Observation of reduced-turbulence regime with tungsten injection in HL-2A edge plasmas

A reduced-turbulence regime has been observed in HL-2A NBI-heated deuterium plasmas. The transition to this regime is achieved by injecting a certain amount of tungsten into the plasma based on the laser blow-off technique. It has been found that the amplitude of geodesic acoustic mode (GAM) zonal flow and turbulent vortex size together with eddy tilting angle are all significantly increased in the edge region after tungsten injection. However, the frequency of GAM zonal flow remains nearly unchanged. Measurement shows the nonlinear coupling degree of turbulence dramatically increases while the collisional damping of GAM zonal flow drops slightly. We conclude that the increased nonlinear coupling is the main cause of the excitation of GAM zonal flow, which consequently results in the reduction in turbulent transport as observed in this experiment. These results indicate that tungsten ions play an active role in turbulence-GAM dynamics through a symmetry-breaking mechanism, which could help us to better understand the inherent physical mechanisms governing turbulent transport in the presence of high-Z impurity ions in fusion plasmas.


Introduction
Turbulence is recognized to be the main cause of particle and energy losses in magnetically confined plasmas [1].The Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.reduction in turbulent transport by sheared E × B flow has been intensively studied since the first discovery of the highconfinement mode (H-mode) in ASDEX in 1982 [2].In recent decades, it has been widely accepted that turbulence may be reduced or suppressed by sheared mean flow and zonal flow (both the near zero low-frequency zonal flow and geodesic acoustic mode (GAM)) [3,4].Therefore, extensive studies have been performed to understand the physical mechanisms responsible for the excitation of zonal flow and the resulting reduction in turbulent transport in magnetized confinement plasmas.
Many external perturbation methods, e.g.biasing, resonant magnetic perturbation (RMP) and impurity injection, etc, have been developed and used to study the dynamics of zonal flow and turbulent transport in some fusion devices.For example, the amplified zonal flow by direct current biasing was thought to act as a key trigger for the transition to improved confinement in TJ-II [5] and TEXTOR [6].The GAM-like oscillation flow (f ≈ 15 kHz) stimulated by alternating current biasing technique seems to be responsible for the reduced turbulent transport as reported in ISTTOK [7].A similar idea was proposed to drive a GAM-like flow by the application of a variable RMP coil current with acoustic frequencies [8], aiming to modify turbulent transport in DIII-D.The entirely damped GAM zonal flow induced by the 1.4 kA-RMP was found to be correlated with the increased edge turbulence observed in the MAST experiment [9].
Recently, studies of the role played by impurity ions on turbulence and plasma confinement have been extensively carried out, such as, neon seeding in DIII-D [10], nitrogen seeding in AUG [11], helium seeding in T-10 [12], boron injection in EAST [13] and LHD [14], and carbon and tungsten injection in HL-2A [15,16].A study that has attracted great attention is the one on tungsten, mainly because tungsten has been chosen as the plasma-facing material in ITER due to its high erosion resistance and good thermal conductivity [17].However, for a fusion reactor, the tungsten level is usually constant, and in the case of edge-localized mode eruptions, a transient increase in tungsten will occur [18,19].Several simulation studies indicate that tungsten has a stabilizing effect on trapped electron mode (TEM) turbulence when the impurity ion density profile is inwardly peaked [20], and the high-Z impurity could directly affect the GAM dynamics via Landau damping when the plasma toroidal rotation is sufficiently large [21].To our knowledge, there are still few experimental reports on the effect of tungsten ions on edge turbulence, GAM zonal flow and the resulting turbulent transport in magnetically confined plasmas.
In this paper, we report the observation of a reducedturbulence regime triggered by the increased GAM zonal flow due to tungsten injection in HL-2A edge plasma.The experimental findings demonstrate that the enhanced energy transfer from turbulence is the main cause of the amplification of GAM zonal flow in the presence of tungsten ions, which consequently leads to the reduction in turbulent transport.The remaining sections of this paper are organized as follows: section 2 is the description of the experimental setup; section 3 presents the experimental results including the comparison of spectral characteristics, evidence for the GAM zonal flow, the dynamics of zonal flow-turbulence affected by the tungsten ions and the coupling between zonal flow and turbulent transport; section 4 provides summary and discussion.

Experimental setup
The impurity injection experiments were performed in NBIheated deuterium plasmas in HL-2A tokamak (R = 1.65 m, depicts the arrangement of the reciprocating probe system [22] and the laser blow-off (LBO) system [23] both located at the outer mid-plane toroidally separated by 6.38 m in HL-2A.The main diagnostic used in our experiments was a doublestep probe array, as sketched in figure 1(b), where the probe tips were made from high-conductivity carbon materials with a diameter of 1.5 mm, an exposed length of 2.5 mm and a step height of 3 mm.At the first step, two tips (tip 1, tip 2) aligned along the magnetic field line are biased with −190 V for measuring V + and V − signals, and the other two tips (tip 3 and tip 4) poloidally separated by 6 mm (∆d θ = 6 mm) are used to measure floating potentials (V f3 and V f4 ).Here, the tips are carefully adjusted to minimize the phase error arising from the finite tip separation cross-field lines.A similar setup was used for the second step.According to the triple-probe principle [24], the local T e and n e are estimated by k, Z, m i and R s represent the effective collection area, Boltzmann constant, charge number, ion mass and resistance, respectively.The fluctuation-driven particle flux is calculated as ⟨Γ r ⟩ = ⟨ñ e ṽr ⟩, where ñe and ṽr = Ẽθ /B t = ( Ṽf3 − Ṽf4 ) / (B t ∆d θ ) denote the density and radial velocity fluctuations, respectively.In the triple-probe measurement, the plasma potential fluctuations were usually deduced from Ṽp = Ṽf + α Te , where α is the sheath drop coefficient and it is assumed to be 2.It is generally found that using the floating potential as a proxy for the plasma potential leads to an overestimation of the fluctuation-driven radial transport.It should be noted that here the triple-probe measurement might overestimate the temperature fluctuations.The main cause is that probe measurement is not performed at the same position.As a result, the method cannot distinguish between a fluctuation in the parameters or its local gradient and can therefore only give an upper limit for temperature fluctuations [26].The deepest radial position of probe measurement in this experiment was set at about 2.5 cm inside the LCFS, i.e. ∆r = −2.5 cm, where ∆r denotes the displacement of tips away from the LCFS.Here, ∆r = 0 represents the approximate location of LCFS calculated by the equilibrium fitting code with an accuracy of 5 mm, and the negative sign means inside of the LCFS.The sampling rate of the probe data is 1 MHz with a resolution of 12 bits.In addition, the tungsten was horizontally injected into the plasma from the outer mid-plane using the LBO system and the impurity related information was recorded by multiple diagnostics, such as extreme ultraviolet spectrometer [27], bolometer arrays [28], etc.Note that the total number of injected tungsten particles could be accurately controlled by changing the size of the LBO spot.It was roughly estimated to be about (1 ∼ 1.2) × 10 18 in the present experiment with the thickness (∼5 µm), density of the tungsten layer (∼19.35g cm −3 ) and the size of the laser spot (∼1 mm) on the target.In fact, in the experiment most of the tungsten particles from the LBO do not reach the plasma edge due to the formation of debris.In our study, the ionized tungsten particles are assumed to be entirely confined and uniformly distributed within a volume V p ∼ 4m 3 .Thus, the tungsten density is roughly estimated to be XB ≈ 0.05 (T e = 60 eV) is the inverse photon efficiency and I W 6+ is the measured radiation intensity of W 6+ .Thus, the ratio of tungsten to electron density is roughly calculated to be n z /n e ∼ 10 −4 [23], which is likely modest for the sustainable plasma performance in HL-2A.The results presented in this study are well reproducible as a nearly identical amount of tungsten is injected under similar discharge conditions.

Typical time evolutions of discharge parameters
Given in figures 2(a) and (b) are the typical discharge waveforms including the line-averaged density (n e ), the radiation power (P rad ), and the trajectory of the reciprocating probe (∆r) together with the plasma horizontal displacement (FDh) for shot 29655.The probe starts to move inwards from t = 700 ms to t = 800 ms, and then remains at a pre-set radial position for a period of time before it finally returns.It should be noted that the plasma parameters, e.g.ne , P rad , etc, remain almost unchanged as the probe is inserted into the plasma edge, as shown in figure 2(a), implying a negligible effect of the probe on the plasma state.The start time for the tungsten injection is set at t = 900 ms, which is also confirmed by the remarkable rise of P rad .Here, we note that the plasma horizontal displacement remains rather stable during the impurity injection phase, as evidenced in figure 2(b).In order to study the plasma behavior after the tungsten injection, zoomed-in plots are given in figures 2(c)-(f ) as an example to show the variation of plasma parameters in detail.The radiation intensity of tungsten (I W ) is characterized by the quasi-continuum of tungsten recorded by the EUV diagnostic [27].The edge electron temperature, density and the fluctuation-driven particle flux are all simultaneously measured by the double-step Langmuir probe staying at ∆r = −2.5 cm.The normalized collisionality was estimated to be v * ≈ 6.92 × 10 −18 qRZ eff n e lnΛT −2 e ϵ −3/2 , where q is the edge safety factor ∼ 4, Z eff is the effective charge number, ϵ = r/R is the inverse aspect ratio and ln Λ ≈ 14.7 is the Coulomb logarithm.The time sequence is divided into three phases.Phase I is named 'without tungsten'.Phase II is termed the 'transition phase', where both the H α emission and edge electron temperature significantly drop, whereas the plasma edge density (n e ) exhibits a less pronounced change after tungsten injection.Meanwhile, v * rises rapidly and then quickly decays within 50 ms, i.e. t = 900-950 ms.It is clearly seen that the turbulent transport starts to reduce from t = 900 ms (tungsten injection) and then remains at a low level in this phase, implying that the tungsten ions might play a stabilizing role in turbulence through the increasing collisionality [20,29].Phase III is called the new state of reduced-turbulent transport.Here, an important observation is that the plasma could continue to retain the low transport regime in phase III as the tungsten concentration gradually reduces, even if it is no longer present.This suggests that the reduced-turbulence state might not be closely related to the tungsten concentration.Some alternative physical processes, such as zonal flow, might be potential candidates for determining turbulent transport.In addition, it should be pointed out that impurity injection might change the radial profiles of density and temperature, which could affect the turbulence drive and neo-classical radial electric field.Unfortunately, data on the radial profiles of density (n e ) and temperature (T e ) in the edge region are unavailable in this experiment.However, we compared the radial profiles of density and temperature measured in the core plasma (ρ < 0.8), and found that both n e and T e in core plasma exhibit a slight rise and their profiles become steeper after tungsten injection.The potential effect of impurity injection on the n e and T e profiles will be our focus in future studies.

Change in turbulent spectrum due to the injected tungsten
In order to study the basic physical mechanisms determining the turbulent transport affected by the tungsten ions, we calculate the turbulent spectrum using the fluctuation signals recorded by the double-step Langmuir probe.In HL-2A edge plasmas, the potential fluctuation is generally dominated by a low-frequency coherent mode, which has been confirmed to be a GAM zonal flow by two probe arrays toroidally separated by 80 cm [30].The GAM usually has a local maximum at about 2-3 cm inside the LCFS [31].Plotted in figures 3(a) and (b) are the time traces of frequency spectra of floating potential and density fluctuations both measured at ∆r = −2.5 cm. Figure 3(a) shows that the coherent fluctuation in the floating potential immediately reduces after the tungsten injection, and then it starts to increase in phase II.At the end of this phase, the coherent fluctuation was observed to be substantially enhanced and its amplitude significantly exceeds the initial level in phase I.Note that the mode frequency remains nearly unchanged and it has a peak at f ∼ 11.7 kHz, which is well consistent with the theoretical prediction of the GAM frequency f th GAM ≈ 12.5 kHz estimated by 1 2 /(2π R) using the local electron temperature T e = 90 eV (assuming T i ≈ T e ) and edge safety factor q ≈ 4. No clear activity in the density fluctuation is found to be associated with the ∼11.7 kHz oscillation, as shown in figure 3(b), which might be related to the fact that the probe measurement is approximately located at the mid-plane with poloidal angle θ ∼ 0 • and therefore the GAM-induced density fluctuation is almost undetectable at this position due to its sinθ dependence [32] Te )sin(θ), where k r is the radial wave number, ρ i denotes the ion gyroradius and e φ Te represents the normalized potential fluctuation.Based on the above facts, i.e. the frequency scaling and the spectrum characteristics, we conclude that the observed coherent fluctuations are essentially attributed to the GAM zonal flow.On the other hand, one can see that the GAM floating potential markedly rises, while the density fluctuation in 20-80 kHz exhibits an evident drop in phase III, compared to that in phase I.This opposite behavior demonstrates that the turbulence level can be significantly affected by the GAM zonal flow.
To further clarify the change of turbulent fluctuation, we compare the frequency spectra of floating potential and density fluctuation within two time slices, i.e. ∆t 1 = 800−900 ms (labeled 'without tungsten') and ∆t 2 = 950−1050 ms (labeled 'with tungsten'), which are indicated by two shaded areas at the top in figure 3(a).In each time slice, the ensemble realization number is estimated to be N ≈ 194 by using the ∼1024 width Hanning-window and overlapping 50% for the neighboring ensembles.Consequently, the frequencyresolution could reach ∆f ≈ 0.98 kHz.In comparison, in figures 3(c) and (d), it can be clearly seen that the amplitude of the GAM zonal flow in the floating potential significantly increases after the tungsten injection, whereas the floating potential fluctuation level in 20-100 kHz slightly reduces.A substantial reduction in the fluctuation level occurs in the density fluctuation below 100 kHz, as illustrated in figure 3(d).The comparison given here shows the presence of opposite behavior between turbulence and GAM zonal flow.

Evidence for the enhanced interaction of GAM and turbulence
The bispectral analysis technique [33] has been widely used to study the nonlinear coupling in several experiments [34][35][36].The squared auto-bicoherence is defined as b It is clearly shown that the bicoherence values along the f 2 = ±11.7 kHz and f 2 = − f 1 ± 11.7 kHz lines in the case with tungsten ions are much larger than those without tungsten injection, indicating that the nonlinear coupling of fluctuations is significantly enhanced with tungsten injection.In order to quantitatively compare the degree of nonlinear coupling, we calculated the summed squared bicoherence , as illustrated in figure 4(c).It is found that the coupling peak at f ≈ 11.7 kHz dramatically increases from 1.3 × 10 −2 -2.3 × 10 −2 , suggesting the enhancement of the nonlinear coupling.In addition, it should be noted that the nonlinear coupling mainly occurs in the low-frequency fluctuation part (20 kHz < f < 60 kHz).Here, we roughly estimate the poloidal wave number (k θ ) of power spectral density using two-point correlation analysis [37] and found the k θ is in the range of k θ = 1.5 ∼ 2.1 cm −1 , which is consistent with the TEM turbulence.On the other hand, the turbulent spectrum, as sketched in figure 3(d), displays the quasi-coherent mode characteristics as well, which is in good agreement with the previous observations in Tore Supra and AUG devices [38].The experimental results presented here indicate that this low-frequency fluctuation (20-60 kHz) might be essentially attributed to TEM turbulence.
To further elucidate the energy transfer between lowfrequency turbulence and GAM zonal flow, we estimate the frequency spectra involving cross power, coherence and phase shift between the envelope of density fluctuation filtered in 20-60 kHz (ñ env e,AT ) and radial electric field ( Ẽr ), and compared them in figures 5(a)-(c).The positive sign of the phase shift means that ñenv e,AT leads the Ẽr .It can be clearly seen that the cross power and coherence have a peak at the GAM frequency (f = 11.7 kHz) and both exhibit an apparent increase after the tungsten injection.Meanwhile, one can see that the phase shift remains nearly unchanged (∼0.5 π) in both cases, indicating that the variation of prey (ñ env e,AT ) leads the change of predator ( Ẽr × B flow) by about π/2, which is qualitatively consistent with the theoretical prediction by the predator-prey model [39].Similar results have been reported in other fusion devices, such as JFT-2M [40], TEXTOR [41] and HT-7 [42].
Here, it should be pointed out that Ṽf and ñenv e,AT signals were used to attempt to study the predator-prey relation in some experiments [43,44].In fact, the variation of Ẽr advances Ṽf fluctuations by about π/2 ( Ẽr = −ik Ṽf ), thus the phase difference between ñenv e,AT and Ṽf is close to π, assuming that the predator-prey model is valid.However, for a phase difference around π, it is hard to conclude the causality between predator and prey.Therefore, the calculated cross-spectra between ñenv e,AT and Ẽr signals are suitable to show the predator-prey relationship.In addition, no apparent modulation activity of the high-frequency fluctuations (100-500 kHz) by GAM zonal flow was found in this experiment, implying that the highfrequency turbulence makes little contribution to the excitation of the zonal flow.

Dynamics of zonal flow-turbulence affected by the tungsten ions
In order to study the role played by tungsten ions inthe turbulence-zonal flow dynamics, a simple model of the power balance between turbulence and zonal flow has been applied [45]: , where v ZF 2 is the energy of zonal flow, F RS v ZF = − ∂ ∂r ⟨ṽ r ṽθ ⟩v ZF denotes the rate of work done by the turbulent Reynolds stress on the zonal flow and µ means the damping rate of the zonal flow.F RS v ZF and µv ZF 2 represent the driving and damping terms of the zonal flow, respectively.Apparently, their competition determines the zonal flow dynamics.Here, we first study the effect of tungsten ions on the GAM damping.In fact, the simulation work [21] has demonstrated that the tungsten impurity has influence on both frequency and damping rate of GAM zonal flow via Landau damping mechanism since the plasma toroidal Mach number is larger than 0.5.This is mainly due to the Coriolis drift and centrifugal drift of the heavy impurity induced by the toroidal rotation.However, there have been few experimental reports on the impact of tungsten ions on the GAM dynamics.As an example, the time traces of the radiation intensity of tungsten I W , the effective charge number (Z eff ) measured by the visible bremsstrahlung diagnostics [46] and the central frequency f c, GAM together with the GAM amplitude are plotted in figures 6(a)-(c).Here, the GAM central frequency is estimated with the weight-frequency power spectrum S (f ), i.e. f c,GAM = , where [f 1 f 2 ] denotes the full width at half maximum of the GAM.It was observed that the GAM frequency remains nearly unchanged after tungsten injection excluding the period of 900-950 ms.The Z eff has an apparent rise from 3.5 to 5.5 after tungsten injection (the average charge is about 5 in the edge region).Here, it should be noted that the measured toroidal Mach number is low (M = 0.2-0.3) in HL-2A edge plasma for similar discharge conditions [47,48].Hence, the tungsten ions might play less of a role in the Landau damping of the GAM zonal flow via wave-particle interaction in the low-toroidal rotation case (M < 0.5), which is qualitatively consistent with the simulation work [21].In addition, when combining figure 6(b) with figure 6(c), one can see that the GAM frequency exhibits a slight drop along with the transient increase in Z eff at the early stage of phase II (t = 900-920 ms), indicating that the impurity could affect the dynamics of GAM zonal flow.This is qualitatively consistent with the theoretical simulation work [49], that is, the GAM frequency decreases with the increased Z eff in the large effective charge limit (Z eff ⩾ 3) in deuterium plasmas.
Next, our study is concentrated on the driving term for GAM zonal flow, i.e.F RS v ZF = − ∂ ∂r ⟨ṽ r ṽθ ⟩v ZF , which represents the work done by turbulent Reynolds stress on zonal flow.Unfortunately, in our study, the term F RS v ZF could not be directly calculated due to the absence of multistep probe measurement.Therefore, the coherence γ ñenv e , Ṽf between the floating potential and the envelope of density fluctuation filtered in 20-60 kHz is used as a rough estimation degree of nonlinear energy transfer from turbulence to GAM zonal flow [41].On the other hand, it should be kept in mind that as discussed above, tungsten ions play a negligible role in Landau damping of zonal flow, but the collisional damping rate of GAM zonal flow still remains [32].In our case, the damping rate by considering the Z eff effect [50] could be roughly expressed as 3, v ie represents the ion-electron collisional frequency.The time traces of the driving term ( γ ñenv e , Ṽf ) and the collisional damping rate of GAM ((γ damp )) are plotted in figure 6(d), which shows that the coherence ( ñenv e , Ṽf ) exhibits a slight drop, while the GAM collisional damping rate ((γ damp )) rises remarkably after the tungsten injection in phase II, which might be responsible for the reduction in GAM zonal flow observed in this phase, as shown in figure 3(a).However, it is clearly seen that the amplitude level of the GAM zonal flow increases substantially at the end of phase II and exceeds the initial fluctuation level in phase I, as evidenced in figure 6(c).Apparently, a complex interaction along impurity ions, turbulence, zonal flow and equilibrium radial electric field might occur in phase II.However, the study of the physical mechanism determining the GAM zonal flow dynamics is left for the future.Phase III is characterized by the enhanced GAM zonal flow together with lower turbulence, as shown in figures 3(a) and (b), and the study of the reduced-turbulence regime in this phase is the focus of our study.It is clearly demonstrated that the increased nonlinear coupling is the main cause of the enhancement of the GAM amplitude.Similar experimental results have been reported in DIII-D plasmas, that is, the increased nonlinear coupling between turbulence and lowfrequency fluctuation was thought to act as a trigger for the L-H transition [34].
According to the theoretical prediction [51], the turbulence energy can be transferred to the zonal flow since the turbulent eddies are elongated or tilted by a straining-out process.Therefore, the generation of zonal flow might be closely correlated with the turbulent vortex shape involving the size, titling angle, etc.In experiments, the poloidal correlation length (L θ ) of turbulent vortex can be directly computed by using the inverse values of the wavenumber spectral widths (σ k ) measured by two poloidally separated probes, i.e.L θ = 1 ⟨σ k ⟩ , where As shown in figure 7(a), the time trace of L θ and the equilibrium poloidal velocity ( Vθ ) along with the error bars are calculated from the standard deviation.The results shows that L θ is visibly increased after the tungsten injection, along with the change of Vθ , implying that the increased E × B shear flow might play an active role in stretching turbulent eddies.Similar experimental results have been reported in several devices, such as LAPD and TEXTOR [52,53], but the mechanism responsible for the enhancement of E × B flow remains unresolved.For simplification, here we calculate the joint probability distribution function (PDF) of the poloidal ( Ṽθ ) and radial ( Ṽr ) velocity fluctuations as P = P( Ṽθ , Ṽr ) = N/N 0 , where N means the number of events that occur in the interval, and N 0 represents the time series dimension.The data were recorded by the double-step Langmuir probe array staying at ∆r ≈ −2.5 cm.The comparison in figures 7(b) and (c) is a joint-PDF of Ṽθ and Ṽr without and with tungsten injection, respectively.One can see that the joint-PDF has an elliptical distribution shape across the first and third quadrants.In fact, the averaged ⟨ Ṽr Ṽθ ⟩ represents the Reynolds stress tensor, and therefore the asymmetric distribution of the joint-PDF results in a non-zero Reynolds stress.The apparent joint-PDF distribution of Ṽθ and Ṽr is more asymmetric in the case with tungsten injection compared to that without tungsten, suggesting a stronger Reynolds stress drive for the generation of GAM zonal flow.On the other hand, the value of Ṽθ / Ṽr represents the tilting degree of the structure, which means symmetry breaking of the eddy structure in order to generate the nonzero Reynolds stress.It can be seen that the tilting angle of the Reynolds stress tensor, Ṽθ / Ṽr , evidently increases after tungsten injection, implying that stronger straining-out of turbulent eddies indeed occurs in the presence of tungsten ions.
The results presented here indicate that the increased energy transfer is the main cause of the excitation of the GAM zonal flow.

Suppression of local turbulent transport due to the increased zonal flow
The radial particle flux in the frequency domain can be decomposed as the following formula, Γ r (f ) = phase shift between ñe and Ṽf .To study which term plays a major role in the suppression of the particle flux, we estimate the variation in each term using the probe data with two time slices, i.e. ∆t 1 = 800−900 ms (without tungsten) and ∆t 2 = 950−1050 ms (with tungsten) and compared them in figure 8.It is observed that the low-frequency fluctuation below 20 kHz makes almost no contribution to particle transport, which mainly results from the near-zero poloidal wave number predominated by the GAM zonal flow.In the highfrequency part, i.e. 20-100 kHz, it is found that the density fluctuation level is substantially reduced with tungsten injection compared to that without tungsten.However, the poloidal wave number (k θ ), the fluctuation level below 100 kHz in floating potential ( Ṽf ), the coherence (γ ñe Ṽf ) and phase shift between ñe and Ṽf exhibit less pronounced change.This comparison clearly indicates that the reduction in the radial particle flux is mainly attributed to the reduced power in ñe rather than the phase shift, which is in agreement with the previous experimental report [54].The opposite behavior of the particle flux and the GAM amplitude manifests that the particle transport is coupled with the GAM zonal flow, that is, the tungsten ions play an active role in the dynamics of the GAM zonal flow and the resulting turbulent transport.In addition, we note that the phase shift (θ ñe Ṽf ) between the potential and density fluctuations remains near zero or π at GAM frequency in the case of 'with tungsten' as denoted by the red curve in figure 8(e), which is well consistent with the simulation result [55].The observed deviation of the phase shift might be related to the non-adiabatic response of passing electrons [56].
The local transport reduction associated with increased GAM zonal flow is recognized in figure 9, where the horizontal axis denotes the fluctuation level of GAM zonal flow Ṽenv f,GAM estimated by the envelope of the floating potential fluctuation filtered in a GAM frequency of 8-15 kHz.The vertical axis denotes the time-averaged particle flux ⟨Γ r ⟩, which is generally thought to be overestimated mainly due to the use of floating potential as a proxy for the plasma potential [26].The analysis data recorded by the double-step Langmuir probe at ∆r = −2.5 cm were taken from several shots with analogous discharge conditions.One can see that the distribution of particle flux against the GAM amplitude is localized in two distinct regions, i.e. the blue-square point stays in the region with a weaker GAM zonal flow and a higher particle flux without tungsten injection.It is found that the distribution region moves towards the lower-right direction with stronger GAM zonal flow and lower transport denoted by the red-circle symbols in the scenario with tungsten injection as sketched in figure 9, implying a negative relationship between the GAM zonal flow and the radial particle flux.The obtained results demonstrate the active role played by the tungsten ions in the suppression of edge turbulent transport due to the increased GAM zonal flow.

Summary and discussion
In summary, a reduced-turbulence regime driven by tungsten injection has been observed by using a double-step Langmuir probe in the HL-2A edge plasma.The experimental results indicate that the GAM amplitude and the size of the turbulent vortex together with the eddy tilting angle are all increased in the presence of tungsten ions.Evidence shows that the GAM zonal flow can gain more energy from turbulence via the nonlinear coupling, while the collisional damping of the GAM zonal flow exhibits a slight drop.In this experiment, it was found that no apparent role was played by the tungsten ions in the GAM Landau damping, which is mostly correlated with the low toroidal rotation.Therefore, we conclude that the increased nonlinear coupling constitutes the dominant contribution to the enhancement of the GAM zonal flow, which consequently results in low turbulent transport.This study could help us to better understand the physical mechanism determining turbulence and associated transport response to the high-Z impurity ions in tokamak plasmas.
However, some issues still remain to be discussed.First, the energy transfer rate and the work done by turbulent Reynolds stress were not directly estimated due to the absence of a multistep Langmuir probe measurement.Second, the GAM zonal flows were observed to significantly increase with a time delay (∼50 ms) after tungsten injection.However, it remains unclear what the key trigger is for the excitation of the GAM zonal flow again in phase II.This is important for our understanding of the zonal flow physics and is left for future study.Third, in our experiment, we only study the dynamics of the GAM zonal flow affected by tungsten in the low toroidal rotation case, but it is not yet understood how the tungsten ions affect the zonal flow behavior and the associated turbulent transport in the high toroidal rotation case.Fourth, the impurity density profile is not directly measured, which might also play a role in destabilizing or stabilizing turbulence, e.g. the TEM, ion temperature gradient, etc.Finally, no core fluctuation measurements are available at present and it is not clear if there are potential links between edge turbulence and core fluctuation in the presence of tungsten ions in magnetically confined plasmas.

Figure 1 .
Figure 1.Measurement layout of the reciprocating probe and LBO systems (a); sketch of the double-step Langmuir probe (b).Innermost position of probe measurement inside LCFS is about 2.5 cm.

Figure 2 .
Figure 2. Time trace of the line-averaged density together with the radiation power (a), trajectory of reciprocating probe and the plasma horizontal displacement (b), zoomed-in plots of the Hα emission, the radiation intensity of tungsten (c), electron temperature, density (d), the normalized collisionality ν * (e) and turbulence-driven radial particle flux (f ) measured by the probe remain at ∆r = −2.5 cm.

Figure 3 .
Figure 3. Time-frequency spectra of floating potential fluctuation (a) and plasma density fluctuation (b) both measured at ∆r = −2.5 cm.Comparison of the resulting spectra of floating potential fluctuation (c) and electron density fluctuation (d) without and with tungsten injection denoted by blue and red lines, respectively.Corresponding time slices are indicted by two shaded areas at the top in figure (a).
is the Fourier transform of the fluctuation signal x (t), N is the ensemble number and subscript i represents the ensemble index.Comparison in figures 4(a) and (b) is made with the contour-plot of the squared bicoherence of the floating potential signals measured at ∆r − 2.5 cm.

Figure 4 .
Figure 4. Contour plots of the squared auto-bicoherence of floating potential fluctuations ⟨ Ṽf Ṽf Ṽ * f ⟩ without tungsten injection (a) and with tungsten injection (b), and the comparison of the resulting summed bicoherence ∑ b 2 (f ) (c).Probe measurement is localized at ∆r = −2.5 cm.

Figure 5 .
Figure 5. Frequency spectra of cross power (a), coherence (b) and phase shift (c) between the envelope of ñe filtered in 20-60 kHz and Ẽr without (blue curve) and with (red curve) tungsten impurity.

Figure 6 .
Figure 6.Time trace of radiation intensity of tungsten I W (a), the Z eff (b), the GAM central frequency and the RMS of the floating potential fluctuation filtered in the GAM frequency (c), the coherence ( γ ñenv e , Ṽf ) together with the GAM collisional damping rate (γ damp ) (d).Measurement position of the probe remains at ∆r = −2.5 cm.

Figure 7 .
Figure 7. Time trace of the poloidal correlation length (L ) together with the poloidal equilibrium velocity ( Vθ ) (a).Comparison of the joint-PDF between the poloidal and the radial velocity fluctuations without (b) and with (c) tungsten.

Figure 8 .
Figure 8.Comparison of the decomposed radial particle flux in the frequency range within two time slices (without and with tungsten).Poloidal wave number k θ (a), the auto-power spectra of Ṽf (b) and ñe (c), the coherence (d) and sine value of the phase shift (e) between Ṽf and ñe, and the radial particle flux (f ).

Figure 9 .
Figure 9. Distribution of the time-averaged radial particle flux against the GAM amplitude without and with tungsten denoted by blue-square and red-circle symbols, respectively.