# Characteristics of edge temperature ring oscillation during the stationary improved confinement mode in EAST

A.D. Liu, X.L. Zou, X.M. Zhong, Y.T. Song, M.K. Han, Y.M. Duan, H.Q. Liu, T.B. Wang, E.Z. Li, L. Zhang, et al.

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A.D. Liu, X.L. Zou, X.M. Zhong, Y.T. Song, M.K. Han, et al. Characteristics of edge temperature ring oscillation during the stationary improved confinement mode in EAST. Nuclear Fusion, 2023, 64 (1), pp.016013. 10.1088/1741-4326/ad0acd. cea-04788929

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# Characteristics of edge temperature ring oscillation during the stationary improved confinement mode in EAST

A.D. Liu<fnref n="1" /> ID, X.L. Zou<fnref n="2" />, X.M. Zhong<fnref n="1" />,*, Y.T. Song<fnref n="3" />,*, M.K. Han<fnref n="4" /> ID, Y.M. Duan<fnref n="3" />, H.Q. Liu<fnref n="3" /> ID, T.B. Wang<fnref n="6" />, E.Z. Li<fnref n="3" /> ID, L. Zhang<fnref n="3" />, X. Feng<fnref n="5" />, G. Zhuang<fnref n="1" /> and EAST I-mode Working Groupª

E-mail: zhongxm@mail.ustc.edu.cn and songyt@ipp.ac.cn

Received 28 June 2023, revised 30 October 2023

Accepted for publication 7 November 2023

Published 21 November 2023

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CrossMark

## Abstract

The I-mode is a natural edge localized mode (ELM)-free regime with H-mode-like improved energy confinement and L-mode-like particle confinement, making it an attractive scenario for future tokamak-based fusion reactors. A kind of low-frequency oscillation has been widely observed, with a frequency between stationary zonal flow and geodesic-acoustic mode (GAM) zonal flow. In EAST, most stationary I-mode shots have such a mode, called edge temperature ring oscillation (ETRO). This mode probably plays an important role in development and maintenance of the I-mode, while investigations are needed to clarify the differences between ETRO and similar mode low-frequency oscillation in other devices, such as limit cycle oscillation (LCO). In this paper, the properties of ETRO are described in detail, including the structure of its magnetic components, its radial propagation characteristics, statistics of its central frequency, a linear analysis of the alternating transition turbulences and a comparison with GAM and LCO. Although some similarities can be found between ETRO and both GAM and LCO, the main features are not identical. ETRO is probably a novel type of finite frequency zonal flow or pressure gradient-induced drift that is unique to the I-mode. It is found that modest fueling can reduce ETRO intensity while maintaining I-mode confinement, suggesting that supersonic molecular beam injection could be used as an effective tool to control ETRO.

Keywords: I-mode, stationary, GAM, zonal flow, turbulence transition, I-phase

(Some figures may appear in colour only in the online journal)

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Original Content from this work may be used under the terms of the [Creative Commons Attribution 4.0 licence](https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

<footnote n="1">¹ School of Nuclear Science and Technology, University of Science and Technology of China, Anhui, Hefei 230026, China</footnote>

<footnote n="2">² CEA, IRFM, F-13108 St Paul Lez Durance, France</footnote>

<footnote n="3">³ Institute of Plasma Physics, Chinese Academy of Sciences, Anhui, Hefei 230021, China</footnote>

<footnote n="4">⁴ Southwestern Institute of Physics, Chengdu 610041, China</footnote>

<footnote n="5">⁵ Advanced Energy Research Center, Shenzhen University, Shenzhen 518060, China</footnote>

<footnote n="6">⁶ ITER Organization, Saint Paul Lez Durance, 13115, France</footnote>

<footnote>ª See the appendix.</footnote>

<footnote>* Authors to whom any correspondence should be addressed.</footnote>
# 1. Introduction

Although the high-confinement mode (H-mode) [1] has been considered as the baseline operational scenario for the International Thermonuclear Experimental Reactor (ITER) [2], the heat load caused by large edge localized modes (ELMs) due to relaxation of edge pressure and current is still one of the most crucial issues in fusion research [3]. An alternative improved confinement regime (the I-mode), featuring high energy confinement comparable to the H-mode and moderate particle confinement comparable to the L-mode [4], may be a possible solution, and has been widely investigated in various divertor tokamaks [5–9]. Generally, the I-mode is usually obtained under an unfavorable configuration, i.e. the $B \times \nabla B$ ion drift direction pointing away from the X-point. In C-Mod and AUG, the I-mode is always accompanied by the weakly coherent mode (WCM). Additionally, during L-I-H transitions the geodesic-acoustic mode (GAM) may play an important role through nonlinear flow-turbulence coupling [10]. During a stationary I-mode in EAST, a low-frequency coherent mode, named edge temperature ring oscillation (ETRO), was identified and reported. ETRO is a radially localized edge temperature ring oscillation with a poloidally symmetric structure in the pedestal region [8, 11]. Additionally, ETRO is present in the I-mode with helium plasma [12]. Moreover, it was found that ETRO plays a crucial role in maintaining the 1000 s Super I-mode [13]. The ETRO frequency falls between limit cycle oscillation (LCO) and the GAM in EAST, implying that it is probably not the stationary zonal flow that triggers marginal transition from L-mode to H-mode [14] nor the ordinary GAM zonal flow [15]. Recently, a similar mode, called low-frequency edge oscillation (LFEO), has also been reported in C-Mod and AUG [16, 17]. However, LFEO is found in only 40%-60% of I-mode shots and exhibits different characteristics from ETRO. LFEO is considered as a GAM [16]. Given that most stationary I-mode shots in EAST are accompanied by ETRO and it probably plays an important role in sustaining the stationary I-mode, this paper systematically investigates the characteristics of ETRO, particularly in comparison with GAM and LCO.

The remainder of this paper is organized as follows. Section 2 displays typical stationary I-mode shots and the emergence of ETRO. In section 3, ETRO structures are displayed, including the radiation components and magnetic components. Section 4 presents the turbulence transition accompanied by ETRO and the linear simulation results, as well as the method for separating the two types of turbulence based on the direction of oscillation of ETRO. The statistics of ETRO frequency are given in section 5, as well as the evolution of ETRO during I-mode to H-mode transition. The effect of supersonic molecular beam injection (SMBI) on ETRO, edge plasma flow and turbulence is discussed in section 6. GAM and LCO are compared in section 7. Subsequently, a summary of the characteristics of ETRO is provided.

# 2. Stationary I-mode in EAST

The most noteworthy feature of the I-mode in EAST is that it can spontaneously last for several seconds. Figure 1 shows two typical stationary I-mode discharges, 69976 and 71436. The discharge parameters are plasma current $I_p = 400–500$ kA and toroidal magnetic field $B_t = 2.2$ T, with the up single null (USN; unfavorable) configuration. From top to bottom in figure 1, the curves give the auxiliary heating power, the chord-averaged density and edge $D_\alpha$ signal, the edge $T_e$ evolution from the Thomson scattering system, the plasma stored energy $W_{MHD}$ and $H_{98}$ factor, the time-frequency spectra of temperature fluctuation from the edge electron cyclotron emission (ECE) channel and the turbulence rotation velocity $v_\perp$ from the Doppler reflectometry (DR) edge channel. The auxiliary heating in 69976 included a 1.4 MW low hybrid wave (LHW) and 2 MW ion cyclotron resonance heating (ICRH), and $W_{MHD}/H_{98}$ were both increased to a new plateau with no distinct change in the $D_\alpha$ signal during the transition. The central frequency of ETRO is 8–9 kHz, while the WCM frequency is about 40–70 kHz, both of which appeared during I-mode confinement. The auxiliary heating in 71436 included 1.5 MW LHW and 0.5 MW electron cyclotron resonance heating (ECRH), and as $W_{MHD}/H_{98}$ increased to a new plateau the $D_\alpha$ signal was continuously increased during the transition. The central frequency of ETRO is 10 kHz. The plasma entered into H-mode at about 7.8 s in 71436.

ETRO is a structure that exhibits both poloidal symmetry and radial localization, and is dominated by electron temperature fluctuations. Figure 2 shows the two most intuitive pieces of evidence to support the definition. Figure 2(a) depicts the cross-sectional distribution of second singular value decomposition (SVD) from the tomography reconstruction based on a 64-channel bolometer array. The tomography technique, a powerful data processing method, has been widely adopted in line-of-sight type diagnostic systems in tokamaks. In this study, we employ a novel algorithm named Gaussian process tomography. Further details of this algorithm can be found in a paper by Wang *et al* [18]. After reconstructing the radiation distribution in the cross section, SVD can be used to extract the primary patterns. Generally, the first topo of SVD represents the equilibrium quantity while the second represents the most significant oscillatory mode. It can be found that the values for the second topo on the $\rho=0.9$ flux surface are noticeably higher, hinting that radiation perturbation has an in-phase symmetry structure localized at $\rho=0.9$ ($\rho$ being defined as the square root of toroidal flux). Figure 2(b) displays the distribution of correlation coefficients at the ETRO frequency between the 128-channel electron cyclotron emission imaging (ECEI) signals and one-channel ECE signal. Based on the ECE and ECEI measurements, the relative temperature perturbation of ETRO is about 5%-9% [11]. Given the much smaller density perturbation at the ETRO frequency compared with the temperature perturbation, as will be demonstrated in figure 7 below, it can be concluded that the electron
<figure><img src="image_5.png" /><figcaption>**Figure 1.** From top to bottom, temporal evolution of (a) auxiliary heating power, (b) chord-averaged density and $D_\alpha$ signal, (c) edge $T_e$, (d) plasma stored energy $W_{MHD}$ and $H_{98}$ factor, (e) time-frequency spectrum of the edge ECE signal and (f) time-frequency spectrum of turbulence rotation velocity from DR measurement in typical stationary I-mode shots 69976 and 71436.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 2.** (a) Distribution of the second singular value decomposition (SVD) result through tomography reconstruction based on 64-channel bolometer arrays. (b) Distribution of coherence coefficients at the ETRO frequency between multi-channel ECEI signals and one ECE channel signal.</figcaption></figure>

temperature perturbation is primarily responsible for the sym-
metric radiation structure. More details about this can be found
in our previous paper [11].

Evolution of the edge turbulence intensity and the rotation
velocity ($v_\perp$) measured through multi-channel DR [19, 20]

during L-mode to I-mode transition are shown in figure 3. The
measured perpendicular wavenumber $k_\perp$ at the cutoff layer
is about 4–6 cm$^{-1}$. In shot 69976, it can be seen that a dis-
tinct WCM and ETRO appear simultaneously after $t = 3.27$ s;
before that time the GAM can also be present, with a smaller
<figure><img src="image_7.png" /><figcaption>**Figure 3.** (a) Plasma stored energy $W_{\text{MHD}}$ and $H_{98}$. (b) Evolution of turbulence intensity with $k_{\perp} = 4-6 \text{ cm}^{-1}$ (integration over turbulence spectrum from 1000 kHz to 1000 kHz), ETRO (integration over $v_{\perp}$ spectrum from 6 kHz to 12 kHz) and WCM (integration over $v_{\perp}$ spectrum from 40 kHz to 100 kHz) intensities. (c) Time-frequency spectrum of turbulence rotation velocity $v_{\perp}$ at $\rho \sim 0.9$ from Doppler reflectometry during L-mode to I-mode transition.</figcaption></figure>

intensity than ETRO. Meanwhile, the turbulence intensity is significantly decreased. Second harmonics of ETRO can also be seen directly.

Another typical type of L–I transition is shown in figure 4. In shot 71436, the L–I transition is much slower than that in shot 69976. The turbulence intensity decreases slowly from $t = 2.4$ s to $t = 2.55$ s, while WCM and ETRO both show a slow increase with nearly identical growth trends. Figure 4(d) indicates that the low-frequency components of the $v_{\perp}$ spectrum appear chaotic during the slow transition stage, while GAM, ETRO and WCM may all be present. These phenomena may be attributed to the marginal injection heating power during this shot, with only 1.5 MW LHW and 0.5 MW ECRH.

### 3. Features of ETRO structure

ETRO can be found in various edge plasma diagnostics, including magnetic coils, divertor probes, $D_{\alpha}$ filterscopes, ECEs, bolometers, soft x-rays, DR and occasionally the polarimeter-interferometer (POINT) [21]. The toroidal symmetry of ETRO's magnetic perturbation can be recognized directly by the 16 groups of toroidal magnetic probes ($\partial B_{\theta}/\partial t$). In figure 5, the original signals from eight magnetic probes during the I-mode are shown, as well as the corresponding time-frequency spectrum.

The poloidal symmetry of ETRO's radiation perturbation phase in figure 2 is estimated through tomography
<figure><img src="image_8.png" /><figcaption>**Figure 4.** (a) Plasma stored energy $W_{MHD}$ and $H_{98}$. (b) Chord-averaged density and edge $T_e$. (c) Evolution of turbulence intensity (integration over turbulence spectrum from −1000 kHz to 1000 kHz), ETRO (integration over $v_\perp$ spectrum from 7 kHz to 13 kHz) and WCM (integration over $v_\perp$ spectrum from 40 kHz to 100 kHz) intensities. (d) Time-frequency spectrum of turbulence rotation velocity $v_\perp$ at $\rho \sim 0.9$ during L-mode to I-mode transition in shot 71436.</figcaption></figure>

reconstruction. Poloidal symmetry can also be estimated through coherence analyses between the DR signal and the bolometers, as illustrated in figure 6. Figure 6(a) displays the distribution of the 64-channel extreme ultra-violet (XUV) array in the cross section, where there are four groups each consisting of 16 channels. The detectors are all located around the middle plane [22]. It is apparent that channels XUV8 and XUV60 pass through the I-mode pedestal region from the top and bottom, respectively. Figures 6(b)–(d) show the spectra of cross-power, coherence coefficient and cross-phase between four bolometer signals (XUV8, XUV25, XUV40 and XUV60) and one reference DR signal. All the spectra display clear peaks at the ETRO frequency. The coherence coefficients of channels XUV8 and XUV60 are the highest, with

XUV60 exhibiting the largest intensity and coherence coefficient due to its proximity to the X-point. Additionally, the cross-phases of all channels at the ETRO frequency are similar, implying symmetrical radiation fluctuation phases along the flux surface. The fluctuation amplitude is highest at the top, again consistent with the tomography reconstruction results in figure 2 [11].

The question remains as to whether ETRO exhibits density fluctuations. Figure 7 shows the coherence coefficient spectra between two channels from POINT and the reference DR signal used in figure 6. POINT in EAST has 11 chord-averaged horizontal channels [21]. Channel 1, the top chord located at $Z = 42.5$ cm, and channel 11, the bottom chord located at $Z = -42.5$ cm, are illustrated in the bottom panel of
<figure><img src="image_9.png" /><figcaption>**Figure 5.** (a), (c) The original signals from eight toroidal magnetic probes in shots 69976 and 71436, respectively; the averaged values are vertically shifted for clarity. (b), (d) The time-frequency spectrum from one probe.</figcaption></figure>

figure 7. It is unsurprising that a distinct coherence coefficient can still be found at the ETRO frequency for the two channels, indicating that ETRO still contains distinguishable density components. Additionally, like the poloidal distribution of radiation perturbations, the density perturbations produced by

ETRO reach their maximum around the up and down X-point. However, the coherence coefficient of density fluctuation is significantly smaller than that of radiation fluctuation shown in figure 6. Considering that the ETRO peak cannot be estimated directly from the self-power spectrum of the POINT signal,
<figure><img src="image_10.png" /><figcaption>**Figure 6.** (a) Arrangement of the 64-channel XUV array and ray tracing of the DR measurement. Frequency spectra of (b) cross-power, (c) coherence coefficient and (d) cross-phase between four XUV signals and the DR signal during the I-mode.</figcaption></figure>

the relative density perturbation amplitude of ETRO should be below 2% based on the phase noise level of the POINT system [21].

The poloidal distribution of magnetic components of ETRO is shown in figure 9 through coherence analyses between poloidal magnetic probes and one reference DR signal. The intensities and phases along the poloidal direction demonstrate that the *m* = 1 structure dominates the poloidal magnetic components of ETRO, with a significantly lower intensity at the low-field side (LFS) than the high-field side (HFS). Furthermore, the phase folding occurring at approximately *θ* ~ 1.3π implies the existence of other harmonic components [23]. The *m/n* = 1/0 structure is identical to LCO [24] but different from GAM. Both theory and experiment indicate that the magnetic component of GAM is dominated by an *m* = 2 structure [15].

Further evidence is the second harmonics of ETRO, as shown in figure 8, where the peaks at 14–15 kHz can be found from the spectra of the DR phase and soft x-ray and ECE

spectra. As mentioned above, just based on the central frequency values it could be concluded that these peaks should be the second harmonics of ETRO. It needs to be emphasized here that sometimes the GAM frequency closely resembles the second harmonic of ETRO. To distinguish between them, two methods exist. First, increasing the frequency resolution of the power spectrum. Normally, the GAM frequency will not be exactly twice that of ETRO when the frequency resolution is 0.5 kHz or 0.25 kHz, while ETRO and its second harmonic frequency is strictly two-fold. Additionally, GAM is typically not visible in the ECE and XUV spectra, whereas ETRO and its harmonics would dominate the ECE and XUV signals. In our previous paper [11] the ETRO harmonics in the DR phase signal could be well explained as the amplitude asymmetry of turbulence rotation velocity *υ*⊥ resulting from the alternating turbulence transitions $\vec{v}_{\perp} = \vec{v}_{E \times B} + \vec{v}_{pha}$, where $\vec{v}_{E \times B}$ is the plasma $E \times B$ rotation and $\vec{v}_{pha}$ is the turbulence phase velocity, while the second harmonics of GAM were observed only in the bicoherence analyses [25] or for the GAM driven by the
<figure><img src="image_11.png" /><figcaption>**Figure 7.** (a) Cross-power and (b) coherence coefficient spectra between POINT channel 1 and 11 and DR signals during the I-mode. (c) Arrangement of POINT diagnostics. (d) ETRO did not appear in the autopower spectra of POINT signals.</figcaption></figure>

energetic particle [26, 27], further suggesting that ETRO could not be a GAM.

## 4. Turbulence transition accompanied by ETRO

In a previous paper [11], alternating turbulence transitions accompanied by ETRO were presented. In the following, we will show how to separate the two types of turbulence by the direction of ETRO. Figure 10(a) shows the evolution of ETRO obtained by filtering from the DR phase signal, and figure 10(b) illustrates the time-frequency spectra of turbulence during the same period. It can be found that

turbulence within the frequency range of -800 kHz to 200 kHz (electron diamagnetic drift direction) resulted in $v_⊥$ becoming negative, whereas turbulence within the frequency range of 200-600 kHz (ion diamagnetic drift direction) led to $v_⊥$ becoming positive. In the following, we refer to the two types of turbulence as ET and IT for simplicity. From the principle of DR measurement $v_⊥ = v_{E×B} + v_{pha}$, it can be concluded that assuming a constant $v_{E×B}$, $v_⊥$ would lead to varying fluctuation amplitude as ET and IT dominance changes. This explanation clarifies the presence of ETRO's harmonics in the $v_⊥$ spectrum. Then, by the direction of ETRO, we can separate IT from ET. In the simplest way, turbulence is predominantly IT when $v_{ETRO}$ is positive, and predominantly ET
<figure><img src="image_12.png" /><figcaption>**Figure 8.** The power spectra of signals from DR, bolometer, soft x-ray, ECE, Mirnov probe and divertor Langmuir probe in I-mode shot 69327.</figcaption></figure>

when it is negative, as shown by the different colored arrows in figure 10(a). Based on this method, the averaged turbulence spectra corresponding to ET and IT can be obtained, as illustrated in figure 10(c).

Figure 11(a) shows the extreme values of $v_⊥$ plotted against $R/L_e$ during ETRO evolution. Considering that the detected turbulence wavenumber is $k_⊥ = 4–6 \text{ cm}^{-1}$ ($k_⊥ρ_s = 1.2–1.9$) and $\eta_e = L_{n_e}/L_e$ increased significantly during L–I transition, trapped electron mode (TEM) instabilities could be driven at the I-mode edge region by a temperature gradient since $\eta_e > 1$ [28, 29]. Alternatively, given that $\nabla T_i \simeq \nabla T_e$ is plausible [6], an ion temperature gradient (ITG) could also be triggered when $\eta_i > 1$. To calculate the linear growth rates of the ITG and TEM the toroidal gyrokinetic eigenvalue code HD7 [30, 31] was utilized with the following experimental conditions: $R/L_{n_e} = R/L_{n_i} = 9$, $R/L_{T_i} = 20$. The linear growth rates of ITG and TEM intersect around $R/L_e = 39$, as shown in figure 7(b), suggesting a possible occurrence of ITG–TEM

transition at this value, which is consistent with the experimental results.

Based on the linear simulation, it is probable that ET is dominated by TEM and IT is dominated by ITG. A simplified predator–prey model could describe the ETRO cycle as follows: when $\nabla T_e$ exceeds a certain threshold, dominant turbulence changes from ITG to TEM, leading to a sudden increase in the outward particle/energy flux and then a decrease in $T_e$, which in turn causes a shift back to ITG as the dominant mode in the pedestal region. The cycle chain can maintain I-mode confinement for an extended period by keeping $\nabla T_e$ oscillating around the margin. Manz’s study suggested that differences in parallel heat conduction may play a crucial role in the decoupling process of the I-mode, and as long as the dominant turbulence is not ITG other turbulence such as TEM or the microtearing mode are also subject to the heat conduction difference [32]. These findings are in qualitative agreement with the IT/ET transition results, implying that transport
<figure><img src="image_13.png" /><figcaption>**Figure 9.** The poloidal distributions of (a) Mirnov coils, (b) cross-power intensities, (c) coherence coefficients and (d) cross-phases between magnetic fluctuations and the DR signal at the ETRO frequency in shots 69976 and 71436.</figcaption></figure>

decoupling in the I-mode occurs mainly during the emergence of ET. This issue needs further investigation with the help of nonlinear simulations.

Bicoherence analysis is a powerful technique for investigating three-wave nonlinear interaction. The cross-bispectrum $Bi(f_1,f_2) = \langle A_{\text{turb}}(f_1)A_{\text{turb}}(f_2)\nu_{\perp}^*(f_1+f_2)\rangle$ ($A_{\text{turb}}$ is the Fourier transform of turbulence amplitude from DR measurement) [33] during the I-mode can be calculated and the squared bicoherence defined as the normalized cross-bispectrum $bi^2(f_1,f_2) = Bi(f_1,f_2)^2/\langle|A_{\text{turb}}(f_1)A_{\text{turb}}(f_2)|^2\rangle\langle|\nu_{\perp}^*(f_1+f_2)|^2\rangle$ illustrated in figure 12(a). The frequency resolution is 1 kHz in this analysis, and $bi^2(f_1,f_2)$ with $f_1+f_2=f_{\text{ETRO}}$ are all significantly above the noise level. In order to show the couplings at other frequencies more clearly, the values illustrated in figure 12(a) are modified as $\log10(bi^2(f_1,f_2))$. Then it can be found that the values of $bi^2(f_1,f_2)|_{f_1+f_2=f_{\text{WCM}}}$ are also significantly higher than the background noise, indicating the existence of nonlinear couplings between WCM and ambient turbulence. Figure 12(b) shows all the values of $bi^2(f_1,f_2)$ with $f_1+f_2=f_{\text{ETRO}}$. The peaks identified in the figure represent the self-interaction of ETRO, the interaction between its second and third harmonics, between ETRO and WCM, and between ETRO and IT/ET, respectively, indicating significant

nonlinear couplings between ETRO and nearly all turbulence components.

## 5. Center frequency of ETRO

Note that although the GAM always disappears at the location where ETRO is generated it can still be detected at other radial positions. Based on I-mode discharges with ETRO and GAM coexisting, the central frequencies of ETRO and GAM as a function of squared electron temperature near the pedestal top are shown in figure 13, as well as the GAM frequency based on the AUG empirical formula $f_{\text{GAM}} = (Cs/2\pi R_0)4\pi([1+\kappa_b]^{-1} - \epsilon_0)$, where $\kappa_b$ is the boundary elongation and $\epsilon_0 = a/R_0$ [15]. Here we use the temperatures at different positions for the frequency scaling, while the GAM is usually deeper than where ETRO is strongest. Although the electron temperature used here is slightly different than that at the GAM generation location, the proportional relationship between GAM frequency and $C_s$ is still clear. Moreover, it appears that ETRO frequency has a similar trend to GAM, suggesting that ETRO may still be categorized as an ion acoustic model. Considering that the frequency of ETRO is about two
<figure><img src="image_14.png" /><figcaption>**Figure 10.** Temporal evolutions of (a) turbulence rotation velocity $v_{\perp}$ at ETRO frequency and (b) turbulence spectra during the 0.6 ms I-mode in shot 69976. ET means turbulence in the electron diamagnetic drift direction while IT means turbulence in the ion diamagnetic drift direction. (c) The averaged turbulence spectrum and spectra of ET/IT separated through the direction of $v_{\text{ETRO}}$.</figcaption></figure>

to three times smaller than that of GAM, a possible candidate is the low-frequency band of the kinetic GAM, with the theoretical frequency of $f_{\text{GAM}}^{\text{theo}} = 0.2\sqrt{1-1.4/q^2Cs/(2\pi qR_0)}$ [34, 35]. However, a low-frequency GAM is only a theoretical solution considering the finite-gyroradius effect and has never been reported experimentally. For I-mode edge plasmas with $q=4-6$ at the ETRO location, $f_{\text{GAM}}^{\text{theo}}$ is more than an order of magnitude smaller than the standard GAM, which is also inconsistent with the experimental frequency.

To further reveal the nature of ETRO, the temporal evolution of ETRO during I-mode to H-mode transition is illustrated in figure 14, together with data on radiation signal, electron density and corresponding gradient, electron temperature and corresponding gradient,

and the normalized electron collisionality $\nu_{*e}$, defined as $\nu_{*e} = 6.921 \times 10^{-18} q_{95} R n_e Z_{\text{eff}} \ln \Lambda / (T_e^2 \epsilon^{3/2})$, with major radius $R$, effective ion charge $Z_{\text{eff}}$, Coulomb logarithm $\ln \Lambda$ and inverse aspect ratio $\epsilon$ [36]. Pedestal burst instability (PBI) is the transition stage between a stationary I-mode and H-mode and has previously been extensively studied [37, 38]. Approaching the PBI stage, the ETRO frequency declined and ultimately reached approximately 2 kHz. It is important to note that in this process $T_e^{\text{ped}}$ is certainly increased, implying that ETRO cannot be classified as an ion acoustic model, at least in such a non-stationary case. The consistency between the decreased $\nu_{*e}$ and ETRO frequency suggests that ETRO is probably a stationary zonal flow with finite frequency, especially as it ends up with a frequency close to LCO
<figure><img src="image_15.png" /><figcaption>**Figure 11.** (a) $v_\perp$ versus $R/L_{Te}$ from experimental data. (b) The normalized linear growth rate $(\gamma/\omega_e^*)$ of TEM and ITG versus $R/L_{Te}$ from HD7 gyrokinetic simulation.</figcaption></figure>

[14]. However, it should be noted that, after $t = 10.85$ s, $v_{*e}$ remained almost constant but the ETRO frequency decreased more rapidly, indicating the existence of unidentified influencing factors. Consequently, additional research is required to address this issue.

## 6. SMBI fueling effect on ETRO

SMBI [39] is utilized in EAST for fueling and density feedback control. It has been found that even modest SMBI can influence the intensity of ETRO without disrupting I-mode confinement. Figure 15 displays the evolution of ETRO and IT/ET intensities, along with the related rotation velocity shear $\partial v_\perp / \partial r$, $\nabla T_e^{\text{ped}}$ and $\nabla n_e^{\text{edge}}$ during a stationary I-mode in shot 75357. Here SMBI was used to maintain the chord-averaged density at the set value, and the number of SMBI pulses varied

from two to six, each with a pulse interval of 2 ms. As demonstrated in figure 15(b), ETRO intensity decreased significantly after SMBI injection, and the intensity decreased further as the pulse number increased. Figure 15(e) illustrates the evolution of $v_\perp$ shear from the $v_\perp$ radial profile. Usually, if the magnetic field is not excessively large it is possible to have four or five channels inside the last closed flux surface (LCFS), and the radial range of the $v_\perp$ well is approximately 2–3 cm. Note that the velocity shear $\partial v_\perp / \partial r$ is estimated from the inside of the $v_\perp$ well, which is usually located at $\rho = 0.85–0.9$, where ETRO occurs [11, 37]. The velocity shear in figure 15(e), estimated from two adjacent DR channels with about 1 cm spatial resolution each, is significantly reduced by SMBI injection. This decrease is probably due to the neoclassical poloidal flow damping resulting from the edge plasma temperature drop, as shown in figure 15(c). The evolution of the plasma parameters is consistent with other tokamak devices [40, 41].
<figure><img src="image_16.png" /><figcaption>**Figure 12.** (a) The normalized cross-bispectrum $bi^2(f_1, f_2)$; (b) $bi^2(f_1, f_2)$ with $f_1 + f_2 = f_{ETRO}$.</figcaption></figure>

The most interesting result is the opposite evolution of IT and ET with SMBI injection, as shown in figure 15(d). Here IT enhancement is likely due to the weakened flow shear, while the decrease in ET is probably due to the decrease in edge plasma temperature. As illustrated by the simulation in section 4, ET is most likely driven by $\nabla T_e$ in the pedestal region, and the injection of neutral particles from SMBI would directly mitigate the driving source of ET. The decrease in ETRO intensity is a combination of ET decrease and IT enhancement. It should be noted that at $t = 2.74$ s, even two pulses could slightly influence ETRO and IT/ET intensities, further suggesting that SMBI could be an effective tool for

controlling ETRO and turbulence in the I-mode edge plasma region.

## 7. Discussion

The symmetric structure of ETRO strongly suggests that it is probably a kind of zonal flow or field. In toroidal plasmas, two kinds of zonal flow exist [42]: low-frequency (or stationary) zonal flow [43] and GAM [15, 44]. Based on its frequency range of 6–11 kHz, ETRO is more likely to be of the GAM type. However, much experimental evidence indicates
<figure><img src="image_17.png" /><figcaption>**Figure 13.** The central frequencies of the GAM and ETRO versus squared electron temperature near the pedestal top in 20 I-mode discharges with coexisting GAM and ETRO. The dashed line is the empirical formula for AUG.</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Figure 14.** Temporal evolutions of (a) $v_{\perp}$ spectrum from DR, (b) $W_{\text{MHD}}$ and XUV signal, (c) $T_e^{\text{ped}}$ and $\nabla T_e^{\text{ped}}$ at the pedestal region, (d) $n_e$ and $\nabla n_e^{\text{edge}}$ at $\rho \sim 0.9$ and (e) $v_{*e}$ at the pedestal top during I-mode to H-mode transition in shot 101558.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>**Figure 15.** Temporal evolutions of (a) chord-averaged density, SMBI and $W_{\text{MHD}}$ signals, (b) ETRO spectrum and intensity, (c) $T_e^{\text{ped}}$ at the pedestal region, (d) $n_e$ at $\rho \sim 0.9$, (e) rotation velocity shear and (f) ET/IT turbulence intensity in I-mode shot 75357.</figcaption></figure>

that ETRO is not a typical GAM. Figure 16 shows an L–I transition without LHW heating. In this shot, the electron temperature from ECE and the ion temperature from charge exchange recombination spectroscopy [45] in the edge region were both measured. It was observed that during L–I transition both $T_e$ and $T_i$ increased while the chord-averaged $n_e$ remained nearly unchanged. The measured location of the DR edge channel [20] only depends on the density profile and the magnetic field, which remain unchanged during the L–I transition. In the L-mode, the frequency of GAM is approximately 18 kHz, as per the dispersion relationship $\omega_{\text{GAM}} \approx \sqrt{2C_s/R}$, where R and $C_s$

are the major radius and the ion sound velocity, respectively. Then GAM frequency will inevitably increase during I-mode. However, ETRO frequency is just 7–8 kHz and its second harmonic is also below 18 kHz, indicating that ETRO and its second harmonics are both unlikely to be GAM.

In shot 69327, four DR channels are situated inside the LCFS, indicated by vertical dashed lines in figure 17(a); the radial distributions of the GAM during the L-mode and ETRO intensity during the I-mode can then be estimated, as shown in figure 17(b). It can be found that ETRO intensity decays radially outward much more rapidly than inward, which represents
<figure><img src="image_20.png" /><figcaption>**Figure 16.** From top to bottom: temporal evolutions of (a) auxiliary heating power, (b) plasma stored energy $W_{\text{MHD}}$ and $D_{\alpha}$ signal, (c) chord-averaged density, edge $T_e$ and $T_i$, and (d) time-frequency spectrum of turbulence rotation velocity $v_{\perp}$ during L-I transition in shot 69327.</figcaption></figure>

a common feature of ETRO and should be closely related to the turbulent transitions at this location [11]. On the other hand, the outward decay of the GAM in the edge plasmas is expected to be milder, since the GAM propagates outwardly more than inwardly, as has been widely reported in both experiments and simulations [15, 46, 47]. On the other hand, envelope modulation and suppression due to shear flow have been widely reported as the most common interaction between the GAM and turbulence [15]; this is markedly different from the ET/IT transition phenomena, as previously discussed.

The question now remains whether ETRO can be considered a form of LCO, a symmetric structure that arises during L-H transition [14, 24, 48-52]. LCO also possesses harmonics and magnetic components featuring an $m/n = 1/0$ configuration. However, there are certain dissimilarities, as the frequency of ETRO remains higher than LCO and its corresponding temperature/density perturbations significantly differ. LCO has large potential perturbation and modest density perturbation [51]. Table 1 compares the main characteristics of ETRO, GAM and LCO.
<figure><img src="image_21.png" /><figcaption>**Figure 17.** (a) The density profile and the measurement positions of multi-channel DR. (b) The radial distributions of GAM intensity during L-mode and ETRO intensity during I-mode.</figcaption></figure>

<table><caption>**Table 1.** Comparison between ETRO, GAM and LCO.</caption><thead><tr><th></th><th>ETRO</th><th>GAM [15]</th><th>LCO/I-phase/M-mode [52]</th></tr></thead><tbody><tr><td>Scenario</td><td>I-mode</td><td>L-, I-, H-mode [53]</td><td>L–H/H–L transition</td></tr><tr><td>Spatial range</td><td>T<sub>e</sub> pedestal region</td><td>Edge plasma, mainly inside LCFS</td><td>From pedestal to far scrape-off layer</td></tr><tr><td>Frequency range</td><td>6–11 kHz</td><td>Typical 10–12 kHz</td><td>&lt;5 kHz</td></tr><tr><td>Harmonics</td><td>Yes</td><td>No</td><td>Yes</td></tr><tr><td>Frequency scaling</td><td>Seems ∝ C<sub>s</sub> for stationary case but frequency decrease before I–H transition</td><td>∝ C<sub>s</sub></td><td>∝ (B<sub>t</sub><sup>1/2</sup>I<sub>p</sub><sup>3/2</sup>)/(T<sub>e</sub>n<sub>e</sub>) [24]<br>∝ V<sub>Alfven,θ</sub> [50]</td></tr><tr><td>Magnetic perturbation</td><td>m/n = 1/0</td><td>m/n = 2/0</td><td>m/n = 1/0</td></tr><tr><td>n<sub>e</sub> and T<sub>e</sub> perturbation</td><td>T&#x0303;<sub>e</sub>/T<sub>e</sub> ~ 5%–9%</td><td>T&#x0303;<sub>e</sub>/T<sub>e</sub> ~ n&#x0303;<sub>e</sub>/n<sub>e</sub> ~ 0.1%–0.3% [15]</td><td>n&#x0303;<sub>e</sub>/n<sub>e</sub> ~ 0.1%–0.7% [51]</td></tr><tr><td>v<sub>E×B</sub> perturbation</td><td>Unknown</td><td>(ptp<sup>a</sup>) 0.2–1 km s<sup>-1</sup></td><td>(ptp) 3–6 km s<sup>-1</sup> [48]</td></tr><tr><td>Specialty</td><td>Accompanied by ET/IT transition</td><td></td><td>Accompanied by high-frequency mode [52]; two kinds of Lissajous diagram [49, 54]</td></tr></tbody></table>

## 8. Conclusion

Considering that ETRO may have a crucial function in sustaining the stationary I-mode in EAST, the main characteristics of ETRO can be summarized as follows:

(1) The poloidal symmetry of ETRO's radiation perturbation phase can be confirmed through radiation reconstruction (figure 2) or coherent analyses between the XUV array and

DR signal (figure 6). As shown in figure 7 and as measured by ECEI (figure 2), the temperature perturbation of ETRO is much stronger than the density perturbation, allowing for an estimate of the ring structure of the temperature perturbation phase. Additionally, the radiation perturbation has an amplitude up-down poloidal asymmetry, being stronger closer to the active X-point. The poloidal asymmetry of ETRO's amplitude is much like that of GAM, which also has amplitude poloidal asymmetry related to

<footnote><sup>a</sup> ptp means peak to peak.</footnote>
the poloidal dependences of turbulence amplitude and correlation length, and the mean $E \times B$ velocity as well [15].

(2) Direct evidence for the symmetry of the potential perturbation of ETRO has not yet been obtained. However, based on the fact that the pressure sideband of GAM should exhibit an $m/n = 1/0$ up-down asymmetry [15, 42], it is unlikely that ETRO is a GAM.

(3) During L-mode to I-mode transition with edge $T_e$ and $T_i$ both increasing, ETRO would appear with a lower frequency than GAM in the L-mode (figure 16), suggesting that ETRO is not necessarily the successor to L-mode GAM.

(4) ETRO has distinct second harmonics in various diagnostics (figure 8), while the harmonics observed in the $v_⊥$ spectrum are caused by amplitude asymmetry resulting from the different phase velocities of the IT-ET turbulence transition.

(5) The magnetic component of ETRO is dominated by an $m/n = 1/0$ structure (figures 5 and 9), similar to the M-mode in JET and I-phase in AUG [52], but different from the typical $m = 2$ structure of GAM's magnetic component.

(6) Radial propagation differs greatly among ETRO, GAM and LCO. ETRO decays rapidly outward but slowly inward (figure 17), while GAM usually propagates outward and LCO can always be observed in the SOL region.

(7) The primary characteristic of ETRO is the accompanying turbulence transition between IT and ET (figure 10), and a preliminary simulation suggested that ET is probably a TEM and IT is probably an ITG. This differs significantly from the modulation coupling between GAM/LCO and turbulence.

(8) While the statistics of discharges with GAM and ETRO coexistence demonstrate a weakly positive correlation between ETRO frequency and $T_e^{\text{ped}}$, ETRO frequency is typically two to three times lower than that of GAM (figure 13). This result could not be clarified by the current theoretical dispersion relation of a kinetic GAM.

(9) The ETRO frequency decreases quickly and ultimately reaches LCO frequency as the I-mode transitions to the H-mode, with increasing $T_e^{\text{ped}}$ and decreasing $v_{*e}$ (figure 14), indicating that collisional damping also plays a significant role during I-H transition.

In summary, the properties of ETRO are not consistent with the GAM and are also significantly different from LCO. Its frequency is always several times larger than LCO, but two to three times lower than GAM. The most distinctive attribute of ETRO is the accompanying reciprocating transitions of ET/IT turbulence. It is probably a novel type of finite frequency zonal flow or pressure gradient-induced drift, and will be further investigated in future work.

## Acknowledgments

The authors are thankful for fruitful discussions with Professor Guo Zhibin. This work was supported in part by the

Natural Science Foundation of China under Grant Nos. U1967206, 11975231 and 11922513, the National MCF Energy R&D Program under Grant Nos. 2022YFE03010003 and 2018YFE0311200, the Collaborative Innovation Program of Hefei Science Center CAS No. 2022HSC-CIP023, and the Fundamental Research Funds for the Central Universities WK3420000018.

## Appendix

### EAST I-mode Working Group

Y.T. Song<fnref n="1" />, X.L. Zou<fnref n="2" />, E.Z. Li<fnref n="1" />, B. Zhang<fnref n="1" />, Y. Chao<fnref n="1" />, F. Chen<fnref n="1" />, X.Y. Chen<fnref n="3" />, Y.X. Cheng<fnref n="1" />, Y.Q. Chu<fnref n="1" />, B.J. Ding<fnref n="1" />, R. Ding<fnref n="1" />, Y.M. Duan<fnref n="1" />, Y.F. Jin<fnref n="1" />, S.Y. Lin<fnref n="1" />, A.D. Liu<fnref n="3" />, H.Q. Liu<fnref n="1" />, B. Lv<fnref n="1" />, L.Y. Meng<fnref n="1" />, C.M. Qin<fnref n="1" />, H.L. Wang<fnref n="1" />, L. Wang<fnref n="1" />, P. Wang<fnref n="1" />, S.X. Wang<fnref n="1" />, X.J. Wang<fnref n="1" />, Y.F. Wang<fnref n="1" />, Z. Wang<fnref n="1" />, C.B. Wu<fnref n="1" />, T.Y. Xia<fnref n="1" />, L.Q. Xu<fnref n="1" />, G.H. Yan<fnref n="1" />, Y. Yang<fnref n="1" />, L. Yu<fnref n="1" />, F.L. Zhang<fnref n="1" />, L. Zhang<fnref n="1" />, X.J. Zhang<fnref n="1" />, Y. Zhang<fnref n="1" />, X.M. Zhong<fnref n="3" />, R.J. Zhu<fnref n="3" />, G.Z. Zuo<fnref n="1" />.

## ORCID iDs

A.D. Liu https://orcid.org/0000-0002-3164-7320

X.M. Zhong https://orcid.org/0000-0002-1751-111X

M.K. Han https://orcid.org/0000-0001-8735-8440

H.Q. Liu https://orcid.org/0000-0001-6892-358X

E.Z. Li https://orcid.org/0000-0002-3713-4833

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