Gas puff imaging measurements during resonant magnetic perturbations on the HL-2A tokamak

The gas puff imaging diagnostic is used for the investigation of the poloidal flow and turbulent fluctuations at the plasma edge and scrape-off layer (SOL) on the HL-2A tokamak. The impact of resonant magnetic perturbations (RMPs) on the edge poloidal velocity ( Vθ ) are investigated and compared during the operation of a stair-like rising RMP coil current ( IRMP ). The application of the RMP is observed to modify the poloidal velocity significantly. When IRMP exceeds 4 kA, the turbulence poloidal velocity at the edge changes direction from electron to ion diamagnetic drift. This phenomenon is explained by the electron loss along the perturbed radial magnetic field (Br) with RMP, with the experimental evidence provided that the edge electric potential increases significantly. A strong impact of the RMP on the properties of plasma density fluctuations in the SOL is also observed. With RMP, both skewness and kurtosis are smaller in the SOL and large-scale turbulence structures (small kr and kθ ) are suppressed in both edge and SOL. These results can improve our understanding of the interaction between RMP and edge turbulence and in particular, the edge poloidal flow.


Introduction
Finding ways to mitigate type-I edge localized modes (ELMs) is of great interest because it is one of the major challenges on the way towards ITER [1].Resonant magnetic perturbations (RMPs) have frequently been used for MHD control, including ELMs mitigation and error field correction.The experiment on the DIII-D tokamak showed that the application of RMP 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.can lead to full ELMs suppression [2,3].Measurements made on TEXTOR by Langmuir probe arrays show that with RMP, the fluctuation poloidal velocity changes its direction from electron to ion diamagnetic drift direction, consistent with the observed reversal of the E r × B flow [4,5].Similar results have been reported on the same machine using reflectometer [6].Besides, researchers found that the application of RMP increases the rotation in the scrape-off layer (SOL) and brakes it on the edge.In MAST, when RMPs were applied, an asymmetrization of the ion saturation current fluctuation probability density function (PDF) changing toward non-Gaussian shapes was observed, and RMP can also be effective to modify the radial electric field and the poloidal rotations [7].
The plasma edge poloidal shear flow has always been an active area of research since 1990 when researchers on the DIII-D tokamak found that marked changes in the edge radial electric field and the poloidal rotations were important signatures of the L-H transition [8].Several diagnostics have been used for the study of poloidal flow over the past years.However, the measurements made by Langmuir probes or reflectometer are usually limited to one-dimensional measurements and cannot give a comprehensive picture in the poloidalradial two-dimensional plane, especially turbulent structures in the cross section.Along with the rapid progress of fast cameras in recently years, improved spatiotemporal resolution of plasma fluctuation measurements by gas puff imaging (GPI) [9] diagnostic can give direct two-dimensional plasma images and allow the investigation of poloidal propagation of turbulence in a larger range.
In this paper, we will present the experimental results obtained with the HL-2A GPI diagnostic [10,11] and supported by Langmuir probe measurements, focusing on the impact of the RMP on the poloidal velocity and edge plasma density fluctuation properties in ohmic plasmas.The causes for the inward displacement of the poloidal flow shear layer are analyzed in detail and new experimental evidence supporting the explanation is presented.The measurements include V θ fieldmap calculated by the TDE (time delay estimation) method, skewness and kurtosis profiles, and wavenumber spectra for both edge & SOL.
This paper is organized as follows: the experimental approach, RMP coils and the GPI system are detailed in section 2. We set the RMP coil current to be stair-like rising with time to show the threshold of RMP coil current for the significant modification to poloidal flow on HL-2A more clearly.The impact of RMP on edge poloidal shear flow and plasma density fluctuation properties are presented in section 3 and the corresponding physical processes are analyzed.Discussions and conclusions are devoted in section 4.

Main parameters evolution
HL-2A is a medium-size tokamak which is operated with deuterium plasmas and typically operated under a limiter or lower single null divertor configurations [12][13][14][15].Its major radius is R = 1.65 m and minor radius is r = 0.4 m.Heating powers are 3 MW of neutral beam injection, 2 MW of low hybrid current drive, and 5 MW of electron cyclotron resonance heating.The experiments (shot #32653 and #32654) are operated in ohmic discharge under a limiter configuration.
The time evolution of main discharge parameters in the experiment (shot #32654) are shown in figure 1 (e) RMP coil current.These parameters remain almost constant during the application of RMP.Helium is used as the GPI working gas and is puffed into the plasma edge starting at 500 ms and continuing for 5 ms to observe the evolution of poloidal flow and turbulence structures.Time period from 450 ms to 850 ms is divided into eight parts, marked as part x to part and each for 50 ms.Part x, part y and part are periods before or after RMP applying, i.e.I RMP = 0 kA, as a reference.From 550 ms to 800 ms (part z to part ~), RMP is applied with stair-like coil currents.The maximal current of I RMP = 4.7 kA is applied during part } and the applied RMP coil current sequence for all parts is illustrated in figure 1(e).#32653 and #32654 shots are identical shots with similar results, and we present #32654 results in this paper.

Setup of RMP coils on the HL-2A
The ELM control RMP coils system installed on HL-2A [16,17] consists of 2 × 2 coils symmetrically distributed along the midplane, with two rows of coils (upper and lower with a separation of poloidal angle ≈66.5 • ), as shown in figure 2. These four coils are connected through a connecting board, which can adjust and control the current direction of each coil individually.When the current in the coil 2 and 3 flows in clockwise direction (shown in red), the perturbated field (δB) points to the plasma core.And this current is defined as '+', otherwise '−'.The current connection in figure 2 is '−', '+', '+', '−' in the coil 1, coil 2, coil 3 and coil 4, respectively.This RMP coil system generates multiple RMP field components.By applying the coil currents flowing in the opposite direction in each row, as in this experiment, perturbations with odd n number (mainly n = 1,3) are excited.

GPI diagnostic on HL-2A
A GPI diagnostic was developed on the HL-2A tokamak to investigate two-dimensional plasma edge turbulence in the poloidal-radial plane [10,11].Its spatial resolution is  1.25 mm × 1.25 mm and time resolution is 2-10 µs.This diagnostic system can measure the edge plasma density evolution in a 15 cm × 15 cm outer-midplane region, as is shown by the red box in figure 3. The magnetic surfaces are reconstructed by EFIT [18] during a limiter discharge.The last closed flux surface (LCFS, also a separatrix) is shown by the blue line and the fixed limiter by red.A detailed description of this GPI diagnostic on the HL-2A can be found in [10,11].

Calculation of edge poloidal velocity (V θ )
The TDE [19,20] velocity technique using cross-correlations between two spatially separated signals is utilized to calculate the average V θ field in every 50 ms from part x to part .GPI's high spatiotemporal resolution promises a favorable method to measure the two-dimensional evolution of poloidal velocity.
The poloidal velocity field in the GPI viewing area in part x is shown in figure 4. The negative velocity in the SOL indicates it is moving along the ion-diamagnetic drift velocity (downward) direction, while a positive velocity in the edge indicates it is moving along the electron-diamagnetic direction.The LCFS (separatrix) obtained by EFIT reconstruction is shown by the black dotted line, which matches the reversal of poloidal turbulence propagation velocity perfectly.
Edge Langmuir probe array which can move along the midplane have long been the main tool to measure onedimensional edge/SOL poloidal V θ profile on HL-2A.Earlier experiments on HL-2A tokamak showed that there was not much difference between the phase velocity measured by TDE and the mean flow poloidal velocity calculated by E r × B /B 2 [21,22].In order to verify this conclusion, the measurements   than a Langmuir probe array can, as shown in figure 4, because probe tips cannot endure the high heat flux in deep plasma.Profiles measured by both diagnostics indicate that the poloidal velocity changes its sign while crossing the separatrix, resulting in a strong poloidal velocity shear.In this article, this layer where V θ = 0 is marked as layer I just for convenience in this paper.

Impact of RMP on poloidal flow
Theoretical predictions [22] have indicated that the application of RMP has a major impact on the radial electric field E r .GPI data are analyzed to infer the impact of different RMP amplitudes on V θ field.From part z to part ~, RMP are applied with increasing current amplitudes.The average V θ fields for these eight parts are calculated, as are shown in figure 6 which means poloidal flow in the box changes direction from electron-diamagnetic to ion-diamagnetic drift direction.The radial location of layer I moves deeper along with the increasing RMP coil current.A maximal moving distance of about 4 cm is realized when I RMP = 4.7 kA and a larger moving distance is expected with a higher I RMP which is unfortunately limited by the ability of the RMP system on HL-2A in this experiment.It is to be noted here that this 4 cm moving distance is far larger than the displacement of the magnetic axis shown in figure 1(d), so RMP is the only reason for radial re-distribution of poloidal velocity.When the coil current decreases, layer I moves outwards and when finally, RMP is turned off in part , layer I moves back to separatrix.
Similar experimental phenomena were reported on several tokamaks using different diagnostics before [4,6,7], and the threshold of significant movement of layer I is I RMP = 4 kA on the HL-2A tokamak.The maximum disturbed B r with I RMP = 4 kA RMP is B r = 73.6Gauss, and it mainly contains m = 3, 4, 5 and n = 1, 3 components.The maximum component m/n = 4/1 is 1.6 Gauss at ρ = 0.94.
A possible explanation for the inward shift of the poloidal velocity profile proposed in earlier reports is that the application of the RMP changes the magnetic topology in edge [4,7]: magnetic field lines that lied on a closed magnetic surface now have radial component (towards the wall) with RMP.Since the electrons thermal velocities are much faster than massive ions, the loss of electrons along the disturbed magnetic field lines is much more than ions, which charges the plasma edge positively.Recent comprehensive theoretical investigation gives a detailed physical process in which the stochastic RMP driven magnetic fields produce a radial electron current density, which drives particle transport [23].We now try to find experimental evidence to verify this explanation.The time evolution of (a) the radial electric field E r at R − R sep = −4 cm (ρ = 0.9) and (b) the electric potential (V f ) at R − R sep = −3.7 cm (ρ = 0.91) from 550 ms to 850 ms is shown in figure 7. When I RMP reaches 4.7 kA, the radial electric field at R − R sep = −4 cm is close to zero, which is consistent with the experimental phenomenon of poloidal velocity modification in figure 6.According to the explanation, the displacement of inversion point is due to the accumulation effect of electron loss, which charges the edge electric potential positively.There are many possible factors affecting the frequency range of turbulence fluctuations, like the nonlinear energy transfer from higher frequency turbulence to lower frequency turbulence, larger turbulence structure [24] and the displacement of shear layer with the application of RMP.Future work will be focused on the detailed study of the turbulence frequency changes with RMP and the comparison between the experimental observations with the simulation work is being done.

Impact of RMP on turbulence density properties
The intensity of the GPI signal (I GPI ) can be simplified as [9]: where n 0 is the helium density, n e and T e are the local plasma density and electron temperature, respectively, and the function f is the ratio of the density of the upper level of the radiative transition to the ground state density times the rate of decay of the upper level.Researches show that GPI signal fluctuations ( ĨGPI ) are proportional to the plasma density fluctuations when the plasma density is relatively low (n e ⩽ 10 18 m −3 for helium as the GPI working gas) [9,[25][26][27]: To prove that this result is also valid for the HL-2A, we crosscheck the GPI intensity fluctuations with the ion saturation current fluctuations ( Ĩsat ) data by Langmuir probes on the same flux surface.The Ĩsat data is generally believed to be proportional to the plasma density fluctuations (i.e., Ĩsat ∝ ñe ) [25].The comparison results are shown in figure 9.It is clearly seen that the fluctuation events are observed by both diagnostics and these two signals demonstrate a strong correlation.Furthermore, the cross-correlation coefficient of Ĩsat and ĨGPI is calculated, and 92.1% cross correlation is found, which verifies the strong correlation between the two signals.Thus, the conclusion that GPI is also a diagnostic for plasma edge density fluctuations is verified on the HL-2A.
The impact of 4.7 kA RMP on the PDF of plasma density fluctuations are studied using GPI diagnostic data.The characteristics of turbulent fluctuations are characterized using statistical features like PDF.The profiles of the skewness and kurtosis of the ñe are calculated, defined as the third-order and fourth-order moments of the fluctuation data [22,28,29].Skewness and kurtosis profiles with and without RMP are illustrated in figure 10.
The impact of the RMP on turbulence density fluctuations is displayed quite clearly: both skewness and kurtosis are reduced by the RMP in the SOL at 0-3 cm from separatrix.This result is in agreement with measurements on TEXTOR  [30].Furthermore, we calculate the turbulence k-spectrum to investigate the impact of RMP on turbulence of different scales.
The turbulence k r -spectrum (S (k r )) with (red line) and without RMP (blue line) are given in figure 11.Figures 11(a) and (b) are measured in the edge and SOL, respectively.The negative value in figure 11 means the turbulence is moving outwards to the wall.The S (k r ) with RMP is lower than that without RMP, especially small k r components, which means large-structure turbulence.When RMP is applied, the peak of k r is reduced by 16% in the edge.While, in the SOL the peak is reduced by 60% with RMP, much larger than that at the edge.
We also calculate the turbulence k θ -spectrum (S (k θ )) with and without RMP both in the edge and SOL.The results are shown in figure 12.The negative value in figure 12 means that the turbulence is moving along electron-diamagnetic drift direction.The impact of RMP on S (k θ ) is quite similar to it on S (k r ) as shown in figure 11.When RMP is applied, the peak of k θ is reduced by 45% in the edge and 67% in the SOL.The suppression effect of RMP on S (k θ ) is more obvious than it on S (k r ).In other words, the suppression effect of large-structure turbulence in the poloidal direction is more obvious than in the radial direction.
In conclusion, large-scale turbulence structures are suppressed by RMP in both edge and SOL, especially in the SOL.
In simulations [31], it is shown that before the RMP, the modes with k ∥ ≈ 0 on rational surfaces are subject to strong instabilities, whereas during the RMP the modes are damped by resistivity because k ∥ becomes finite and nonzero.This enhances the sheath dissipation.The sheath dissipation tends to reduce the charge separation, thus decreases the radial velocity of the large eddy structures [32].Thus, the enhanced sheath dissipation by nonzero k ∥ suppresses the large eddy turbulence structures.The simulation results offer a possible explanation for the suppression of RMP on turbulence structures, and searching for experimental evidence still needs further work.

Discussion and conclusion
Edge poloidal shear flow (also the electric field) is the key to understand L-H transition and turbulence transport in magnetic confinement devices, especially in future fusion reactors like ITER.Improved diagnostics allow us to study it in a larger measurement range and better spatial and time resolutions.GPI diagnostics on the HL-2A tokamak is used to investigate the impact of the RMP on the poloidal turbulence transport properties at the edge and the SOL, mainly focusing on poloidal flow and density fluctuations.These results show good similarities with those obtained using several other diagnostics during RMP operations on other tokamaks.We observe that RMPs have significant impact on both poloidal flow and turbulence structure properties when the RMP coil currents exceeds the threshold (4 kA).
When I RMP exceeds 4 kA, the inversion point of poloidal velocity (layer I) starts to shift further inside.A maximal moving distance of 4 cm is realized when I RMP = 4.7 kA.The edge potential start to increases from 650 ms (I RMP = 4 kA), and the potential turns positive during I RMP equals to the 4.7 kA time period.This modification is explained by increased electron loss along the disturbed radial magnetic field line when RMPs are applied, and the increase in boundary potential and the change of radial electric field provide strong experimental evidence.
The edge turbulent energy concentration frequency range changes from 0-40 kHz to 0-20 kHz during the application of 4.7 kA RMP.We argue that the nonlinear energy transfer from higher frequency turbulence to low frequency turbulence happens with the application of RMP.However, there are also other mechanisms that also affect the turbulence frequency, such as larger turbulence structure and the displacement of shear flow.We believe that this will be an interesting topic for future works and that a comparison between the experimental observations with the simulation work is being done.Future experimental work will focus on the detailed study of the turbulence energy transfer with RMP.
The GPI line emission and I sat data by Langmuir probes on the same flux surface are compared, and a strong cross correlation (92.1%) is found, confirming that the GPI is a diagnostic for plasma edge density fluctuations.The impact of RMP on n e fluctuations is studied.GPI line emission intensity data are used to calculate skewness and kurtosis profiles as well as the wavenumber spectrum S(k).Results show that both skewness and kurtosis are reduced by RMP in the SOL.And large-structure turbulence (small k r , k θ ) is suppressed by RMP in boundary plasma, especially in the SOL.
There are also some improvements we can make in the future.We will try several puffs during the investigated time period instead of just once in the beginning to ensure that the GPI signal remains approximately constant during the observation.If the emission lights are strong enough, we can set a fast camera exposure time 2.5 µs to have a better time resolution, and therefore we can study the plasma edge turbulence propagation properties and large-scale turbulence structures in more details.
These results can improve the understanding of the mechanisms of RMP interaction with the edge-SOL turbulence and particularly on the edge poloidal flow, and these may help to find a way to control edge turbulent transport and reduce plasma-wall interaction in ITER and future fusion power plants.
2019YFE03060002, National Natural Science Foundation of China under Grant Nos.U1867222, U1967206 and 51821005 and the Sichuan Natural Science Foundation under Grant Nos.2022NSFSC1791 and 2020JDTD0030.

Figure 2 .
Figure 2. The RMP coils are shown in blue and red on the HL-2A tokamak.

Figure 3 .
Figure 3.The GPI geometry on HL-2A tokamak.The last closed flux surface is shown by the blue line and the fixed limiter by red.GPI viewing area is illustrated by the red box near the outer midplane.

Figure 4 .
Figure 4. Average V θ field map in the poloidal vs. radial plane (GPI viewing area).The black dotted line is the separatrix reconstructed by EFIT, in perfect match with the reversal of turbulence poloidal velocity.R − Rsep < 0 means the edge (inside the LCFS) where V θ is along the electron-diamagnetic drift velocity direction.R − Rsep > 0 means SOL where the direction of V θ is opposite.

Figure 5 .
Figure 5. V θ profile measured by GPI (a) and Langmuir probes (b) during the same time period.These two ways to measure poloidal velocity show a good consistency.

Figure 6 .
Figure 6.Average poloidal velocity (V θ ) fields of part x to part during the shot.Blue boxes are fixed at R − Rsep = −4 ∼ 0 cm (ρ = 0.9 ∼ 1) to show the modifications of V θ more clearly.The black dotted line is the separatrix.The applied RMP coils current values are marked at the corner of every sub-figure.
(x-).The blue boxes in these eight subfigures are fixed at R − R sep = −4 ∼ 0 cm to show the change of V θ more clearly.The black dotted line shows a separatrix.The applied currents of RMP coils are marked at the lower right in every sub-figures.Velocity field of part z is quite similar to those of part x and part y, which indicates that 2 kA current RMP has little effect on the position of poloidal flow and layer I remains at separatrix.When I RMP > 3 kA (part {|}~), poloidal flow in the box changes obviously: a clear stratification appears.A clear layer I (where V θ = 0 layer as mentioned before) exists at the radial location of about R − R sep = −1.3cm (ρ = 0.968).Between this layer and separatrix, V θ is positive.In part |, layer I moves inward obviously compared with those in part x-{, and it moves further in part } with a maximal coil current of 4.7 kA.When I RMP reaches 4.7 kA (part }),

Figure 7 .
Figure 7.The time evolution of (a) the radial electric field Er at R − Rsep = −4 cm (ρ = 0.9) and (b) left: the electric potential (V f ) at R − Rsep = −3.7 cm (ρ = 0.91) and right: RMP coil current (I RMP ) from 500 ms to 850 ms (part y to part ).The application of I RMP > 4 kA RMP increases V f significantly, consistent with the explanation of the inward shift of the poloidal velocity profile.

Figure 7 (
b) gives strong evidence for this process.The edge potential start to increases from 650 ms (part |, I RMP = 4 kA), and the potential turns to positive during part }.

Figure 7 (
b) not only gives experimental evidence for the explanation of the displacement of the inversion point, but also shows that the threshold of significant displacement on HL-2A is indeed 4 kA.The color plots of the wavenumber-frequency spectral density, S(k, f ) of part x to part are shown in figure8.The measurements are fixed at a radical location R − R sep = −3 cm (ρ = 0.925) around the midplane.In part }, the poloidal velocity at R − R sep = −3 cm is explicitly reversed from the electron to ion-diamagnetic drift direction with maximum RMP current 4.7 kA.Furthermore, the turbulent energy concentration frequency range changes from 0-40 kHz before RMP to 0-20 kHz during the application of RMP.

Figure 8 .
Figure 8.The color plots of the wavenumber-frequency spectral density, S(k, f ) of part x to part .The measurements are fixed at radical location R − Rsep = −3 cm (ρ = 0.925) around the mid-plane.In part }, the poloidal propagation is explicitly reversed from electron to ion-diamagnetic drift direction with maximum RMP current 4.7 kA.

Figure 9 .
Figure 9.The fluctuation amplitude of GPI line emission ( ĨGPI , blue line) and ion saturation current ( Ĩsat, red line).These two signals demonstrate a strong correlation.

Figure 10 .
Figure 10.(a) Skewness and (b) kurtosis profiles without (blue) and with (red curve) RMP, both skewness and kurtosis are reduced by the RMP in the SOL.

Figure 11 .
Figure 11.The turbulence kr-spectrum S (kr) with (red line) and without RMP (blue line).Figures (a) and (b) are measured in the edge and SOL, respectively.The negative value in (a) and (b) mean the turbulence is moving outwards.The S (kr) with RMP is much lower than it without RMP, especially small kr components.

Figure 12 .
Figure 12.The turbulence k θ -spectrum S (k θ ) with (red line) and without RMP (blue line).Figures (a) and (b) are measured in the edge and SOL, respectively.The negative value in (a) and (b) means that the turbulence is moving along the electron-diamagnetic drift direction.The S (k θ ) with RMP is much lower than it without RMP, especially small k θ components.