Interplay among turbulence, flow and impurities for sustaining magnetic island

As ubiquitous structures in magnetized fusion plasmas, magnetic islands (MIs) would short-circuit adjacent magnetic flux surfaces and result in a reduced pressure gradient and fluctuations inside the island; it is widely accepted that due to the stabilizing of drift wave instability, the turbulence intensity inside MIs is much lower for larger islands. Here, we provide the first observations that strong turbulence could be generated inside a large radiation MI, which is probably driven by the electron temperature dip due to strongly localized impurity radiation. Moreover, the flow velocity inside the MI is strongly correlated with the turbulence intensity, and the impurity concentration rate suddenly increases as the flow velocity reaches a threshold value, strongly suggesting that turbulence and flow inside the island play important roles in trapping heavy impurities and sustaining radiative MIs.


Introduction
A magnetic island (MI) is a ubiquitous structure caused by magnetic reconnection in astrophysical and laboratory plasmas, such as Earth's magnetosphere, solar flares and magnetically confined plasmas.In tokamak, MIs are a serious concern since the nested structure of magnetic flux surfaces can be destroyed, resulting in significant degradation of the plasma confinement.Moreover, turbulence and multiscale interactions have been found to play an important role in regulating turbulent transport and affecting plasma confinement, while microscopic turbulence and transport are also important for MI dynamics physics.The interactions among turbulence and flow, pressure and current profiles within an MI can result in complicated island evolution, and the associated physics have been extensively studied in various fusion devices [1][2][3][4][5][6][7].Recently, the inhomogeneous turbulence distribution around an MI and the modulation between turbulence and the MI were experimentally investigated in a tokamak [8][9][10].For large MIs, the quasicoherent mode or turbulence appears or intensifies outside the island boundary [11] or at the reconnection site [6], and can spread into the island with attenuated amplitudes.On the other hand, a special MI with inhomogeneous radiation or impurity inside the island was widely observed decades ago, although the physical mechanism remains unclear [12][13][14][15].Severely, these radiative MIs are accompanied with minor/major disruptions, which would cause excessive heat and particle loads onto main plasma facing components and are a major concern on the way towards a nuclear fusion demonstration power plant.
Here, for the first time, we report the experimental observations that strong turbulence and flows (measured by the Doppler reflectometry (DR) [16]) can be generated as the impurity concentration inside a large MI (measured by the absolute extreme ultraviolet (XUV) arrays [17]) with an electron temperature dip in the vicinity of the O-point (measured by the electron cyclotron emission (ECE) [18]).The turbulence is probably driven by the non-monotonic electron temperature caused by the localized impurity radiation.The temperature gradient is defined as R 0 /L Te = −(R 0 /T e ) * (dT e /dr).Flow inside the radiative MI would synchronously be enhanced with increasing turbulence intensity, and then strongly influences the impurity concentration, resulting in a local electron temperature dip, which could potentially sustain the driving for the turbulence.These results indicate complex couplings between turbulence, flows and impurity transport, unveiling a possible sustaining mechanism of large radiative MIs.
The paper is organized as follows.In section 2, the experimental conditions and the timing alignment between DR and ECE are presented.The experimental turbulence observations in the vicinity of the MI O-point and the X-point in both the radiative MI and normal MI cases are shown in section 3, as well as the plasma parameters and the profiles.Investigation on the possible mechanism on the (radiative MI) O-point turbulence is presented in section 4.Then, an analysis on the interactions among turbulence, flow and impurities is carried out.The final section is the summary.

Experimental conditions and diagnostics
The experiments were executed on Experimental Advanced Superconducting Tokamak (EAST) [19,20] with a major radius R 0 = 1.85 m and a minor radius a = 0.45 m, plasma current I p ⩽1.0 MA, toroidal field B T ⩽ 3.5 T, and flexible double null or single null plasma geometry.EAST was equipped with a SiC-coated graphite lower divertor and an ITER-like tungsten upper divertor [21].The EAST features complete RF wave heating, including lower hybrid wave heating (LHW), ion cyclotron resonance heating, and electron cyclotron resonance heating (ECRH), as well as two neutral beam injection (NBI) systems.The arrangement of diagnoses is shown in figure 1.The electron temperature T e is measured by an ECE array [18] (at P-port).The radiation is measured by 64-channel absolute XUV arrays located at horizontal P-port [17].For simplify, the chord XUV33 across the middle plane is marked as 'Z = 0', while the chord XUV23 & XUV43 tangent to q = 2 surface is marked as 'Z = −0.25 m' and 'Z = 0.25 m' in the following.The turbulence around the MI is measured through DR [16,22,23] (at G-port) with a perpendicular wavenumber k ⊥ ∼ 4-6 cm −1 (kρ s ∼ 1) [16].
This investigation is based on the turbulence measurement in the vicinity of the O-point and at the X-point.Before further analysis, it is crucial to align the timeline since DR and ECE measurements are not situated in the same toroidal port or poloidal position.The timing calibration contains two steps.In the first step, time delay due to the diagnosis trigger between the DR and the ECE is figured out as t trig = −0.17ms.Then, the phase delay resulted from the 3D MI geometry is calculated, as displayed in figure 2. The P-port and Gport has a toroidal angel difference 337.5 • − (360 + 135) • = 157.5 • .According to the ray-tracing calculation made latter in figure 5, the poloidal angle difference between the DR (Gport) and the ECE (P-port) is δθ ∼ 60 • with an error ∼±10 • , and the error is estimated from the DR measurement location shift between the island O-point profile and X-point profile.Combining with the island rotating directions (the magnetic field line is along the top-left to bottom-right direction at the low field side), the total timing alignment between DR and ECE is δϕ = δϕ toroidal * n − δθ * m = 157.5 • − 60 • * 2 = 37.5 • (±20 • ), and the total correction time for the DR signal is ∆t cali = t trig − δϕ/f island = −0.17-37.5/360/fisland = −0.189ms (±0.02 ms).

Experiment observations
Firstly, the plasma parameters for the radiation MI discharge (85501, at left) and the normal MI discharge (85498, at right) are displayed in figure 3. The two adjacent discharges have similar discharge parameters: plasma current I p = 0.5 MA (panels (a1) and (b1)), toroidal field B T0 ∼ 2.5 T, safety factor q 95 ∼ 5.5, H-mode favorable upper single null geometry, as well as the 1.3 MW co-NBI, ∼0.8MW ECRH power injecting (panels (a2) and (b2)).There is only a slight difference in LHW power shown in black curves.In 85498, the LHW power varied from ∼1 MW to ∼1.8 MW, while in 85501 the  power was stable 0.8 MW.After the NBI injected at t ∼ 2.2 s, the plasmas transfer from the L-mode into the H-mode which could be recognized by the D α drop in (a5) and (b5).As the particle confinement improved in H-mode, the line-averaged density in (a1)/(b1) and the core radiation in (a6)/(b6) continuously ramp up due to the impurity concentration until the radiation collapse.The following H-L back transitions appeared at t = 2.75 s in 85501 and t = 2.98 s in 85498, as marked by the vertical dash lines.Because the radiation signal at Z = 0 is consistently saturated, the precise moment of the collapse cannot be established.Amounts of impurities would escape from the core to the edge due to the collapse, which could be seen from the decrease of radiation signal at Z = 0. MIs resulted from tearing instablility would appear in the process of outward escape of impurities, as shown in the spectrogram of Mirnov coils in (a8) and (b8).The MI frequencies are proportional to the toroidal rotation from CXRS in (a7) and (b7).The island growth is probably caused by the current perturbation increasing due to the resistivity change, same as previous reports and analyses [12][13][14].Later, the plasmas would reenter into H-mode as sufficient impurities escape from the core region.This is accompanied by the toroidal rotations and MI frequencies stabilizing, while the L-H transitions are marked by another vertical dash lines.Until now everything has been fairly consistent in the two discharges, the difference occur at t = 2.88 s in 85501.From (a6), it could be seen that from that moment both the two XUV signals (Z = 0 and Z = −0.25 m) began to strengthen and showed similar trends, suggesting that the impurities are concentrated inside the island.Such process did not occur in 85498.The physical mechanism that leads to the difference between the two shots is still unclear.One possible explanation is the toroidal rotation after the second L-H transition in (a7) and (b7), which stabilized at a larger value 68 ± 2.6 km s −1 (t = 2.966 s) than the 85498 (43 ± 3.9 km s −1 at t = 3.666 s) and may cause the different impurity/radiation dynamics.In the following, the island in 85501 after t = 2.88 s is called radiative MI, while the island in 85498 is called normal MI for comparison.
The density and temperature profiles for the two cases are displayed in figure 4, from the polarimeter/interferometer [24] and ECE measurement, respectively.The time slices are chosen as t = 2.966 s for 85501 and t = 3.64 s for 85498.It could be found that the density profiles at the X-point are similar at the island region R ∼ 1.98-2.06m, while the density at the O-point for the 85501 is much lower than that in 85498.The island region could be seen from the flattened temperature profiles, which are marked by the dotted lines.The estimated island width is about 8-10 cm.The temperature of radiative MI region is much smaller than that of normal MI, which is mainly due to the stronger impurity radiation.Moreover, an electron temperature increase is found at R = 2.02-2.08m for the O-point of 85501, and such abnormal temperature profile inside the MI is called the electron temperature dip in the following.Before conducting further turbulence analysis, a raytracing routine with above density profiles was employed to estimate the measurement location and wavenumber of DR as MI rotating, as shown in figure 5.The lines labeled '94.8' indicate the cut-off layer for 94.8 GHz for the given profiles, while unmarked lines represent the incident microwave trajectories.According to the trajectories in figures 5(a) and (b), the measuring location for the O-point in 85501 is the deepest, which reaches about R = 2.01 m as converting to the mid plane.Moreover, it was found that the DR's cut off layer could reach the inner separatrix for 85501 O-point only when the density profile decreases to the level depicted by the black curve in figure 4(a), which is distinctly beyond the margin of error.Another factor affecting the location of the DR is the decrease of the poloidal magnetic field due to MI, which is estimated as ∼0.2 cm and is negligible.Considering that full-width of the island in discharge 85501 is about 10 cm, which could be seen in figure 4, turbulence measurement location would alternate between inside and outside as MI rotating.Besides, the geometry of MI would also influence the resonant turbulence wavenumber of DR, because the divergence between the cut-off layer and the local magnetic surface would change as electromagnetic wave crossing MI.The effect is stronger at the MI boundary region but much less for O-point measurement, and would slightly strengthen the low-frequency part of the turbulence S(f ) spectra.Since the topology varied at every moment and it is laborious to calculate each individual wavenumber, we have opted to use a wider error range of wavenumbers (0%-50%) for the sake of simplicity.
Figure 6 displayed the turbulence time-frequency spectra ((a1), (b1)) and turbulence amplitude evolutions ((a2), (b2)) for the two cases.The dashed lines for each case mean a single MI period, and the turbulence amplitude is averaged under a Fourier window length of 0.1 ms.In 85498 normal MI case (right), one turbulence peak could be observed during one island period, as shown in the turbulence time-frequency spectra in figure 6(b1) and the integrated turbulence amplitude (b2).The turbulence should be driven from the enhanced gradient formed around the island separatrix, which has been reported in both DIIID [8] and HL-2A [10].While in 85501 radiative MI case (left), two turbulence peaks with opposite rotation speed appeared during each MI period in figure 6(a1).To separate the two turbulence peaks, the turbulence frequency ranges with f tur = k ⊥ * V ⊥ > 0 in blue and f tur < 0 in red are integrated in figure 6(a2).Based on the timeline alignment in figure 2, the turbulence peak with a Doppler shift f tur < 0 corresponds to the X-point, and the other turbulence with f tur > 0 appears when the DR measurement location passing through O-point.The time-averaged turbulence spectra were shown in figures 6(a3) and (b3), and the O-point/X-point situations are plotted separately.It should be emphasized that theoretically fluctuations inside the island should be strongly reduced due to the short-circuit effect, especially for large island.Here for radiative MI, the turbulence amplitude of O-point is even stronger than that of X-point.The Doppler shift f tur is determined by the turbulence perpendicular velocity ⃗ υ ⊥ = ⃗ υ E×B + ⃗ υ pha , where ⃗ υ E×B is the plasma E × B rotation due to the radial electrical field and ⃗ υ pha is the turbulence phase velocity.The Doppler shift at X-point for normal MI is much smaller than that in radiative MI suggested that the radial force balance in the two discharges are much different, which may also due to the different impurity accumulation.

Turbulence driven
The most interesting phenomenon in figure 4(b) is the distinct temperature dip inside the radiative MI, which was plotted separately in figure 7(a) for clarity.Temperature drop of the dip is about 0.1-0.2keV in the radiative MI, which is most likely caused by local impurity radiations.The temporal evolutions of XUV array are shown in figure 7(b), and it could be clearly seen that how the radiation rotating with the two islands.Three typical time slices are chosen and marked by the dashed lines as t1, t2, and t3. Figure 7(c) displayed the radiation distribution at the three time slices.At t1 slice, two islands both located at the mid-plane, and for the horizontal chord of the XUV, they are inseparable.When the island rotates vertically, two distinct radiation peaks are observed at the time slices t2 and t3.The width of these peaks corresponds to the width of the radiative island and aligns with the width estimated from the electron temperature profile.The radiation power loss could be divided into two parts, the unchanged background part (purse line), which is from the ambient plasmas, and the fluctuated part, which is from the rotating island.It could be estimated that the fluctuated part is nearly 1/3 of the total radiation power loss.The total radiation power loss P rad could be directly measured by the calibrated XUV array, and checked by the simple power balance calculation through P rad = P abs − P loss − dW dia dt , where P abs is the absorbed power from the heating, P loss is the particle loss power, and W dia is the diamagnetic stored energy.Thus, the radiation power caused by the radiative MI is estimated about 200-367 kW from t = 2.9 s to t = 3.0 s. Figure 7(d) displayed the EUV signals, which can recognize the kind of the impurities through wavelength of the radiation lines [25].The dominant high-Z impurity lines are shown and 'W uta ' means the summed W radiation lines in the wavelength range of 4.5-7.0nm consisting the ionization stages from W27+ to W44+ [25].It could be seen that main impurities in discharge 85501 are Fe, Mo and W, while W uta is nearly 1000 times of the FeXVIl line.Assuming that the radiation inside MI is all caused by tungsten and its density inside MI is uniform, the density could be estimated through P rad = n e n I RV, where n I , R, V are the impurity density, the impurity cooling rate, and the radiative island  There are several possible mechanisms to explain the turbulence at O-point.Firstly, the possibility that impurities directly drive turbulence is investigated [27].As mentioned above, based on the EUV spectrometry measurement [25] and T e at q = 2 surface, tungsten (W) is recognized as the main impurity contributing to the O-point radiation, resulting in a radiation power loss of 0.27 MW at t = 2.96 s estimated from the XUV [17] measurement.The maximum W density is estimated as n W /n e ≲ 0.002 through power balance calculation.The density gradient of tungsten could be estimated as R 0 /L n = 10-20 through SXR inversion.Turbulence simulation based on the toroidal gyrokinetic eigenvalue code HD7 [28] shows that a minimum impurity ion concentration of 2% is required for impurity mode turbulence excitation [27].Thus, turbulence excited by high-Z impurities should be essentially excluded.Although the 0.2% W concentration inside q = 2 MI is too low to directly drive microinstabilities, the radiation power loss is almost 9% of the total auxiliary heating power (∼14% of the absorbed power P abs ), which could certainly modify the Te profile in the vicinity of the O-point and the temperature dip could also be a possible source for triggering turbulence inside MI.
Based on the timeline alignment made in section 2, the temporal evolution of turbulence and radiation, as well as the temperature gradient inside MI, are plotted together in figure 8.The radiative MI is on the left side (a1, b1, c1, d1), and the normal MI is on the right side (a2, b2, c2, d2).Panels (a) to (d) refer to the temporal evolution of the T e profile, the −(R 0 /T e ) * (dT e /dr) at the outer side of O-point, the radiation signal at Z = −0.25 m and the turbulence spectrum, while all signals are calibrated according to the ECE signal at mid-plane.As MI rotating, the measurement location of DR changes from the O-point to the X-point periodically, as shown in figure 2. Panel (d2) is the normal MI with distinct turbulence only appearing near the X-point, and the fluctuation intensity is modulated by the MI frequency, consistent with previous reports in DIII-D [8], HL-2A [10] and K-STAR [6].For the radiative MI, panel (d1) shows that the Doppler shift continuously moves from the positive to negative direction as the measurement position changes from the O-point to the X-point, yielding abnormal doublet peaks in the turbulence spectra, as shown in figure 6(a3).Then it could be found that for radiative MI the turbulence enhancement inside MI corresponds to the peak of the radiation signal and the peak of the inverted T e gradient in the vicinity of the O-point, suggesting that the non-monotonic radial temperature profile may be the driving source of turbulence inside radiative MI.
However, for the temperature dip inside radiative MI, there are two T e gradients (R 0 /L Te = −(R 0 /T e ) * (dT e /dr)), the positive one at the inner side and the inverted one at the outer side.Panels (a), (b), (c) are the radiation strength (the radiation difference between the O-point and X-point for each MI period (measured at Z = −0.25 m)), R 0 /L Te at the O-point (in blue and red) and X-point (in black), and the turbulence amplitude at the O-point (in purple) and X-point (in black), respectively.The data processing is detailed as follows.Firstly, the exact X/O moments are chosen by the maximums and minimums of the filtered Te signal, and the turbulence amplitude (averaged with a Fourier window length of 0.1 ms) and temperature gradient at these moments are chosen.Finally, these turbulence amplitude and temperature gradient R 0 /L Te are averaged within 2 ms (about 11 MI cycles) to further decrease the random noise.From figure 9, as the radiation increasing, the turbulence intensity and the absolute values of T e gradient inside MI all increased, while only the T e gradient at X-point remained almost unchanged.It should be noted that although the ray tracing in figure 5(a) suggested that the turbulence measurement location is at the inner side of MI (positive R 0 /L Te ), the possibility that turbulence may trigged by the inverted R 0 /L Te could not be ruled out, because that turbulence spreading [29,30] and DR measurement principle [31][32][33] should both be considered.So, the relationships between turbulence amplitude and positive R 0 /L Te and inverted R 0 /L Te are both plotted in panel (d).It could be found that the gradient threshold to trigger turbulence at O-point is only R 0 /L Te = −1 ∼ −2 at the outer side or R 0 /L Te = 1 ∼ 2 at the inner side, while the gradient threshold at X-point is R 0 /L Te = 5 ∼ 6, implying that the turbulence can be easily excited under a smaller gradient inside radiative MI.Considering the impurity played the key role to link the turbulence generation and the temperature profiles inside MI, it is much difficult to estimate the plasma dynamic balance including both impurity transport and MI geometry.Thus, the simulation including both the MI geometry and micro-turbulence for radiative MI is a challenging issue and would remain for future study.

Turbulence, flow and impurities
Although the turbulence type at O-point is unknown (the turbulence at X-point is probably TEM [34]), how the flow changed as the turbulence evolution inside radiative MI could be analyzed.From figures 6(a1)-(a3), it can be found that the flow rotations in the vicinity of the O-point and X-point have similar magnitudes but opposite directions, suggesting strong flow shear around the MI separatrix.Actually, turbulence suppression by the flow shear can be directly seen in figure 6(a1); when the Doppler shift crosses zero, distinct interruptions of turbulence intensity appear.Such opposite rotations are due to vortex E × B flows, which have been experimentally reported in LHD [35] and TJ-II [36] devices.The nonlinear couplings between the turbulence, vortex flows and shear flows in the normal MI have been widely reported [6,10,37], while for radiative MI the situation is much more complex due to that impurity transport is also involved.In figures 10(a)-(c), the evolution of the MI width, radiation gradient, flow and turbulence intensity in the vicinity of the O-point are respectively displayed before the minor disruption at t = 2.936 s.The width of the radiative MI in panel (a) is estimated according to the formula w ∝

√
Br [38] and calibrated by the electron temperature profile in figure 4(b), where Br is the radial magnetic fluctuation from the Mirnov coils.In panel (b), the radiation difference between the O-point and X-point (measured at Z = −0.25 m) can be regarded as an indicator of W inhomogeneity inside the MI.The velocity at O-point υ O-point is calculated from the Doppler shift of DR. Figure 10(c) shows that the growth trends of turbulence intensity and flow velocity inside the MI are nearly the same, and the relationship between them is displayed again in figure 10(d) for clarity.Such a positive correlation might imply that the flow is probably vortex flows [39] or shear flows [40] driven by the Reynolds stress of turbulence [41].Moreover, although the turbulence intensity, flow velocity, and radiation gradient almost double, the island width is nearly unchanged, suggesting the balance of radiative MI is quite robust to trap the impurities and turbulence during this period.The relationship between the impurity gradient and υ O-point is shown in figure 10(e), which distinctly displays two different stages.When the turbulence is weak and υ O-point < 6.5 km s −1 , the impurity gradient is nearly unchanged, while as the υ O-point exceeds 6.5 km s −1 , the impurity gradient begins to grow rapidly, implying that there exists a threshold of flow velocity on impurity transport.Such a threshold effect may also be related to the low/high accessibility states of large MIs in DIII-D [42][43][44], which may also be determined by turbulence and flow intensity.How the impurity accumulated inside the island as the flow shear around the separatrix increasing?One possible explanation is the turbulence spreading which could overcome the flow shear [29,30,[44][45][46][47][48], while impurity could be carried by the turbulence spreading into the island.Another explanation is the neoclassical convection [49,50].Figures 3(a7) and (b7) suggested that toroidal rotation should be large enough to generate the radiative MI, implying that the inward pinch may play an important role in the impurity transport.

Summary
The radiative MI, which is also called an 'impurity snake' when it is located around the q = 1 surface, is usually longlived and shows excellent stability and particle confinement [12][13][14][15], and its formation and stability mechanisms have not been fully understood.Experiments in the EAST tokamak firstly reveal that strong turbulence could be driven by the local T e dip caused by impurity concentration inside a radiative MI at the q = 2 surface.In addition, the excitation threshold of absolute T e gradient is just R 0 /L Te = 1 ∼ 2, much smaller than the threshold at X-point.The flow reversal around the island separatrix is consistent with the experimental results in helical devices [35,36].The flow velocity and the turbulence intensity almost synchronously increase as the impurities gradually accumulates inside the MI, while the island width changes little; as the flow velocity reaches some threshold value, the impurity concentration appears to accelerate.The results are much different from the turbulence distribution around a normal MI from previous experiments and simulations and provide a novel pattern of the interplay among turbulence, flow, and impurity transport within radiative MI.

Figure 1 .
Figure 1.Measurement arrangements for the main diagnoses: the electron temperature, radiation, and turbulence are measured by ECE (P-port), XUV array (P-port) and DR (G-port) respectively.

Figure 2 .
Figure 2. Phase delay calibration between the Doppler reflectometry (ñe) and the ECE (Te).The left, and right panels are the observed 2/1 island at the G-port and P-port at the same time t0.

Figure 4 .
Figure 4. Electron density (left) and electron temperature (right) profiles comparison between the radiative MI (85501) and the normal MI (85498).The data are from t = 2.966 s for 85501 and t = 3.64 s for 85498.

Figure 5 .
Figure 5.Under the density profiles in figure 4(a), ray tracing for the 94.8GHz DR is estimated, (a) for shot 85501, (b) for shot 85498.

Figure 6 .
Figure 6.Comparison of the turbulence time-frequency spectra and turbulence amplitude evolution between the 85501 radiative MI case (left) and the 85498 normal MI case (right).Bottom panels are the time-averaged turbulence spectra with δt ∼ 0.1 ms.

Figure 7 .
Figure 7. Radiation and impurity analyses on the radiative MI (85501): (a) electron temperature profiles, (b) the radiation map, (c) radiation spatial distributions at three typical time slices, (d) counts of the high-Z impurity lines.

Figure 9 .
Figure 9.Comparison of the turbulence amplitude to the temperature gradient R 0 /L Te = −(R 0 /Te) * (dTe/dr) for both the X-point and the O-point (including the inner side and the outer side).(a), (b), and (c) are the radiative strength (at island O-point), electron temperature R 0 /L Te , and the turbulence amplitude evolution during t = 2.87-2.97s in discharge 85501, respectively.

Figure 10 .
Figure 10.Turbulence and flow intensities versus radiation gradient inside an MI before minor disruption.The evolutions of (a) island width, (b) radiation gradient along the poloidal direction (∇ θ Rad.) inside the MI, (c) turbulence intensity and flow velocity υ O-point at O-point, (d) relationship between turbulence intensity and υ O-point , and (e) relationship between ∇ θ Rad. and υ O-point .