Characterization of SOL profiles and turbulence in ICRF-heated plasmas in EAST

Scrape-off layer (SOL) profiles and turbulence in ion cyclotron range of frequency (ICRF)-heated plasmas are investigated by the reciprocating probe diagnostic system (FRPs) and gas puff imaging (GPI) diagnostic in EAST. A radio-frequency (RF) sheath potential reaching up to 100 V is identified proximate to the ICRF antennas. Notably, the amplitude of this RF sheath potential escalates in response to rising ICRF power and inversely with plasma density. When a RF sheath is present in the far SOL, a pronounced density ‘shoulder’ forms in front of the ICRF antennas, while the ‘shoulder’ fade away as the antenna and associated RF sheath shift outwards. A strong E r shear is revealed by measurements from both FRPs and GPI. Analysis of the poloidal wave number-frequency spectrum reveals suppression of high-frequency turbulence in the far SOL due to the RF sheath. This effect is manifested in the reduced autocorrelation time τ c and reduced average blob size δ blob of the SOL plasma. Intriguingly, the poloidal propagation direction of the low-frequency turbulence reverses from the electron to the ion diamagnetic drift direction at the RF sheath location. A surge of tungsten impurity is potentially attributed to the heightened interaction between the SOL plasmas and the wall material. Shifting the ICRF antennas outward, to alleviate heat spots, results in the relocation of the RF sheath to the shaded region of the main limiter. This shift amplifies the radial velocity of blobs in the far SOL and concurrently diminishes the SOL density when compared to conditions without ICRF injection. The properties of ion saturation current fluctuations are consistent with the stochastic model predictions.

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Introduction
Ion cyclotron range of frequency (ICRF) wave heating stands as a primary technique envisioned for next-generation fusion reactors, aiming to optimize performance and extend pulse duration.Within the ITER framework, ICRF distinguishes itself as the sole auxiliary heating methodology explicitly designed for direct ion heating.However, empirical assessments across different devices have highlighted an escalation in core plasma impurities attributable to ICRF heating [1,2].While the underlying processes remain not fully elucidated, the radio-frequency (RF) sheath generated in the scrape-off layer (SOL) region-stemming from the interplay between ICRF waves and plasma-is believed to be instrumental in the onset of impurity sputtering [3,4].
It is generally acknowledged that both the slow wave (SW) emanating directly from the ICRF antennas and the fast wave transitioning into SWs within the SOL region can give rise to RF sheaths by generate the parallel electric field E || [5,6].The fundamental principle underlying RF sheath physics hinges on the fact that electrons traverse more rapidly than ions within the RF bias electric field to the surface of the material, and the resulting sheath is called the RF sheath.In the absence of RF wave field, this sheath is called Bohm sheath or thermal sheath.This differential motion culminates in the formation of a rectified sheath potential, serving to equilibrate the fluxes of electrons and ions, thereby maintaining a time-averaged quasineutral plasma state [7,8].When the near sheath region tends to steady state, the sheath current disappears, so we can get a sheath potential enhanced by RF [9]: T e e ln I 0 (ζ) . ( Here, the intensity of RF waves can be substituted for ζ = |eϕ rf0 /T e |.The RF voltages ϕ RF govern the potentials of the rectified or DC RF sheath.The sheath, which is originally only a few Debye length scales thick, benefited from the rectification effect dominated by RF and was able to propagate along the magnetic field lines and be significantly enhanced. The probe connected to the magnetic field line of the ICRF antennas on the WEST verified the presence of the radial RF sheath in the SOL region [10].On the Alcator C-Mod, it has been frequently observed that the plasma potential at the surface of the engaged ICRF antenna can escalate beyond 100 V, significantly overshadowing the typical plasma potential of around 10 V.In specific extreme experimental setups, the RF sheath potential can even escalate to 400 V [11][12][13].Owing to the plasma's inherent high conductivity, the RF sheath's direct current (DC) voltage, denoted as V DC , generates E × B convection in SOL [14][15][16].Notably, this E × B convection, spurred by the DC voltage V DC from the RF sheath, has been measured using the gas puff imaging (GPI) on Alcator C-Mod [15].In studies conducted on ASDEX Upgrade, SOL turbulence was observed to be attenuated by the RF sheath [17].This suppression subsequently leads to modifications in SOL density, driven by the E × B convection instigated by the RF sheath.Empirical support for this phenomenon has been documented through edge measurements utilizing probes [18][19][20], edge reflectors, and lithium beam emission spectroscopy (Li-BES) [21,22].Additionally, the RF sheath has the capacity to propel high-energy ions, intensifying the plasmawall interaction (PWI) [23].The consequential augmentation of heat loads on the wall during ICRF episodes has been captured using infrared cameras across diverse experimental platforms such as JET [24,25], Tore Supra [26,27], NSTX [28], and WEST [10].A notable outcome during ICRF is the heightened propensity for high-Z impurities, like tungsten [29], molybdenum [1], beryllium [30], and nickel (observed on JET [31]), as well as titanium and iron (documented on EAST [32]), to infiltrate the core plasma.
This study showcases recent findings on the characterization of SOL profiles and flows within ICRF-heated plasmas on EAST.Measurements of the ICRF-induced RF sheath in the far SOL have been executed utilizing the mid-plane fastmoving reciprocating probes (FRPs) system.For a deeper comprehension of SOL plasma modifications during ICRF heating, the FRPs system was employed to analyze changes in the far SOL profiles and turbulence dynamics.Additionally, the GPI methodology was used to gauge the flow patterns stimulated by the RF sheath.These revelations are instrumental both for an enriched understanding of SOL phenomena under RF sheath influence and for devising approaches to enhance ICRF heating efficiency.
The structure of this paper is delineated as follows: section 2 details the experimental setup utilized in this study.Section 3 outlines the characteristics of the ICRF-induced RF sheath.In section 4, we address the modifications in the SOL density profiles due to the RF sheath, considering different ICRF antenna locations.Section 5 delves into the modulation of plasma flows and turbulence in the far SOL.Section 6 offers a discussion on the relationship between tungsten impurity production and density structure during ICRF heating, and finally, section 7 provides a summary of our findings.

Experimental setup
In the 2021 EAST experiment, innovative ICRF antennas were introduced, leading to enhanced heating efficiency in EAST [33].Presently, two identically-configured ICRF antennas have been mounted on the N-port and I-port, operating typically within a frequency range of 20-75 MHz [33].Prior research suggests that the RF sheath induced by ICRF is directly mappable to the field lines of active ICRF antennas [5].The mid-plane FRPs system has been deployed to gauge specific SOL plasma parameters, aiding in analyzing the characterization of plasma parameters such as the RF sheath potential, density profiles, and SOL region turbulence during ICRF heating.Notably, even though the K-port probe is toroidally distanced from the activated ICRF antennas, it retains a magnetic connection with segments of the N-port and I-port antennas, as depicted in figure 1 To investigate ICRF-induced RF sheath characteristics, we utilize a composite probe array, illustrated in figure 2, integrated into the FRPs system.This array comprises two groups of four-tip Langmuir probes (φ f1 , I s1 , φ +1 and φ f2 ; φ f2 , I s2 , φ +2 and φ f3 ), a Mach probe set (I mach1 and I mach2 ), and two floating potential pins (φ f4 and φ f5 ) at the inner stair.Here, the floating potential pins are limned in blue.The four-tip Langmuir probes are able to measure the floating potentials, electron density and temperature.The two Mach probes set ascertain parallel flow velocities.Additionally, the poloidal structure of the turbulence can be derived from the correlation of two floating potential signals among the poloidal spaced pins (φ f1 , φ f2 and φ f3 ; or φ f4 and φ f5 ).The radial electric field can be estimated by pins φ f3 and φ f4 , which are located at two different stairs with a radial distance 8 mm.Each Langmuir pin has a diameter of 2.5 mm and a length of 3 mm.The FRPs system operates with a sampling rate of 1 MHz.It is worth mentioning that since the RF frequency is much higher than the sampling rate of the FRPs system, the RF sheath potential measured in this article is after the averaging correction on the fast RF time scale.Usually, upon activation, the swift-moving probe can attain its target location in a mere 0.5 s, facilitating a swift radial round-trip within a single shot.When measuring the radial distribution of the floating potential, the local radial and poloidal electric fields can be inferred from multiple floating potentials.
The GPI serves as a direct diagnostic tool for SOL flows and turbulence.Neutral gases, like helium, are introduced into the SOL plasma via a manifold, creating a gas cloud at the target surface.The emitted visible light from this gas cloud is subsequently captured by the optical system.The primary components of the GPI mounted directly on the EAST include the optical system and the gas manifold.The optical system is situated at the outer midplane of the P-port, while the gas manifold is positioned equidistantly between the N-port and O-port.The GPI system's objective plane is elevated approximately 27.6 cm above the outer midplane.Additionally, there's a poloidal angle of 35 • between the horizontal plane and the minor radius at the center of this objective plane [34].

Experimental observation of RF sheath potential
With the enhanced power output from the 2021 ICRF heating system in EAST, FRPs are employed to examine the properties of the RF sheath induced by ICRF across varying parameters.In figure 3, the solid black line displays the floating potential profiles from sample #113577, measured in the absence of ICRF.The potential profile exhibits a peak value of approximately 3 V throughout the radial direction, indicating no RF sheath formation.Statistically, the potential without ICRF is less than 10 V of the plasma potential.When contrasted with the solid red line from shot #110444, which had ICRF power injection, an ICRF-induced RF sheath with a potential of 130 V emerged in front of the ICRF antennas.This was significantly higher than the plasma potential observed in #113577.The characteristics of the RF sheath potential influenced by varying ICRF power and different line-averaged densities ne are detailed in subsequent sections.In the correlation between plasma potential and floating potential, the changes brought by temperature are about 3 * T e .In this work, we use the electron temperature measured by the helium-BES (He-BES) diagnostic as the reference data to calculate the plasma potential base on the floating potential.Although the plasma potential increases with RF sheath potential to hundreds of volts, which is much larger than the change brought by temperature to tens of volts, we consider the error caused by temperature as error bars in order to reduce the effect of electron temperature on the trend change of RF sheath potential.

Factors influencing RF sheath potential: experimental observations
The influence of the parallel electric field E || of the SW directly amplifies the plasma flux mapped to the ICRF antennas, ϕ RF = ∫ dsE || .Consequently, the augmentation of SWs further boosts the RF sheath potential [6,14,15].In instances of non-alignment, the ICRF antennas directly instigate the parallel electric field E || of the SW [35,36].The magnitude of E || increases in tandem with the elevation of the ICRF injection power.Moreover, SWs exhibit superior propagation in plasmas of lower density, signifying a more pronounced parallel electric field E || in low-density plasma at equivalent positions.Under both scenarios, the RF sheath experiences an enhancement.
The relationship between ICRF power and RF sheath enhancement is captured by an empirical equation derived from the maximum predicted potential in C-mod, ϕ RFmax ≈ P ICRF 1/2 [15].This suggests that the sheath potential increases as the square-root of ICRF power.A similar positive correlation between ICRF power and sheath potential, has been observed on EAST, as depicted in figure 4. While maintaining all other plasma parameters constant, the red square-dot line illustrates the variation in RF sheath potential as the ICRF heating power from the I-port antenna fluctuates in the lowconfinement mode (L-mode).This is observed when the toroidal magnetic field B T is −2.5 T (a positive sign for B T indicates the same direction as the plasma current), the plasma current I p is 0.35 MA and the line-averaged density <n e > stands at 3.3 × 10 19 m −3 .The blue square-dot line represents the shift in RF sheath potential in response to changing ICRF power in the high-confinement mode (H-mode) with a of B T of 2.5 T, the plasma current I p is 0.45 MA and the line-averaged density <n e > of 4 × 10 19 m −3 .Regardless of the direction (positive or negative) of the toroidal magnetic field, the lineaveraged density, or the operation mode, the RF sheath potential increases with the escalation of ICRF power.
Considering an electrostatic model for the oscillating sheaths, J.R. Myra et al proposed an expression for the RF sheath potential given by ϕ RF = −δ sh • D n /ε sh [37], where δ sh represents the width of the sheath, D n is the electric displacement normal to the wall and ε sh is the sheath dielectric permittivity.In general, the sheath dielectric permittivity is assumed to be 1.At the same time, the electrical displacement is not directly affected by the density, and if the plasma density distribution does not change drastically, the electrical displacement can be considered constant.A noteworthy implication is that the sheath width δ sh is proportional to the fourth power of the Debye length λ De and the Debye length are inversely proportional to the square-root of the density.That means the sheath potential ϕ RF are inversely proportional to the square-root of the density.Therefore, when the plasma density decreases, it will lead to an enhanced sheath potential.Zhang et al discussed in their work [38] that as the plasma density near the antenna increases, the induced RF sheath potential tends to decrease.This observation is substantiated by the downward trend in the blue dot line, representing the RF sheath in L-mode, as shown in figure 5.In fact, H-mode exhibits more effective particle confinement, suggesting that under identical core density conditions as in L-mode, the SOL density in H-mode will be lower.This implies that the ICRF-induced RF sheath potential in H-mode is expected to surpass that in L-mode.

3D simulation of RF sheath distribution
Based on experimental parameters from EAST, such as SOL density and the RF sheath potential measured by FRPs, we employ COMSOL to conduct a 3D simulation of the RF sheath distribution induced by ICRF waves in the vicinity of the antennas.Figures 6(a) and (b) respectively depict the 3D distribution of the RF sheath potential on the first wall within the toroidal range of the ICRF antenna and the 3D distribution of the electric field induced by the RF sheath.The simulation accounts for both fast and SWs, revealing the presence of both near-field and far-field sheath phenomena, as illustrated in figure 6.In figure 6(a), it is evident that ICRF-induced RF sheath extends to a distance of approximately 1.5 m from the antenna loop.Notably, the RF sheath is not localized, suggesting that its effects extend beyond the vicinity of the ICRF antennas.This observation aligns with the simulation findings regarding fast wave dissipation in the SOL on NSTX [39].The most intense RF sheath is concentrated near the antenna, primarily at the upper and lower regions of the antenna box.This pattern is consistent with experimental observations of potential in the large plasma device [16].It is important to note that the sheath potential measured by the FRPs does not represent the maximum value of the RF sheath induced by ICRF.When comparing the RF potential distribution in figure 6(a) with the electric field distribution in figure 6(b), a clear relationship emerges: the RF sheath potential is directly proportional to the higher-order electric field it generates.Furthermore, the electric field induced by the RF sheath rectification exhibits spatial inhomogeneity.

Modifications of SOL density profiles by RF sheath
The ICRF-induced RF sheath rectification introduces a DC voltage at the periphery, denoted as φ DC = φ f + φ RF [40].This rectification process has been observed to result in modifications in the far SOL density profiles on different devices.It is widely believed that the ICRF-induced RF sheath plays a pivotal role in these density modifications.The spatial inhomogeneity of the electric field induced by the RF sheath results in a bias in the DC electric field, driving E × B convection and subsequently leading to local density redistribution.This E × B convection interacts with other SOL transport processes such as turbulence and parallel losses.Consequently, the density measurements obtained by the FRPs in the far SOL regions are influenced by the presence of the RF sheath.When the antennas are positioned in close proximity to the plasma, the radial density profiles in front of the antennas exhibit a shoulder-like structure, with the density 'shoulder' extending radially inward from the location where the RF sheath appears, as depicted in figure 7.However, due to their close proximity to the plasma, severe hot spots develop on the antennas.In an effort to mitigate these heat spots, the ICRF antennas were shifted outward by approximately 1 cm in the 2023 experiment.Consequently, the density 'shoulder' in the far SOL region vanishes following the antenna adjustment, and the density in the far SOL is also reduced compared to conditions without ICRF, as illustrated in figure 8.   7(e).Simultaneously, the density profiles within the pink dashed square exhibit an elevation in front of the radial position of the RF sheath, followed by a rapid decline as they pass through the RF sheath, giving rise to a distinctive 'shoulder' structure in the radial profiles.In contrast, the potential profiles without ICRF injection maintain small amplitude fluctuations of about 10 V, and the density profiles exhibit a gradual and smooth decrease.It is worth noting that in previous studies on C-Mod, it was observed that electron density profiles in the SOL region increased with higher levels of ICRF injection power [14].To address the issue of hot spots at the ICRF antennas, adjustments were made by relocating both the ICRF-N and I antennas to a more suitable position.Following the antenna relocation, the ICRF-induced RF sheath was repositioned to the shaded area behind the limiter.Simultaneously, the density 'shoulder' in the far SOL region is no longer in existence.Figure 8 illustrates the fundamental discharge parameters for shot #120574.The plasma current (I p ) is measured at 0.3 MA, with a plasma line-averaged density (<n e >) of 3.9 × 10 19 m −3 .The safety factor (q 95 ) is about 9.5, the toroidal magnetic field (B T ) holds at 2.5 T, and the plasma stored energy amounts to 178 kJ.The RF heating power includes ICRF-N at approximately 1.2 MW, ICRF-I at around 0.4 MW, ECRH at 1.5 MW, and LHW at 2.0 MW.In figure 8(c), the probe performed two strokes-one without ICRF and the other during a 1.6 MW ICRF period.Here, the initial radial position of the probe is R = 2533 mm.The radial position of the separatrix is 2280 mm.Figures 8(e) and (f ) clearly demonstrate that moving the ICRF antennas outward shifted the RF sheath to the shaded area behind the limiter, and the RF sheath no longer induced a density 'shoulder' in front of the ICRF antennas.The density decreases consistently throughout the far SOL, with levels lower than those observed without ICRF.The introduction of ICRF significantly reduces the density in the vicinity of the antennas, which is also corroborated by measurement through Li-BES on JET [22].
The intensity of density decay is assessed using the density decay length, denoted as λ n , which is estimated as follows: λ n ≈ [∇r logn] −1 [41][42][43].A smaller λ n signifies a more rapid radial decay in density, while a larger λ n indicates a slower decay.The RF sheath induces significant alterations in λ n within the far SOL region.Figures 9(a) and (b) illustrate the density decay length λ n in the far SOL region at different antenna positions.In this figure, the red dots represent the density decay length λ n with ICRF input, while the black dots depict the far SOL density decay length λ n without ICRF injection.Clearly, when the antennas are positioned 10 mm behind the limiter, the density decay length exceeds that observed without the RF sheath.However, as the RF sheath relocates to the shadowed region, λ n with ICRF undergoes a sharp reduction to less than 25 mm, signifying a pronounced decrease in density in front of the antenna.This phenomenon is particularly evident when the ICRF antennas are in close proximity to the plasma, and the RF sheath's influence extends effectively into the SOL plasma.
Figures 10(a   In the subsequent section, where we delve into the investigation of SOL plasma flows modified by the RF sheath, it is deduced that these modifications are attributed to the E × B shear linked with the radial electric field produced by the RF sheath.However, when the density 'shoulder' vanishes as a result of increasing the distance between the antennas and the plasma, we observe an increase in autocorrelation time (τ c ) and a strengthening of the blob, as depicted in figures 10(c) and (d).
In experimental observations, when the antennas are positioned in close proximity to the plasma, allowing the RF sheath to induce the density 'shoulder', a noticeable reduction in the radial velocity of blobs is evident.Conversely, when the antennas are repositioned farther from the plasma, the radial velocity of these blobs increases.To investigate the dynamics of these intermittent structures, known as blobs, in the vicinity of the RF sheath, a conditional averaging method is employed [44].This method utilizes different thresholds (1, 1.5, 2, 2.5 × rms levels) to distinguish intermittent structures with varying amplitudes, based on the fluctuation amplitude of the ion saturation current signal.The resulting conditional averaged radial convection velocity (V r ) serves as an indicator of the radial propagation velocity of the blobs, as depicted in figure 11.Figures 11(b) and (e) clearly illustrate that the RF sheath exerts an inhibitory effect on the radial velocity of the blobs when the antennas are positioned closer to the plasma.This phenomenon may be attributed to the presence of a strong shear flow in the far SOL, driven by the RF sheath.It is worth noting that the larger the blob's amplitude, the greater the particle transport facilitated by the blob.A decrease in radial velocity implies a weakened particle transport within the SOL, which subsequently leads to the formation of a 'shoulder' in the density profile, induced by the RF sheath.However, after relocating the antennas outward, the radial velocity experiences a nearly threefold enhancement, as depicted in figures 11(c) and (f ).The increase in radial velocity results in enhanced particle transport within the SOL, causing a more robust convective particle transport mechanism and, consequently, a local reduction in density.This observation aligns with the findings in the autocorrelation time and blob size illustrated in figure 10.It is important to note that the radial electric field (E r ) generated by the RF sheath not only redistributes the SOL density but also has a significant impact on plasma flow and turbulence, which will be examined in detail in section 5.

Modifications of far SOL plasma flow and turbulence by RF sheath
In the [16] cited, it was noted that the spatial pattern of the local DC electric potential (V DC ) influenced by RF sheath rectification, perpendicular to the background magnetic field B 0 , resulted in the creation of E RF × B 0 convective cells responsible for particle transport across the magnetic field within the RF sheath region.Both the FRPs and GPI techniques were employed to determine the radial electric field (E r ) induced by the RF sheath in the far SOL.Furthermore, both the observed variations in turbulence measured by FRPs and the SOL flows measured by GPI provided support for the presence of E r × B 0 convection resulting from RF sheath rectification.
Using the probe illustrated in figure 2, information regarding the SOL's radial electric field and particle flow is obtained, as depicted in figure 12.Following the induction of the RF sheath in the far SOL region by ICRF, a robust radial electric field E r emerges in that region, as evident in figure 12(b).The probe shown in figure 2   ICRF-biased flux tubes.The impact of the altered parallel flow aligns with the suppression of blobs in figure 10(b) and the reduction in the radial velocity of the blobs in figure 11(d).
By averaging the 2D velocity field measured by GPI along the poloidal direction, we obtained radial profiles of the poloidal phase velocity.Figure 13(a) displays the equilibrium profiles of poloidal velocity V θ for cases with and without ICRF.The radial electric field can be deduced from the poloidal velocity as E r = −V θ B φ , as depicted in figure 13(b).When ICRF is injected, significant poloidal flow reversals occur in the SOL near the limiter.V θ is nearly 0 km s −1 when far from the RF sheath region, increases to 3 km s −1 near the RF sheath, and then reverses to −3 km s −1 as it reaches the ICRF antenna through the RF sheath.This indicates that compared to flows induced by the thermal sheath, convection induced by the RF sheath is more pronounced in the far SOL and reverses the flow near the ICRF antenna.The observed poloidal reversal in V θ , as measured by GPI, aligns with the variations in E r , as measured by the probe, providing further evidence that the RF sheath modifies local density through the generation of E × B flows.It is worth noting that the radial width of the radial electric field E r induced by the RF sheath on EAST is approximately 3 cm, which shows slight variations compared to measurements obtained on C-mod [15].
To assess the statistical characteristics of far SOL turbulence, we present the power spectral density of local density fluctuations, denoted as S(f ), in figure 14. Figure 14(b) highlights a notable suppression of high-frequency turbulence (frequencies greater than 100 kHz) in the presence of ICRF.Notably, the radial position where high-frequency turbulence is suppressed closely aligns with the location of the RF sheath.Conversely, the frequency power spectral density, S(f ), for SOL plasma without the RF sheath does not exhibit such changes throughout the entire SOL, as illustrated in figure 14(a).
The poloidal wavenumber-frequency power spectral density, denoted as S(k θ , f ), is presented in figure 15.This spectrum is derived using the two-point cross-correlation technique [45,46].Figures 15(a)-(d) illustrates the S(k θ , f ) spectrum for SOL plasmas in the absence of ICRF.In this case, the spectrum intensity within the radial range from 2344 mm to 2371 mm is primarily concentrated in the high-frequency range (>100 kHz).For SOL plasmas without ICRF, the S(k θ , f ) spectrum predominantly exhibits high-frequency content across the far SOL.However, the fluctuation level below 100 kHz in the absence of ICRF is significantly lower than during the ICRF phase.In figures 15(e) and (f ), during the ICRF phase, the majority of the poloidal cross-power, represented by S(k θ , f ), is concentrated in the low-frequency region (<100 kHz).The spectrum S(k θ , f ) below 100 kHz experiences enhancement.Conversely, the high-frequency fluctuation observed in figures 15(a)-(d) is suppressed by the presence of ICRF.In the low-frequency region (<100 kHz), a different turbulence mode emerges, exhibiting altered propagation direction.Specifically, as one moves from the far SOL towards the ICRF antennas, the k θ of fluctuations below 100 kHz converts from 1 cm −1 to −1 cm −1 .The propagation of these fluctuations shifts from the electron diamagnetic drift direction to the ion diamagnetic drift direction.This inversion of k θ occurs roughly at the radial position corresponding to the RF sheath, aligning with the location of the shear layer measured by GPI in figure 13.
A stochastic model [47,48], describing the plasma fluctuations in the SOL as a super-position of uncorrelated pulses, provides key insights for the understanding intermittent transport.This model has achieved a wide success in comparison with experimental measurements at one single point by Langmuir probe and GPI diagnostics [49][50][51].According to this model, probability density function (PDF) for the normalized fluctuations Φ obey a Gamma dis- where the γ the ratio of pulse duration time and average pulse waiting time, signifying the degree of pulse overlap [48].In the case of the two-sided exponential pulse shape, the frequency power spectral density is given as ), where ω is the angular frequency of the fluctuations, and τ d is the pulse duration time [52].
Here, the large-amplitude, intermittent bursts in ion saturation current signal and floating potential signal are extracted, and its features statistical characteristics compared to the stochastic model.The PDF of peak amplitude of signals above 2.5 standard deviations, the PDF of the waiting times between these large amplitude fluctuations are depicted in figure 16.It is shown that both the PDFs follow exponential distributions as expected by the stochastic model.They manifest underlying Poisson process of bloby transport, which validate the basis of the stochastic model.As shown in figure 17, the PDFs of the normalized fluctuation by its standard deviation are well fitted by a Gamma distribution expected from the stochastic model.The frequency power spectral density of ion saturation current random fluctuation agrees well the model predictions.Notably, RF sheath can depress the low frequency fluctuation, but it is hard to change the statistical properties originated from a Poisson process.

Behavior of tungsten impurity content during ICRF heating
Ions are accelerated by the high potential of the RF sheath, increasing heat loads and energetic particle flows on the limiter's surface.This results in the thermal deposition of the limiter and an increase in impurities [53].The contamination of impurities in the core presents a significant challenge for achieving steady-state operation with high confinement and long pulses in EAST.The ion energy of the first wall accelerated by the RF sheath electric field is on the order of Z e φ RF [54], and the excitation of high-Z impurities by ICRF has been observed in different devices.It has been observed that ICRF heating simultaneously increases impurity levels in the core plasma, including iron (Fe), molybdenum (Mo), and tungsten (W) impurities in EAST.The extent of impurity generation is directly proportional to the ICRF power input [32,55].
The relationship between the tungsten impurity content in the core and ICRF heating at different power levels is examined in this study, as depicted in figure 18.The solid black line corresponds to the discharge data from shot #107395, the solid blue line represents #107399, and the solid red line corresponds to #107401.These three discharges share  similar parameters except for the ICRF power level.As shown in figure 18(c), the power of the ICRF-N antenna increases progressively from 1.0 MW to 1.6 MW, and ultimately to 1.7 MW, during the 3-6.8 s time interval.During this time frame, there is a gradual increase in tungsten impurity content, as depicted in figure 18(h).A similar trend of increased impurity production is also evident with the power enhancement of the ICRF-I antenna, as shown in figure 18(d).It is worth explaining that the tungsten unresolved transition array is drawn in figure 18(h), which is composed of emission lines from W 24+ up to W 45+ measured by the fast-time-response flat-field extreme ultraviolet spectrometer [56].Between 7 and 10 s, the power delivered by the ICRF-I antenna increases from 1.0 MW to 1.5 MW, and eventually to 1.6 MW.In figure 18(h), it is evident that tungsten impurities increase concomitantly with the rising power levels.Notably, the ICRF   antennas located in two different ports, N-port and I-port, exhibit a similar propensity for exciting tungsten impurities at comparable levels.Specifically, in discharge #107395, where both antennas operate at 1.0 MW, the tungsten impurity content remains consistent between the two ports when power is applied.
The far SOL plasma density plays a crucial role in impurity sputtering.In figure 18, discharge #107401 exhibits the highest impurity content generated by ICRF among the three discharges.During two periods of tungsten impurity sputtering, the far SOL density was measured by a probe.When the density 'shoulder' is elevated to a greater extent by the RF sheath, ICRF results in the production of more tungsten impurities.Figure 19 illustrates the far SOL density profiles of #107401 at different tungsten impurity levels.The red, blue, and black solid lines represent the density profiles when ICRF power is 1.7 MW, 1.6 MW, and 0 MW, respectively.When comparing the density profiles measured by the probe at an ICRF power of 1.6 MW to those at an ICRF power of 1.7 MW, it is evident that the density 'shoulder' is raised to a greater extent by the RF sheath at the higher power level.Specifically, during the time interval of t = 4.7-4.9s with an ICRF power of 1.7 MW, there is a sharp increase in the tungsten impurity content in #107401.Conversely, at t = 8.5-8.8 s with an ICRF power of 1.6 MW, the tungsten impurity content is significantly lower, and at t = 2.7-2.9 s without ICRF, the tungsten impurity content is even lower.As discussed in section 3.2, the RF sheath elevates the SOL density, leading to stronger PWIs and, consequently, increased tungsten impurity production.Indeed, in the experimental setup, the rise in RF sheath potential is correlated with an increase in the temperature on the ICRF limiter, as depicted in figure 20.This observed correlation between RF sheath potential and limiter temperature may be one of the factors contributing to ICRF-induced impurity production.

Conclusions
In this study, we conducted a comprehensive investigation into the characteristics of ICRF-induced RF sheath potential and its interactions with SOL plasma flow and turbulence in the EAST tokamak.Utilizing advanced diagnostics tools such as FRPs and GPI, we identified the presence of a radial electric field (E r ) in the far SOL, primarily induced by the RF sheath.Our findings also revealed that the SOL plasma flows and turbulence are significantly modified by the E × B flows associated with the RF sheath.This in-depth analysis of the RF sheath's behavior enhances our understanding of SOL plasma dynamics during ICRF heating.Moreover, the insights gained from this research can serve as a valuable reference for optimizing ICRF heating efficiency, addressing heat spots, minimizing impurity excitation and so on.
The FRPs, which is magnetically connected to the active ICRF antennas, played a crucial role in observing the ICRFinduced RF sheath.In our study, it was evident that the intensity of the RF sheath potential directly correlates with the increase in ICRF power.Additionally, when the plasma density is raised in the L-mode, the RF sheath exhibits a decrease in intensity.This behavior aligns with the expected characteristics of a SW-induced RF sheath.Furthermore, it was observed that the RF sheath tends to induce E r × B convection, leading to modifications in local plasma density.When the antennas are positioned closer to the plasma, the radial convection velocity of plasma turbulence in the far SOL are reduced.This, in turn, leads to a greater retention of particles within the SOL, consequently forming a density 'shoulder' structure in front of the RF sheath.It has been observed that the presence of the RF sheath-induced density 'shoulder' corresponds to inhibited autocorrelation time (τ c ) and reduced average blob size (δ blob ) within the SOL plasma.Conversely, as the antennas are moved outward, causing the RF sheath to shift towards the shadow region of the main limiter, the radial convection velocity of blobs in the far SOL increases.This heightened velocity results in enhanced particle transport, ultimately leading to a depletion of density in the far SOL.
In the presence of the radial electric field E r associated with the RF sheath, high-frequency turbulence within the far SOL region experiences suppression, while low-frequency turbulence is enhanced.Notably, low-frequency turbulence undergoes a reversal in its poloidal propagation direction, transitioning from the electron diamagnetic drift direction to the ion diamagnetic drift direction at the RF sheath location.This reversal corresponds to a decrease in autocorrelation time and the suppression of blobs.Importantly, the locations where these turbulence changes occur closely align with the shear layer measured by GPI and the RF sheath identified by FRPs.This observation highlights the intricate interplay between E r × B flows and SOL plasma.The stochastic model proposed by O.E. Garcia et al provide key insights for the understanding on the SOL plasma fluctuations.In this paper, we dig into experimental data in EAST.Impressively, the measurements also reach a good agreement with the stochastic model.It has been observed that ICRF tends to excite more tungsten impurities in discharges where the SOL density is raised higher by the RF sheath.Additionally, the temperature on the ICRF antenna increases as the RF sheath potential rises.These phenomena can be attributed to the heightened interaction between SOL plasma and the vessel wall.

Figure 1 .
Figure 1.(a) Toroidal arrangement highlighting of the EAST RF heating system and FRPs.The field-line mapping from the FRPs to both the ICRF-N antenna and ICRF-I antenna is also depicted.(b) A poloidal cross-section showcasing the toroidal locations of the FRPs and GPI.(c) Top-down view of the EAST, illustrating the placements of FRPs, GPI, ICRF, limiter, and LHW.
(a).A poloidal representation of the 2D FRPs and GPI is illustrated in figure 1(b), while figure 1(c) offers a top-down perspective of the ICRF and other heating mechanisms.

Figure 2 .
Figure 2. Illustration of the combined probe located at the EAST's mid-plane K-port.(a) Side view; (b) front view.The blue pins measure the floating potential (P 1 , P 4 , P 7 , P 8 and P 9 ), and the red pins measure the ion saturation current (P 2 and P 5 ) and measure the bias potentials (P 3 and P 6 ).The Mach probe is composed of two red pins (P 10 and P 11 ).

Figure 3 .
Figure 3. Radial profiles of the floating potential within the SOL.The solid red line represents measurements from EAST Shot #110444 with ICRF, whereas the solid black line corresponds to EAST Shot #113577 without ICRF.The separatrix is positioned at a radial distance of 2290 mm, while the ICRF antenna resides at 2360 mm.Notably, shot #110444 exhibits an RF sheath formation due to the presence of ICRF.

Figure 4 .
Figure 4. Variation in RF sheath potential with different ICRF heating powers.The red dotted line represents the maximum RF sheath potential in L-mode with a toroidal magnetic field B T of −2.5 T and a line-averaged density of 3.3 × 10 19 m −3 .In contrast, the blue dotted line portrays the maximum RF sheath potential in H-mode with B T at 2.5 T and a line-averaged density of 4 × 10 19 m −3 .Notably, the magnitude of the RF sheath potential augments with increasing ICRF power.

Figure 5 .
Figure 5. Illustration of the correlation between the line-averaged density <ne> and RF sheath potential.The blue dot line demonstrates the relationship between RF sheath potential and plasma density in L-mode, with an ICRF power of 0.8 MW.

Figure 6 .
Figure 6.3D simulation distribution of RF sheath potential based on COMSOL.(a) The toroidal 3D distribution of RF sheath near the antennas on the first wall and its enlarged view; (b) the toroidal 3D distribution of the electric field inducted by RF sheath on the first wall.

Figure 7 .
Figure 7.For EAST shot #107401: in (a), the plasma current and line-averaged density are shown.Figure (b) displays the plasma stored energy and safety factor q 95 .Figure (c) provides information on the power of ICRF and the displacement of the probe, while (d) shows the power of ECRH and LHW.Profiles of the RF sheath potential measured by the probe are illustrated in (e), and (f ) shows SOL density profiles under the influence of the RF sheath measured by the probe.Notably, the presence of ICRF results in the formation of a 'shoulder' in the density profiles in front of the RF sheath.

Figure 7
Figure 7 displays a typical discharge with the presence of a density 'shoulder' near the ICRF antenna.During this discharge, the plasma current (I p ) is 0.4 MA, the line-averaged plasma density (<n e >) is 4 × 10 19 m −3 , the safety factor (q 95 ) is 8.3, the toroidal magnetic field (B T ) is 2.5 T, and the plasma stored energy is 195 kJ.The RF heating power consists of ICRF-N (∼1.7 MW), ECRH (∼1.3 MW), and LHW (∼1.8 MW).Figure 7(c) depicts two probe stroke moments.The blue line represents the probe stroke moment without ICRF, while the red line represents the moment with 1.7 MW ICRF.It is worth explaining that 'R probe ' represents the depth at which the probe enters the vacuum chamber from the initial radial position R = 2633 mm after being triggered.The measured profiles for floating potential and density are presented in figures 7(e) and (f ), respectively.'R' represents the radial position.The radial position of the separatrix is 2310 mm.When the probe measured with ICRF injection, the floating potential profiles exhibit the formation of an RF sheath in front of the antennas, as depicted in figure7(e).Simultaneously, the density profiles within the pink dashed square exhibit an elevation in front of the radial position of the RF sheath, followed by a rapid decline as they pass through the RF sheath, giving rise to a distinctive 'shoulder' structure in the radial profiles.In contrast, the potential profiles without ICRF injection maintain small amplitude fluctuations of about 10 V, and the density profiles exhibit a gradual and smooth decrease.It is worth noting that in previous studies on C-Mod, it was observed that electron density profiles in the SOL region increased with higher levels of ICRF injection power[14].
Figure 7 displays a typical discharge with the presence of a density 'shoulder' near the ICRF antenna.During this discharge, the plasma current (I p ) is 0.4 MA, the line-averaged plasma density (<n e >) is 4 × 10 19 m −3 , the safety factor (q 95 ) is 8.3, the toroidal magnetic field (B T ) is 2.5 T, and the plasma stored energy is 195 kJ.The RF heating power consists of ICRF-N (∼1.7 MW), ECRH (∼1.3 MW), and LHW (∼1.8 MW).Figure 7(c) depicts two probe stroke moments.The blue line represents the probe stroke moment without ICRF, while the red line represents the moment with 1.7 MW ICRF.It is worth explaining that 'R probe ' represents the depth at which the probe enters the vacuum chamber from the initial radial position R = 2633 mm after being triggered.The measured profiles for floating potential and density are presented in figures 7(e) and (f ), respectively.'R' represents the radial position.The radial position of the separatrix is 2310 mm.When the probe measured with ICRF injection, the floating potential profiles exhibit the formation of an RF sheath in front of the antennas, as depicted in figure7(e).Simultaneously, the density profiles within the pink dashed square exhibit an elevation in front of the radial position of the RF sheath, followed by a rapid decline as they pass through the RF sheath, giving rise to a distinctive 'shoulder' structure in the radial profiles.In contrast, the potential profiles without ICRF injection maintain small amplitude fluctuations of about 10 V, and the density profiles exhibit a gradual and smooth decrease.It is worth noting that in previous studies on C-Mod, it was observed that electron density profiles in the SOL region increased with higher levels of ICRF injection power[14].

Figure 8 .
Figure 8.For EAST shot: #120574.(a) The plasma current and the line-averaged density; (b) the plasma stored energy and the safety factor q 95 ; (c) the power of ICRF and the displacement of the probe; (d) the power of ECRH and LHW; (e) the profiles of RF sheath potential measured by probe; and (f ) SOL density profiles under the influence of the RF sheath, as measured by the probe.
) and (b) display the autocorrelation times (τ c ) and the average blob sizes (δ blob ), as determined from the probe measurements, in the scenario where ICRF generates a density 'shoulder' structure in front of the antennas.The P 7 and P 8 pins of the probe in figure 2(b) are approximately 8 mm radially spaced apart and are used to measure the radial component of the fluctuating electric field E r and poloidal velocity V θ = E r /B.The average blob size is calculated as δ blob ≈ |V θ | • τ b (under the assumption of |V θ | ≫ |V r |, where V θ and V r are the poloidal and radial velocities of a blob).Here, τ b is the average duration of pulse events, which can be obtained from the I s signal.The autocorrelation times τ c is derived from the floating potential signal, which reflects the intensity change of meso-scale fluctuations.It is evident from figures 10(a) and (b) that in SOL plasma exhibiting a density 'shoulder', the local turbulence experiences a decrease in autocorrelation time (τ c ), and the suppression of blob size (δ blob ) occurs.

Figure 9 .
Figure 9. Illustration of the density decay length (λn) in the far SOL region at different antenna positions.Subfigure (a) represents the SOL λn with the antennas located 10 mm behind the limiter, while subfigure (b) depicts the SOL λn with the antennas positioned 20 mm behind the limiter.

Figure 10 .
Figure 10.(a), (c) the autocorrelation times τ c; (b), (d) the average blob size δ blob .On the left are the results from the shot where ICRF induces the density 'shoulder' before the antennas are moved, while on the right are the results from the shot where ICRF fails to induce the density 'shoulder' after the antennas are relocated.

Figure 11 .
Figure 11.Conditional averaging results of (a) Is, and (b) Vr without ICRF events in the far SOL; (c) Is, and (d) Vr for situations when ICRF antennas are closer to the plasma; (e) Is, (f ) Vr for cases when ICRF antennas are farther from the plasma.Events were selected using thresholds of 1, 1.5, 2, and 2.5 times the rms-level of Is.

Figure 12 .
Figure 12.Radial profiles of (a) RF sheath potential, (b) radial electric field Er and (c) Mach number M || , as measured by the probe.The pink dash-dot lines indicate the position of the ICRF antenna.
allows for the measurement of I Mach2 and I Mach1 , which can be used to calculate the Mach number M || , defined as M || = M c × ln [(I Mach2 ) / (I Mach1 )], with M c typically set to 0.4 in SOL plasma.The negative value of the Mach number M || displayed in figure 12(c) suggests that the SOL flow appears to circulate clockwise in the EAST when viewed from the top.In typical ohmic discharges, the SOL flow remains relatively uniform throughout, directed from the LFCS to the ICRF antenna [33].However, during ICRF power injection, M || decreases in the vicinity of the RF sheath, indicating a significant shearing of the parallel flow.This pronounced shear in the parallel flow is likely induced by the E r × B flows resulting from the RF sheath.The alteration in SOL plasma flow may signify changes in transport within the

Figure 13 .
Figure 13.Equilibrium profiles of (a) poloidal velocity V θ ; (b) radial electric field Er = −V θ Bφ, at with or without ICRF.The profiles are measured by GPI.Black dash-dot lines indicate the position of the ICRF antenna.

Figure 14 .
Figure 14.Power spectral density S(f ).(a) #113577 without ICRF; (b) #110444 with ICRF.The radial profiles of the RF sheath are shown on the right.The high-frequency turbulence is suppressed at the RF sheath location.

Figure 15 .
Figure 15.Poloidal wave number-frequency power spectral density S(k θ , f ) without ICRF phase (left panels) and with ICRF phase (right panels).The probe radial position is labeled in each panel.The negative k θ denotes the direction of ion diamagnetic drift.

Figure 16 .
Figure 16.(a) Probability density function of the ion saturation current signal; (b) power spectral density of the floating potential.The black dots are obtained from the signal located radially at the RF sheath, while the red dots are obtained from the signal located radially in front of the RF sheath.The dotted line is the fitting line.

Figure 17 .
Figure 17.(a) The PDFs of the ion saturation current signal local maxima A in the rescaled time series; (b) the PDFs of the waiting times between large-amplitude bursts in the Is time series.The black dots represent the ion saturation current signal located radially at the RF sheath, while the red dots represent the ion saturation current signal located radially in front of the RF sheath.The solid line is the fitting line.

Figure 19 .
Figure 19.Far SOL density profiles measured by the probe during EAST shot #107401 with different ICRF power levels.

Figure 20 .
Figure 20.Correlation between the temperature of the ICRF limiter protector and RF sheath potential.