplane, a frequency-wavenumber spectrum is illustrated in figure 10(c), which delineates the normalized wavenumber range of the 'WCM'.
In the subsequent analysis, cross-correlation examinations were conducted for electron temperature fluctuations, ion temperature fluctuations, density fluctuations, and electrostatic potential fluctuations.The selected perturbation's spatial location was Ψ p = 0.975 at the outer midplane.The crosscorrelations between electron temperature perturbation, ion temperature perturbation, and potential perturbation with the density perturbation are explored.The relevant results are displayed in figure 11.
In the simulation results depicted in figure 10(c), the normalized poloidal wavenumber k θ ρ s for the WCM is approximately 0.04-0.11,which aligns closely with the experimental measured values ranging from 0.03 to 0.11.The k θ is derived from the calculation using the equation n/R k θ = BT Bp .However, not all spatial scales exhibit significant correlations in the fluctuations, as depicted in figures 11(a)-(c).Yet, within the spatial extent of 'WCM', a relatively high correlation (coherence is greater than 0.7) is observed.This is evident from the normalized poloidal wavenumber range for 'WCM' from figure 10(c

Linear analysis
In the simulation work conducted by Lang et al [20] on WCMs, neoclassical effects were taken into account in the resistivity.With the inverse aspect ratio on EAST being approximately 0.24, the resistivity obtained by substituting this value was about four times that of the original.Consequently, a linear simulation of the resistivity scan was carried out.The model used for the linear simulation is also the physical model described in section 3.1, the toroidal mode is set to n = 50.As depicted in figure 12, the instability growth rate decreases with increasing resistivity, indicating that resistivity plays a stabilizing role in the instability in the edge pedestal of plasma.
Otherwise, it is observed that the center frequency of the WCM is inversely proportional to q 95 , as shown in figure 3.However, the reason behind this observation remains unclear.Consequently, a safety factor scan was conducted in the linear simulation to explore the relationship.In experimental statistics, it was first discovered that the WCM frequency is strongly correlated with I p .Since the value of q 95 has a significant  relationship with I p and is a more universal dimensionless parameter, q 95 was chosen for regression analysis.Here, the total current has been modified from the original 450 kA to 600 kA and 800 kA, respectively, corresponding to q 95 values of 5.9, 4.38, and 3.28.The real frequencies for the WCM obtained are shown in figure 13.However, the trend of frequency changing with q 95 in simulations is opposite to that in statistics.It implies that neither the plasma current nor the safety factor are the real parameters that can influence the central frequency of the WCM.It should be noted that the mode frequency mentioned here is not equivalent to the 'WCM' frequency.The actual 'WCM' frequency results from a nonlinear interaction of multiple modes, whereas our findings are from a linear analysis, representing a single mode simulation of the I-mode pedestal instability driving effects.

Summary and discussion
In this study, the first observation of the WCM in a conventional reflectometer on EAST was reported, with the confirmation of its poloidal wavenumber range through a twopoint correlation analysis.Transitioning from the L-mode to I-mode, the density profile at the plasma boundary remains virtually unchanged.However, the increasing difference in the ECE signals at the boundary suggests an augmentation in the electron temperature gradient.The emergence of a WCM aligned with an increase in electron temperature subsequently evolved into a stable state with no substantial alterations in the WCM.ETRO was identified as modulating high-frequency density fluctuations.However, the PCR bispectrum results do not show the interaction between ETRO and WCM.This discrepancy may be attributed to the relatively weak WCM observed in PCR on EAST, manifesting only as a weakening of low-frequency fluctuations without a noticeable enhancement in the WCM frequency band.The RMP is found to delay the onset of the I-mode and sustain it; this might be attributed to a reduction in the E r well due to the RMP, which subsequently leads to an increase in the power threshold for the Hmode.Moreover, the plasma remains in the I-mode phase for approximately 1.5 s after RMP removal, thus the underlying mechanism responsible for this maintenance warrants further investigation.
Statistical analysis unveils an inverse relationship between the central frequency of the WCM and q 95 .However, linear simulation results show that the real frequency of instability is directly proportional to q 95 , which contradicts the trend observed in statistical data.This suggests that neither the current nor the safety factor are the true factors affecting the WCM frequency or there may be a flaw in the MHD model when considering the impact of the plasma current.A comparison of density profiles from low-, medium-, and high-frequency results within the statistical data reveals that higher frequencies correspond to steeper density gradients.It is speculated that I p might merely be a superficial factor, and other parameters could be the actual influencers of the WCM frequency.Further investigation will involve using simulation methods to modify density and temperature gradients to compare mode frequencies and validate this hypothesis.
The magnetic field conditions in EAST are relatively narrow, and the patterns obtained here may not necessarily apply under future conditions of stronger magnetic fields.However, given the current tokamak discharge conditions, such magnetic field conditions are typically what is encountered.Therefore, this statistical analysis in this work remains meaningful for analyzing existing data and studying physical mechanisms.Observations in ECE also revealed a broad-frequency structure resembling the WCM, appearing as early as the L-mode phase.Nonetheless, the frequency range does not correspond to the broaden frequency structure observed in the L-mode of the DR signal.Since the occurrence of this broaden frequency structure in ECE coincides with the timing of implementing ECRH, it raises the speculation that this phenomenon might be induced by ECRH.
Spectral analysis of simulated density fluctuations revealed a broadened frequency structure with a central frequency corresponding to the WCM observed in experiment.Its radial location closely corresponds to the position with the strongest electron temperature gradient, suggesting that the WCM is driven by an electron temperature gradient, consistent with the observed increase in electron temperature in experiment.By conducting a cross-correlation analysis on simulated fluctuations, the observed phase relationship was as follows: α Te > α ni ∼ α ϕ > α Ti .This implies that the 'WCM' is likely triggered by electron temperature fluctuations.Linear simulation results indicate that resistivity plays a damping role in the instability of I-mode plasma boundaries.

Figure 1 .
Figure 1.Boxplot visualization of plasma parameters from database.The normalized parameters of the plasma current Ip are 1 MA, of the toroidal magnetic field B T are 3 T, of the line-averaged density ne are 4 × 10 19 m −3 , of the edge safety factor q 95 are 7, and of the stored energy W MHD are 200 kJ.

Figure 2 .
Figure 2. The last closed flux surface (LCSF) of discharge #126760 at 5.0 s, and the poloridal view of the principal diagnostics in the experimental analysis on EAST, including ECE (dark red circles), TS (pink diamonds), 11 channel points (yellow), DPR (red), DR (azure) and PCR (green).

Figure 3 .
Figure 3.On the left was the method for obtaining the center frequency of WCM (Gaussian fitting), this power spectrum is from the DR data, while the right side displayed the regression analysis results for f WCM .

Figure 4 .
Figure 4. Time trace of two discharges, #126759 (left) and #126760 (right), with the same auxiliary heating power, but the latter with RMP.From top to bottom, the left side displays injected power and loss power, diamagnetic energy, energy confinement time, core line-averaged density, electron temperature located in the core and edge of the plasma, Dα emission, time-frequency spectrum from DR and PCR.The right side shows almost the same parameters, except replacing Dα emission with the voltage of RMP.

Figure 5 .
Figure 5. Left: the two-point correlation analysis result for density fluctuations in the 33 GHz channel of PCR from discharge #126760, recorded between 4 and 6 s.Right: the normalized wavenumber k θ ρs range for WCM, with a frequency filter of 48-88 kHz applied.

Figure 6 .
Figure 6.The normalized cross-bispectrum b 2 i ( f 1 , f 2 ), for (a) X and Z are the density fluctuations, Y is the Envelope; for (b) the X and Z are the density fluctuations, Y is the Envelope 100 kHz+ .The time-frequency spectrum of (c) perpendicular velocity fluctuations, (d) Envelope 100 kHz+ and (e) ECE.All data are from the discharge #126760.

Figure 7 .
Figure 7. Time-frequency spectrum of (a) density fluctuations and (b) perpendicular velocity fluctuations from DR and (c) electron temperature fluctuations from ECE for discharge #126760.(d)-(f ) shows the power spectrum of the three signals of 3-3.5 s and 4-4.5 s.

Figure 8 .
Figure 8.(a) The equilibrium file used for simulation, the magnetic surfaces information from kinetic EFIT, the green lines surrounded showed the range used for simulation, black lines are the first wall of the device.The three figures on the right shows the radial profiles of (b) ion density, (c) electron temperature and (d) ion temperature.Blue lines are the fitting lines of experimental data, and the red lines are the smoothing lines inputted into the simulation mesh.

Figure 9 .
Figure 9.The evolution of density fluctuations and temperature fluctuations.
Figure 11(d) reveals that the density fluctuations and electrostatic potential fluctuations are almost in phase, showcasing drift wave characteristics.Similarly, figures 11(e) and (f ) indicate that the electron temperature fluctuations slightly lead the electrostatic potential fluctuations, whereas the ion temperature fluctuations lag behind them.In summary, the phase relationship among these four quantities is as follows: α Te > α ϕ ∼ α ni > α Ti .This observation suggested that 'WCM' is induced by the electron temperature fluctuation.

Figure 10 .
Figure 10.(a) The radial distribution of the ion density fluctuations spectrum, and the corresponding power spectrum for experimental and simulation data are shown in (b).(c) is the frequency-wavenumber spectrum of density fluctuations.Radial profiles of (c) ion density, (d) electron temperature and (e) ion temperature at 2000τ A are shown with blue lines and their gradient radial profiles are shown with red lines.

Figure 11 .
Figure 11.The cross coherency and cross phase between ion density fluctuations and ion temperature fluctuations, density fluctuations and electron temperature fluctuations, ion density fluctuation and electrostatic potential fluctuations.

Figure 13 .
Figure 13.Linear simulation results for Ip scan, left is corresponding profiles for q, right is the real frequency ωr in linear simulation.