Experimental and numerical investigation of ICRF
induced low-frequency turbulence reduction across the
scrape-off layer on the EAST tokamak

Wei Zhang, Ghassan Antar, Guillaume Urbanczyk, Yan-Long Li, Xin-Jun Zhang, Lu-Nan Liu, Shao-Cheng Liu, Tian-Yang Xia, Ning Yan, Chu Zhou, et al.

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Wei Zhang, Ghassan Antar, Guillaume Urbanczyk, Yan-Long Li, Xin-Jun Zhang, et al. Experimental and numerical investigation of ICRF induced low-frequency turbulence reduction across the scrape-off layer on the EAST tokamak. Physics of Plasmas, 2024, 31 (3), 10.1063/5.0192870. hal-05018612

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# Experimental and numerical investigation of ICRF induced low-frequency turbulence reduction across the scrape-off layer on the EAST tokamak

Wei Zhang ⚫; Ghassan Antar ⚫; Guillaume Urbanczyk; Yan-Long Li; Xin-Jun Zhang ⚫; Lu-Nan Liu ⚫; Shao-Cheng Liu ⚫; Tian-Yang Xia ⚫; Ning Yan ⚫; Chu Zhou ⚫; Xiao-Ming Zhong ⚫; Kang-Ning Geng ⚫; Jia-Hui Hu ⚫; Yi-Fei Jin ⚫; Hai-Lin Zhao ⚫; EAST Team

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Phys. Plasmas 31, 032502 (2024)

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# Experimental and numerical investigation of ICRF induced low-frequency turbulence reduction across the scrape-off layer on the EAST tokamak

Cite as: Phys. Plasmas **31**, 032502 (2024); doi: 10.1063/5.0192870

Submitted: 20 December 2023 · Accepted: 9 February 2024 ·

Published Online: 4 March 2024

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Wei Zhang,<fnref n="1" />,ᵃ⁾ ID Chassan Antar,<fnref n="2" /> ID Guillaume Urbanczyk,<fnref n="3" /> Yan-Long Li,<fnref n="1" /> Xin-Jun Zhang,<fnref n="1" />,ᵃ⁾ Lu-Nan Liu,<fnref n="1" />,ᵃ⁾ ID Shao-Cheng Liu,<fnref n="1" /> ID Tian-Yang Xia,<fnref n="1" /> ID Ning Yan,<fnref n="1" /> ID Chu Zhou,<fnref n="4" /> ID Xiao-Ming Zhong,<fnref n="4" /> ID Kang-Ning Geng,<fnref n="1" /> ID Jia-Hui Hu,<fnref n="1" /> ID Yi-Fei Jin,<fnref n="1" /> ID Hai-Lin Zhao,<fnref n="1" /> ID and EAST Team<fnref n="1" />

## AFFILIATIONS

## ABSTRACT

In magnetic confinement fusion devices, the plasma particle and energy transport depend on the turbulence transport. Ion cyclotron range of frequency (ICRF) wave heating can interact with the turbulence in the plasma edge and change the turbulence transport. To understand their interaction/correlation, the radial modification of turbulence by ICRF in the scrape-off layer (SOL) was investigated using midplane reciprocating Langmuir probe, reflectometry, Doppler reflectometry, and Divertor probes on the EAST tokamak. We showed a first demonstration that this interaction occurs at all radii and affects the turbulence across the whole SOL. It was observed that ICRF attenuates the large-scale turbulence structures (usually in the form of blobs) by breaking them into smaller ones, leading to a suppression of low-frequency turbulence in the whole SOL. Moreover, this turbulence reduction is accompanied by an increase in the high-frequency turbulence fluctuations and an increase in the poloidal velocity in the SOL. This poloidal velocity is generated by the radial electric field during ICRF. Following this, BOUT++ simulations were conducted, and the simulations results are in line with the experimental results. They show that the RF-sheath induced radial electric field can explain the increase in high-frequency fluctuations and suppression of turbulence in the SOL.

© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0192870

## I. INTRODUCTION

Plasma heating with waves in the ion cyclotron range of frequency (ICRF) is widely used to heat the plasma in tokamaks and is considered to be one of the main heating methods for future machines, such as SPARC,<fnref n="1" /> CFETR,<fnref n="2" /> and ITER.<fnref n="3" /> ICRF launches radio frequency (RF) waves into the plasma by antennas positioned at the plasma periphery. They propagate through the scrape-off layer (SOL) before heating the plasma core. Consequently, the RF waves interact with the SOL and edge turbulence. Understanding the RF wave-turbulence interaction is of major importance not only for fusion devices but also for space plasmas where waves interact with turbulence.<fnref n="4" />,⁵

The reduction in turbulence across the separatrix and large transport events, such as edge-localized modes (ELMs), remain key for the current and future magnetic confinement fusion devices, such as tokamaks and stellarators. It enables the control of the particles and the

power that is leaving the confined zone as well as the plasma-wall interaction. Reducing turbulence leads to better control of the plasma density and plasma performance.

Previously, the effects of ICRF on edge plasmas were studied by a wide variety of authors, to cite a few.⁶⁻¹³ It was shown that ICRF generates flows at the plasma edge that extend from the SOL into the plasma edge. They are localized in the radial-poloidal plane in front of the antenna and extend toroidally along the field lines. Progress has been made in understanding the relationship between RF waves and SOL turbulence. Since the first observation of a turbulence decrease when applying ICRF,¹⁴ progress has been made in understanding the relationship between RF waves and SOL turbulence. Large-scale structures, known as blobs or avaloids, were mostly shown to decrease in this process.¹⁵⁻¹⁷ Results obtained on the ASDEX-Upgrade tokamak are in H-mode¹⁸ whereas those for Tore Supra are in L-mode¹⁹ and

<footnote n="1">¹Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, China</footnote>

<footnote n="2">²Physics Department, American University of Beirut, Beirut 11072020, Lebanon</footnote>

<footnote n="3">³Institut Jean Lamour, UMR 7198, CNRS - Université de Lorraine, 2 allée André Guinier, F-54011 Nancy, France</footnote>

<footnote n="4">⁴School of Nuclear Sciences and Technology, University of Science and Technology of China, Hefei 230026, China</footnote>

<footnote>ªAuthors to whom correspondence should be addressed: zw@ipp.ac.cn; xjzhang@ipp.ac.cn; and liulunan@ipp.ac.cn</footnote>
recently in H-mode for the EAST.¹⁸ The effects were detected when the probes were magnetically connected to the active antenna.¹⁶ Moreover, turbulent transport induced by edge localized modes (ELMs) can also be significantly reduced by ICRF.¹⁸,¹⁹ A reduction in turbulence in the SOL was also observed with lower hybrid waves,¹⁶,²⁰ where the plasma current played an important role.

In addition, previous simulations indicated that ICRF fast wave could be scattered by filamentary structures.²¹⁻²⁴ Moreover, these filamentary structures can induce ICRF mode conversion from fast to slow waves.²⁵,²⁶ These effects would decrease the RF efficiency in heating or current drive.

The aforementioned studies mostly use Langmuir probes at fixed positions in the far SOL. In this study, we investigate the RF wave-turbulence interaction across the whole SOL as a function of radial position using midplane reciprocating Langmuir probe, reflectometry, Doppler reflectometry and divertor probes on the EAST tokamak. ICRF influences the turbulence in the entire SOL, accompanied by a decrease in low-frequency fluctuations and an increase in high-frequency fluctuations.

## II. EXPERIMENT SETUP

EAST is a middle-sized tokamak with major and minor radii of about 1.85 and 0.45 m, respectively. It usually operates with a toroidal magnetic field of $B_T = 2.4$ T and a plasma current of $I_p = 0.4–0.6$ MA. In our studies, $B_T$ and $I_p$ are in the clockwise and counterclockwise direction, respectively. Double-null magnetic configuration is used for the studies in Secs. II and III, while the divertor probe database in Sec. IV includes both double-null and single-null magnetic configurations. The auxiliary heating methods include ICRF, lower hybrid (LH), electron cyclotron (EC) range of frequency wave heating and neutral beam injection (NBI), with a total heating power capability larger than 15 MW. It is worth mentioning that since 2020, both I-port and N-port ICRF antennas are upgraded to the new 2-strap antennas by increasing the toroidal distance between straps from 0.225 to 0.425 m.²⁷ This leads to a decrease in the parallel wave number from $k_‖ = 13–14$ to $7.5 \times 10^{-1}$ for the (0, pi) phasing and a decrease in fast wave cutoff density from $\sim 8 \times 10^{18}$ to $2.8 \times 10^{18} \text{ m}^{-3}$. Consequently, the fast wave evanescent layer is decreased by at least 3 cm and the coupling resistance is increased by a factor of about 2. The discharges used in Secs. II and III are all heated with the new ICRF antennas.

In our study, a series of diagnostics were used to measure the SOL turbulence, including the midplane reciprocating Langmuir probe, reflectometry, Doppler reflectometry, and divertor Langmuir probes. The locations of the diagnostics are shown in Fig. 1. In the experiments, the reciprocating Langmuir probe was injected from a position outside of the plasma into the near SOL, thus measuring turbulence in a broad range of the SOL. The reflectometry and Doppler reflectometry used deliberated channels such that the measurement positions are in the SOL or near the separatrix. The divertor probes are distributed along the target plates and naturally measured turbulence at different radial positions in the SOL. With these settings, the influence of ICRF on turbulence at different radial locations in the SOL were investigated.

A series of dedicated discharges were performed for this study, among which #103 790–103 799 and #107 106–107 111 were used in Secs. II and III. A typical plasma scenario (#107 109) is shown in Fig. 2. The plasma current (350 kA), line averaged edge plasma density

($\sim 1.5 \times 10^{19} \text{ m}^{-3}$), and core electron temperature are roughly the same throughout the discharge. In contrast, the core ion temperature becomes larger when ICRF power is switched on, leading to an increase in plasma stored energy and poloidal beta. The core plasma density is also increased due to the enhanced impurity production by ICRF. The midplane reciprocating probe plunges into the SOL for the cases without ICRF, with ICRF-I and with ICRF-N heating. No perturbation of the core or edge plasma density is recorded during the three probe plunges. The plasma position and the magnetic configuration are also unchanged during the two pulses of ICRF and the probe plunges [Fig. 1(b)]. The $D_\alpha$ signal from the upper divertor shows a strong emission reduction in the presence of ICRF. Previous experimental and theoretical studies¹⁹,²⁸ suggest that this effect is owing to the ELM suppression by larger electric field ($E_r$) shear in the SOL. The observed energy confinement time [Fig. 2(f)] is unchanged by ICRF, suggesting that the SOL turbulence modification by ICRF has little influence on the core confinement in this particular set of experiments.

It is important to understand whether the diagnostics have magnetic field line connections with the active ICRF antennas, such as to determine if the influence of ICRF on turbulence is local or global. Note that the magnetic field line connections in the paper also include the field lines passing in front of the active antenna in the SOL. First, the reciprocating Langmuir probe, reflectometry, and Doppler reflectometry are all located in the K-port, which is between ICRF-I and ICRF-N antennas. Field line tracings (Fig. 3) show that these three diagnostics are all magnetically connected to both the ICRF-I and ICRF-N antennas. Thus, they could not be used to determine if the influence on turbulence is global. The divertor Langmuir probes are situated in the D, P, and O-ports. Probes, which are close to and far from the separatrix in the SOL, are chosen for magnetic field line tracings, namely, the divertor U09 and U01 probes, respectively. The results in Fig. 3(b) show that the U09 probe has magnetic field line connections with both the antennas while the U01 probe only has magnetic field line connections with the ICRF-I antenna. Moreover, although the magnetic field lines from U01 probe are not directly connected to the ICRF-N antenna, they are only a few centimeters away from the antenna in the poloidal direction. Previously studies suggest that the maximum sheath potential and largest density modification caused by an active antenna are often near the antenna box corners.⁸ Thus, these field lines may capture the influence from the active antenna and affect the turbulence measured by the divertor probe. On the other hand, it should be noted that these field line connections depend strongly on the plasma equilibrium; thus, they can be obviously different for different discharges. In other magnetic configurations, it is possible that divertor probes close to the separatrix can also have magnetic field line connections with only one of the ICRF antennas.

## III. RADIAL TURBULENCE MODIFICATION BY ICRF

To understand the radial turbulence modification by ICRF, the midplane reciprocating Langmuir probe data are analyzed first. This probe is injected from a position behind the first wall to a position $\sim 1.6$ cm away from the separatrix. The probe tip is biased with a constant voltage of $-200$ V and the ion saturation current ($I_{sat}$) is recorded at a sampling rate of 1 MHz. For the first time, the reciprocating Langmuir probe data showing the effect of ICRF on turbulence at different radial locations in the SOL are presented. In Fig. 4(a), $I_{sat}$ and $-I_{sat}$ are plotted as a function of time for the cases without and with
<figure><img src="image_11.png" /><figcaption>FIG. 1. (a) Top and side views of the EAST tokamak, showing the toroidal locations of RF heating systems and essential diagnostics. The locations of the reciprocating probe, reflectometry, Doppler reflectometry, divertor probes, divertor visible spectrometer (measuring $D_z$) in the poloidal cross section are shown in (b)–(d), respectively.</figcaption></figure>

ICRF, respectively. By adding ICRF, a strong reduction in the intermittent bursts is reported, which in agreement with previous results obtained in L-mode²⁹ and H-mode generated by neutral beam injection.³⁰ Moreover, the largest reduction in turbulence happens around the leading edge of the antenna limiter or a bit behind. This is in the same region where the largest RF-sheath rectified potential or RF-induced convective cells occurs.⁷,³¹ The net decrease in the turbulence amplitude is quantified in Fig. 4(c) where the standard deviation of ion saturation current (i.e., $\delta I_{sat}$) is plotted as a function of distance to the separatrix (i.e., $r$). The fact that the turbulence decrease at the radii along the stroke of the reciprocating probe is confirmed.

It was reported that the large-scale turbulence with large radial velocities that cause the intermittency of the signals in the far SOL are reduced while the high-frequency component increases in the presence of ICRF.¹⁵,¹⁶ The level of intermittency was quantified using the

skewness and the flatness factors, which are the normalized third and fourth-order moments, respectively. As intermittent bursts lead to more positive than negative fluctuations, this leads to an asymmetric probability distribution function (PDF) and, thus, a skewness factor ($S$) greater than 0. These bursts also lead to a PDF with more high-intensity events than what is predicted by a normal distribution, thus, a flatness factor ($F$) greater than 3. In Figs. 4(d) and 4(e), the skewness and flatness as a function of $r$ are plotted, and they are far from 0 to 3 in the far SOL, respectively. The decrease in intermittency is reported at all radii in the near and far SOL.

In addition, probe plunges were recorded in the presence of ICRF that is launching with different phases between the straps ($\Phi$) of the antenna, with values ranging from 45° to 260°. The effects of $\Phi$ on turbulence are studied with the statistical moments averaged for $r \in [15, 25]$ mm and for $r \in [55, 65]$ mm. The former range is defined as the
<figure><img src="image_12.png" /><figcaption>FIG. 2. A typical plasma scenario used in the study. (a) Plasma current, edge and core line averaged density. (b) Radial positions of the reciprocating Langmuir probe, antenna limiter, and separatrix. (c) Heating power of the lower hybrid (LH) and electron cyclotron (EC) range of frequency waves and ICRF. ICRF-I and ICRF-N represent ICRF antennas in the I-port and N-port, respectively. (d) Electron and ion temperature. (e) Plasma stored energy and poloidal beta. (f) $D_\alpha$ and energy confinement time $\tau_E$.</figcaption></figure>

near SOL and the latter as the far SOL, and they correspond to the two spatial regions that are highlighted in Fig. 4.

The results (Fig. 5) show that the averaged $I_{sat}$ decrease by 43% and 50%, and the density fluctuations decreases by 40% and 30% in the near and far SOL, respectively. The skewness decreases from 2 to 0.4 in the near SOL and from 5.5 to 1.6 in the far SOL. The flatness factor decreases from 11 to 4.2 in the near SOL and from 58 to 7 in the far SOL. It is indicated that the near and far SOL have similar behavior in the presence of ICRF, though with different level of turbulence decrease. The turbulence modification is independent of the ICRF antenna used. However, there is not obvious correlation between the turbulence modification and antenna phasing.

Reflectometry is a method by which the plasma density is inferred from the phase delay of the electromagnetic wave that is reflected by a plasma cutoff$^{5,33}$ after being emitted from the edge. The phase can be put in the form $Phase(\omega) = 2\omega/c \int_{r_0}^{r_c} N(\omega, r)dr$, where N is the plasma index of refraction and $r_0$ and $r_c$ are the radial position of the plasma boundary and cutoff layer, respectively. The multichannel reflectometry has four probing frequencies (20.4, 24.8, 33, and 40 GHz) with O-mode launched from the low-field side of the tokamak. It measures fluctuations at four different radial positions in the SOL. The reflectometry is located at 16 cm below the mid-plane with

the line-of-sight perpendicular to the magnetic field. The sampling frequency of the reflectometry is 2 MHz.$^{34}$

The power spectra of the measured reflectometry signal are shown in Fig. 6(a), where the four O-mode channels measure the SOL at $r = +16, +36, +55$, and $+63$ mm. The time trace of ICRF power is also shown so that one can recognize how the reflectometry signal changes in its presence. The results of the four channels clearly show that the high frequency fluctuations are increased during ICRF.

The initial power spectra in the absence of ICRF are different for the four channels. In order to compare the power spectra modifications in the presence of ICRF, the power spectra with ICRF are divided by those without for each channel. The results [Fig. 6(b)] confirm that the high frequency fluctuation is increased by ICRF. This behavior is more prominent as the measured regions moves from the near SOL to the far SOL, and it is accompanied by a decrease in the low frequency fluctuations at $r = +55$ and $+63$ mm. Since most of the power in the turbulent fluctuations is in the low-frequency components, this leads to the net decrease in the density fluctuations in the SOL.

To have a direct comparison with the Langmuir probe signals, we determine the power spectra of midplane reciprocating probe measured $I_{sat}$ on which we perform the same calculation procedure as the reflectometry. The results [Fig. 6(c)] show the tendency of increasing
<figure><img src="image_13.png" /><figcaption>(a) Field line tracing for K-port diagnostics</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>(b) Field line tracing for D-port UO probes</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>(c) Field line tracing for O-port UO probes</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>(d) Tracing points</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>(e) ICRF antenna</figcaption></figure>

<caption>FIG. 3. Magnetic field line tracings for (a) the reciprocating Langmuir probe, Doppler reflectometry, and reflectometry; (b) upper-outer divertor probes in the D-port; (c) upper-outer divertor probes in the O-port; (d) field line tracing starting points for the divertor probes U01 and U09 in the poloidal cross section; and (e) ICRF-N antenna in the torus.</caption>

of the high frequency component of the fluctuations and decreasing of the low ones. This is in agreement with the reflectometry data.

It is worth mentioning that the SOL plasma density profile is also modified by ICRF, as shown in Fig. 7. Both discharges (#107 109 in H-mode and #103 795 in L-mode) suggest that in the presence of ICRF, the near SOL density is decreased while the far SOL density increases. The density modifications by the two antennas are roughly the same. Previous theories and experiments indicate that this type of density modification is due to the generation of density convective cells in the SOL, which is caused by the ICRF sheath rectified potential.⁷,³¹,³⁵,³⁶ This RF potential can generate $E_r$ shear and convective cells in the SOL. These convective cells are usually localized in front of the active antennas and extended toroidal along the magnetic flux tubes. They usually have a radial extension of a few centimeters and center at the antenna limiters.⁷,⁹,¹²,¹³,³⁷,³⁸ Moreover, the convective cells with largest velocity and spatial size are usually found around the top and bottom corners of the antenna limiters. They can enhance the

poloidal shear velocity in the SOL, which is in the same order as the diamagnetic drifts. The enhanced poloidal velocity can distort or even split the large-scale low-frequency turbulence structures, such as blobs³⁹ and change the turbulence behavior.

On the other hand, since the radial positions of cutoff layers of the O-mode channels depend on the density profiles, a significant change of the SOL density profiles may change the radial measurement positions. The density profiles in Fig. 7 show that the largest shift of radial position caused by density modification is ~0.9 cm. It is expected that this change of SOL density will not significantly influence the turbulence measurement positions of reflectometry O-mode channels.

It is worth mentioning that the ICRF-induced density modification shown in Fig. 4(b) is different to the one in Fig. 7. The reason is not totally clear but the following mechanisms are expected. First of all, the measured ion saturation current shown in Fig. 4(b) is both proportional to the density and square root of plasma temperature. It can
<figure><img src="image_18.png" /><figcaption>**FIG. 4.** (a) The reciprocating Langmuir probe measured $+I_{sat}$ and $-I_{sat}$ as a function of time, in which the red and blue lines are the cases with and without ICRF, respectively. The beginning time of probe plunging $t_0$ is subtracted from the time $t$. Note the strong reduction of the spikes when ICRF is present. In (b)–(e), the average, standard deviation, skewness, and flatness of $I_{sat}$ are plotted as a function of the radial position of the probe, respectively. $r$ is the distance to the separatrix. The two vertical dashed lines indicate the positions of the separatrix and antenna. The two shaded rectangles indicate the radial positions of near ($r \in [22, 32]$ mm) and far SOL ($r \in [60, 70]$ mm).</figcaption></figure>

be influenced by the SOL temperature besides density. Moreover, the powered ICRF antenna can induce convective cells in front of the antenna and cause poloidal inhomogeneous density. Since the reciprocating probe and reflectometry are measuring density at different poloidal locations, their measured density profiles should be different. In fact, convective cells and strong poloidal density variation caused by power ICRF antenna were also observed in devices, such as ASDEX Upgrade.³¹ On the other hand, the SOL density measured by

reflectometry is influenced by the cutoff density. The density profiles measured by each diagnostic may not be quantitatively correct, but the trend of density modifications should be fine.

In addition to the reflectometry, Doppler reflectometry is also a non-perturbative diagnostic to characterize turbulence in the SOL.⁴⁰,⁴¹ It launches a set of microwaves into the plasma from the low-field side that are reflected at the cutoff layers. At each reflection layer, while the wavenumber of the wave goes to 0, it matches the values of the local
Shots 107109, 107110, and 107111, 15<r<25 mm, and 55<r<65 mm

<figure><img src="image_19.png" /><figcaption>FIG. 5. The average, standard deviation, skewness and flatness factors of $I_{sat}$ are shown for the near SOL (a1)–(d1) and far SOL (a2)–(d2). x-axis is the phase between the two straps of the ICRF antennas. Different colors represent different discharges. The filled circles are the results without ICRF.</figcaption></figure>

turbulent wavenumbers. This leads to a strong Bragg scattering signal at the wavenumber where turbulence is maximum ($k_{max}$). The signal is, thus, radially localized in space at the cutoff position $r_{cutoff}$ and is proportional to the Fourier transform of the density fluctuations $n(k_{max}, t)$. Ray tracing simulations are used to calculate the scattering location and the perpendicular wave number.42–44 The net convection of the plasma in the direction of the wavevector leads to a shift of the frequency spectra ($S(\omega)$) leading to a maximum signal at an angular frequency $\omega$ that is positive (negative) for convection that is parallel (anti-parallel) to $\bar{k}_{max}$. Using $k_{max}$, the poloidal convection velocity can be determined by $U = (1/k_{max}) \int \omega S(\omega) d\omega / \int S(\omega)$.

To characterize the modification of turbulence at different radial positions, the relative changes of the density fluctuations were calculated with $(dn(t) - dn(0))/dn(0)$, in which $dn(t)$ and $dn(0)$ are the density fluctuations with and without ICRF, respectively. The results are shown in Fig. 8(b1), indicating that the level of fluctuations both inside the separatrix (negative r's) and in the SOL (positive r's) change during ICRF. To quantify the radial dependence of these changes, the

level of fluctuations at $t = 5.6$ s (with ICRF) were plotted in Fig. 8(c). A slight increase in density fluctuations is seen inside the separatrix. As the measured region moves into the SOL, a net decrease is detected. This is in agreement with the reflectometry and the reciprocating Langmuir probe data, and confirms that ICRF affects turbulence across the SOL.

Similarity, the normalized velocity fluctuation is calculated with $(dU(t) - dU(0))/dU(0)$, where $dU(t)$ and $dU(0)$ are the perturbation of poloidal velocity with and without ICRF, respectively. Its dependence on time for different radii is plotted in Fig. 8(b2), showing that it increases mainly in the SOL by 40% during ICRF, and this increase is in the direction opposite to $\bar{k}_{max}$. In the far SOL, the increase is about 15% but in the same direction as $\bar{k}_{max}$. The radial dependence of the average velocity change is plotted in Fig. 8(c), which reflects the onset of a strong poloidal velocity shear.

To describe the change of poloidal velocity more clearly, the absolute value of the poloidal velocities in the SOL were calculated and shown in Fig. 9. In the presence of ICRF ($t = 5.5$ s), a significant
<figure><img src="image_20.png" /><figcaption>FIG. 6. (a1)–(a4) The power spectra of the reflectometry signal as a function of frequency f and time t. The four O-mode channels with f = 40, 33, 24.8, and 20.4 GHz measure the SOL with r = 16, 36, 55, and 63 mm, respectively. r is the distance to the separatrix. The black line shows the ICRF power in arbitrary units. (b) The power spectra normalized by the spectra in the absence of ICRF power. (c) The same normalization for the power spectra of the I\_sat data. The studied discharge is \#103 795, which is a L-mode.</figcaption></figure>

increase in poloidal velocity ($v_p$) in the diamagnetic direction is seen in most of the SOL. The largest $v_p$ is -1.5 km/s, which is in the same order as the poloidal velocity in the pedestal region of a H-mode. In addition, $v_p$ changes its sign at r = 0.03 m. Consequently, the inhomogeneous shear poloidal velocity in the SOL can interact with the large turbulence structures, splitting them and generating smaller turbulence structures. This is considered as one of the most probable mechanisms for the reduction of large-scale turbulence structures and the ultimate decrease in turbulence in the SOL. In fact, this assumption is consistent with the previous experimental observations in ASDEX Upgrade, where big blobs were detected to be distorted or broken up by the poloidal shear flow in the presence of ICRF.<sup>39</sup>

## IV. STATISTICAL ANALYSIS OF DIVERTOR PROBE DATA

In this section, further evidence of the influence of ICRF on SOL turbulence is presented with the divertor Langmuir probe data.

According to the field line tracings (Fig. 3), the D-port UO09 probe, which is close to the separatrix, has magnetic field line connections with both ICRF-I and ICRF-N antennas. However, the D-port UO01 probe which is far away from the separatrix only has magnetic field line connections with the ICRF-I antenna. The turbulence properties as a function of time are analyzed for the two probes. The results (Fig. 10) show that whether the probe has magnetic field line connections with the active antenna or not, the normalized standard deviation, skewness, and flatness of the ion saturation are decreased when the ICRF power is switched on. Consistent with the experimental results presented in the previous section, this indicates the reduction of SOL turbulence by ICRF. The influence of ICRF on turbulence is not limited to the regions which have magnetic field line connections with the antenna, indicating the influence of ICRF on turbulence is a global effect. On the other hand, even if the divertor probes have magnetic field line connections with the active antenna, they are at least 30 m
<figure><img src="image_21.png" /><figcaption>FIG. 7. (a1) Electron density and (a2) ion temperature of #107 109 at the time slices of t = 8, 12, and 18 s. A zoom of the SOL density is also shown in (a1). (b1) Electron density and (b2) the density in log scale of #103 795 at time slices of t = 5.2, 5.5 s. The two vertical dashed lines represent the two separatrix positions (#10 375 is double null configuration). ρpol is the square root of the poloidal magnetic flux.</figcaption></figure>

away from the antenna in the toroidal direction. The antenna may not be able to directly affect the turbulence along field lines in such a long distance. This provides another indication that the ICRF influences the SOL turbulence globally. It is worth mentioning that the RF-induced convective cells often occur in magnetic tubes connected to the active antenna while the reduction in turbulence happens in the whole SOL. The former can cause obvious local density modifications, but the latter does not necessary lead to an apparent SOL density change.

To have a more statistical understanding of the influence of ICRF on turbulence, a database was built by including over 3000 of the most successful EAST discharges from 2018 until 2023. Despite the numerous changes and upgrades in the vessel over the years, Langmuir probes embedded in the upper divertor inner and outer targets were not modified,⁴⁵ making them the only edge diagnostics to offer great

enough consistency to statistically investigate the influence of ICRF on the edge plasma.

For each discharge plateau—defined through a condition on the plasma current—and a time step of 0.15 s, the position of the strike points at the upper divertor inner and outer targets was tracked based on magnetic reconstruction. For each time step, the most relevant location to look at ion saturation currents is considered the closest to the strike points. We, therefore, chose to focus the present analysis on these probes.

Regarding the consistency of the data over a full experimental campaign, it is worth to mentioning that the data collected by probes may undergo some changes. Some of the changes, such as the evolution of the collection surface due to the partial erosion of the tips, were taken into account during probes calibration and data treatment.⁴⁶ However, some other inherent changes, for instance due to lithium
<figure><img src="image_22.png" /><figcaption>**FIG. 8.** Results obtained with Doppler reflectometry. (a1) The density fluctuation and (a2) the velocity fluctuation. (b1) The normalized density fluctuation $(dn(t) - dn(0))/dn(0)$ and (b2) the normalized velocity fluctuation $(dU(t) - dU(0))/dU(0)$ as a function of time for different radial positions. $dn(0)$ and $dU(0)$ are averaged values around $t=5$ s. The ICRF heating power is plotted in black dashed lines. (c) The normalized density and velocity fluctuations (values at $t=5.6$ s normalized to values at $t=5.0$ s) as a function of radial position. $r$ is the distance to the separatrix. The studied discharge is #103 795.</figcaption></figure>

coating, were not considered. Nevertheless, the parameter studied here is derived from ion saturation currents normalized by similar quantities, namely, the cross correlation of adjacent probes which is calculated by $Cx_{12} = \max_{\tau}((I_1(t) \cdot I_2(t+\tau))/((I_1^2)\langle I_2^2 \rangle)^{1/2})$ with $0 < \tau < 0.15$ s. In this way, this parameter becomes dimensionless and shows little sensitivity to the above-mentioned changes.

The statistical results are shown in Fig. 11. For the $Cx_{12}$ values, the closer to 1, the better correlated are the probes data. Divertor probes being about 2 cm distant from each other and radially along the tile surface, for cross correlation close to 1, it basically means that they see similar plasma, and that the edge is dominated with large structures (>2 cm). When the cross correlation drops closer to zero, it means
<figure><img src="image_23.png" /><figcaption>FIG. 9. Poloidal velocity measured by the Doppler Reflectometry. r is the distance to the separatrix. The studied discharge is #103 795.</figcaption></figure>

that probes start seeing substantially different plasma, so that the edge becomes dominated with small structures (<2 cm).

On the inner strike point, cross correlation values are well-spread between 0 and 1 regardless of the level of ICRF power. On the outer strike point, however, as the ICRF power increases, cross correlation converges toward small values (around 0.2).

<figure><img src="image_24.png" /><figcaption>FIG. 10. The ICRF power, ion saturation current, normalized standard deviation, skewness, and flatness of the ion saturation current for the UO01 and UO09 probes, which are located in the upper outer target and in the toroidal D-port. The UO01 probe has magnetic field line connections with the ICRF-I antenna while the UO9 probe has magnetic field line connections with both antennas.</figcaption></figure>

Observations at the outer strike point suggest that ICRF can act upon the transport in the edge by breaking large structures into smaller ones. However, this behavior is not observed at the inner target. We believe that this difference is the result of more straightforward magnetic connections between active ICRF antennas and the outer target rather than the inner target, which would be consistent with observations in other devices like ASDEX¹⁵ and Tore Supra.¹⁶ Further details on the influence of ICRF on the edge plasma near divertor targets will be addressed in a future study.

V. SIMULATION RESULTS

To have a better understanding of ICRF-turbulence interaction, we performed numerical simulations with BOUT++ framework, which has successfully simulated the evolution of edge turbulence.⁴⁷,⁴⁸ During ICRF, the RF rectified sheath can produce an enhanced and spatially inhomogeneous sheath potential, which changes the radial electric field $E_r$ in the SOL. Based on the experimental results shown in the previous sections, this $E_r$ shear is considered as one of the most probable mechanisms causing turbulence reduction in the SOL. To properly take this into account, the edge turbulence and the nonlinear interactions of fluctuations were simulated with the Six-field two-fluid model¹⁴⁸ which covers the dominant MHD physics. The two-field model⁴⁹ in the BOUT++ framework is used to calculate RF sheath rectified potential and, thus, the equilibrium electric field that results from the imposed direct current bias potential driven by the RF sheath.

<figure><img src="image_25.png" /></figure>
<figure><img src="image_26.png" /><figcaption>FIG. 11. Cross-correlation $C_{X12}$ of probes adjacent to the inner and outer strike points on the upper divertor. The color bar shows the level of ICRF power. The studied discharges including both L-mode and H-mode.</figcaption></figure>

The model is 2D, including the radial and poloidal direction, and the RF-sheath effects are mainly limited to a bunch of open magnetic field lines passing in the vicinity of active ICRF antennas. No experimental RF sheath potential is used because of the lack of correlated diagnostics. Figure 12 only shows the radial electric field at the outer midplane. However, the electric field contains a poloidal distribution in the model.

Since the RF frequency is much higher than the turbulence frequency, the RF sheath potential in the SOL can be written as the sum of the Bohm sheath potential and the RF wave potential. Finally, in the model, it is found that a positive electric field forms in the SOL and is smoothly connected across the last closed flux surface to the flow-balanced electric field within the pedestal. The force-balance $E_r$ (without RF sheath) and the RF sheath $E_r$ (with RF sheath) shown in Fig. 12 are used for the case with ICRF and without ICRF, respectively.

We choose the time moment at 5.5 s of shot #103795 for the simulations. The input plasma parameters, including the electron density and temperature profiles, are obtained from diagnostics, such as Thompson scattering and reflectometry. Figure 13 gives the input profiles in the 2-field model, which come from the experimental

measurements. Based on these profiles, we can get the RF sheath electric field $E_r$, which will be used as the input of the turbulence model$^{47}$ to analyze the influence of ICRH on the edge turbulence.

The comparison of skewness of the density fluctuations in the outer midplane are depicted in Fig. 14(a). It can be clearly seen that when including RF sheath $E_r$, the high-frequency component of density fluctuation is significantly enhanced, and the skewness of density fluctuation in the SOL is effectively reduced. While the skewness of measured ion saturation current are all positive values, both positive and negative values of skewness are seen in the simulation. This is because in the simulations, the density fluctuations have both positive and negative values around the outer mid-plane. Figure 14(b) gives the power spectra with RF sheath normalized to the spectra without RF sheath. The simulation results are consistent with the experiments, indicating that a larger $E_r$ shear in the presence of ICRF can lead to the turbulence reduction in the SOL.

To better explain the physical mechanism, we display the poloidal contour plots of the ion density fluctuations with and without RF sheath, as shown in Fig. 15. During ICRF, the enhanced shear flow induced by RF sheath will break up the wave packets, and the strong $E \times B$ shear rate can make the large-scale low-frequency turbulence into small-scale turbulence. Additionally, the nonlinear mode coupling will become stronger with ICRF. There are more high $n$ modes coupled, which can effectively compete the free energy with the low $n$ modes. Here, $n$ is the toroidal mode number. Therefore, the strong nonlinear wave-wave interactions lead to the lack of the dominant modes and the existence of high-frequency fluctuations.

## VI. CONCLUSIONS

Understanding the influence of ICRF on SOL turbulence and using ICRF to control SOL turbulence is important for fusion machines. In this paper, the midplane reciprocating Langmuir probe, reflectometry, Doppler reflectometry, and divertor probes were used to investigate the modification of SOL turbulence by ICRF as a function of radial positions. Among them, the reflectometry and Doppler reflectometry are non-perturbative diagnostics and were used for the first time for this topic. The conclusions made with different diagnostics

<figure><img src="image_27.png" /><figcaption>FIG. 12. The equilibrium electric field profiles at the outer mid-plane. $\psi$ is the poloidal magnetic flux.</figcaption></figure>
<figure><img src="image_28.png" /><figcaption>FIG. 13. (a) The simulation domain: the red curve is the last closed flux surface, the black curves are the inner and outer boundaries, the 64 poloidal blue curves represent the simulation grids. (b) The pressure profile. (c) The density profile. (d) The electron and ion temperature.</figcaption></figure>

are consistent, showing that ICRF suppresses the low frequency turbu-
lence across the whole SOL. The low-frequency component of fluctua-
tion is decreased while the high-frequency component of fluctuation is
increased. Statistical studies with the divertor probe data suggests that

the decrease in the low frequency turbulence level is mainly due to the
splitting of low-frequency large-scale turbulence structures (such as
blobs) into smaller ones. The SOL low frequency turbulence is
decreased even if the considered probe does not have magnetic field

<figure><img src="image_29.png" /><figcaption>FIG. 14. (a) The skewness for the cases without and with ICRF. (b) The power spectra with ICRF normalized to the one without ICRF.</figcaption></figure>
<figure><img src="image_30.png" /><figcaption>FIG. 15. The poloidal contour plots of the ion density fluctuations without RF sheath and (b) the ion density fluctuations with RF sheath.</figcaption></figure>

line connections with the active antenna, indicating that the effects of ICRF on turbulence are global.

Moreover, the poloidal velocity measured by the Doppler reflec-
tometry is shown to be significantly increased when ICRF is switched
on. It is generated by the ICRF induced radial electric field shear and is
in the same level as the one in the pedestal of a H-mode. This radial
electric field shear is considered as one of the most probable reasons
that causing turbulence reduction in the SOL. Furthermore,
BOUT++ simulations were carried out and the results are consistent
with the experiments. They show that the large-scale turbulence struc-
tures are broken into small-scale ones by the radial electric field shear
in the SOL, and this radial electric field shear is supposed to be gener-
ated by the RF-rectified sheath potential. The simulations also indicate
that the radial electric field shear induced nonlinear coupling of high-n
modes can further lead to the increase in high-frequency fluctuations
in the SOL.

In the paper, the ICRF induced turbulence reduction is found
across the whole SOL. A reduction in the transport in the SOL is
expected to lead to a reduction in head load on the main chamber wall
and an increase on the divertor targets. Further deliberated experi-
ments and simulations are needed to discover the consequences of this
SOL turbulence reduction. Moreover, if ICRF induced turbulence
reduction can also happen inside the separatrix, then an enhancement
of core plasma confinement is expected. Future work will continue to
address these issues and explore the related mechanisms.

ACKNOWLEDGMENTS

This work was supported by the National Natural Science
Foundation of China under Grant Nos. 12175273, 12105184, and
11975265, the National magnetic confinement fusion energy
development research project under Grant Nos. 2022YFE03190200
and 2019YFE03070000, the Comprehensive Research Facility for
Fusion Technology Program of China under Contract No. 2018-
000052-73-01001228, and Users with Excellence Program of Hefei
Science Center, CAS under Grant No. 2021HSC-UE014.

AUTHOR DECLARATIONS

Conflict of Interest

The authors have no conflicts to disclose.

Author Contributions

**Wei Zhang:** Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Resources (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). **Chu Zhou:** Data curation (equal); Formal analysis (equal); Investigation (equal). **Xiaoming Zhong:** Data curation (equal); Formal analysis (equal); Investigation (equal). **Kangning Geng:** Data curation (equal); Formal analysis (equal); Investigation (equal). **J. H. Hu:** Data curation (equal); Formal analysis (equal); Investigation (equal). **Yifei Jin:** Data curation (equal); Formal analysis (equal); Investigation (equal). **Hailin Zhao:** Data curation (equal); Formal analysis (equal); Investigation (equal). **Ghassan Youssef Antar:** Formal analysis (equal); Methodology (equal); Writing – review & editing (equal). **Guillaume Urbanczyk:** Formal analysis (equal); Methodology (equal); Writing – review & editing (equal). **Yan-Long Li:** Data curation (equal); Formal analysis (equal); Methodology (equal); Writing – review & editing (equal). **Xinjun Zhang:** Formal analysis (equal); Resources (equal); Supervision (equal). **Lunan Liu:** Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Writing – review & editing (equal). **Shaocheng Liu:** Data curation (equal); Formal analysis (equal); Investigation (equal). **T. Y. Xia:** Formal analysis (equal); Investigation (equal); Methodology (equal). **N. Yan:** Data curation (equal); Formal analysis (equal); Investigation (equal).

DATA AVAILABILITY

The data that support the findings of this study are available from
the corresponding author upon reasonable request.
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