Non-uniformity of fluctuation characteristics inside an edge magnetic island in Heliotron J

Non-uniform fluctuation characteristics are observed within an edge magnetic island in Heliotron J. The island possesses a long connection length comparable to the confined region. These fluctuations are measured using a Langmuir probe. The island’s presence is confirmed through the plasma response, observed in the modulation amplitude of electron temperature and its phase delay relative to the heat source in a heat modulation experiment. Within the island, the electron density is notably high, accompanied by distinct profiles of electron temperature and electric field, likely attributable to the magnetic island. Contrary to expectations, density fluctuations within the edge magnetic island are not locally minimized, despite the reduced gradient of the profile within the island. Statistical analysis shows a suppression of intermittent transport inside the island, while intermittent fluctuations increase towards the exterior. A further analysis to segregate turbulence-driving and spreading factors reveals that both turbulence-driven and spreading contributions are comparably significant inside the island. Additionally, the non-uniform turbulence results in a spatially structured fluctuation-driven particle flux. Overall, the experimental findings indicate that fluctuation characteristics exhibit notable non-uniformity both inside and near the island. This non-uniformity potentially complicates heat transport and may lead to three-dimensional, asymmetric transport within and at the periphery of the islands.


Introduction
Understanding the impact of magnetic islands on plasma confinement in fusion devices is crucial.Typically, fusion plasma 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.experiments strive to avoid the formation of rational surfaces or magnetic islands within the confined region, as these islands are believed to connect different flux surfaces via the X-point of the separatrix, thereby degrading plasma confinement.For instance, neoclassical tearing modes that produce magnetic islands can diminish plasma energy and potentially lead to disruptions in high beta plasmas [1].Consequently, the suppression of magnetic islands using electron cyclotron current drive is often necessary [2].
Conversely, some studies have identified beneficial aspects of magnetic islands in relation to confinement characteristics.Within these islands, turbulence-driven transport is reduced, potentially enhancing confinement [3,4].The flow along magnetic field lines around the O-point of the island and the associated radial electric field structure have been examined [5,6].Discussions have emerged regarding the use of radial electric field shear around magnetic islands to control the foot position of electron internal transport barriers [7,8].Additionally, the interaction between magnetic islands and turbulence has been extensively reviewed [9].
Non-axisymmetric magnetic fields, including magnetic islands, are employed to manage heat and particle transport in the scrape-off-layer (SOL) and divertor regions, as well as in the confinement region.In the SOL and divertor regions, where parallel transport predominates, the geometry of a magnetic island can serve as a means to control heat and particle flow from the core to these regions.In tokamaks, resonant magnetic perturbation fields are introduced to control edge localized modes and mitigate heat and particle fluxes to the divertor [10].In stellarator/heliotron devices, the intrinsic three-dimensional field is utilized to test helical and island divertor concepts in large-scale devices [11,12].Attempts have been made to control magnetic islands through external perturbation fields in both tokamaks and stellarator/heliotron devices, with LHD achieving a relatively balanced energy state in the high-density region by managing particle transport in the peripheral region [13].Additionally, the placement of magnetic islands has been reported to influence plasma performance during rotational transform experiments in W7-X [14].
However, the specific impact of magnetic island structure on fluctuations and fluctuation-driven transport requires further experimental investigation.At the periphery of the boundary between confined and unconfined regions, both parallel and perpendicular transport coexist and interact.Additionally, perpendicular transport, influenced by diffusive and nondiffusive mechanisms like turbulence and blobs, impacts SOL plasma and broadens the divertor plate's footprint [15].Previous research has shown that perpendicular transport often correlates linearly with the gradient of the SOL, but this relationship is modified by magnetic islands in the island divertor concept [16], suggesting that the effects of fluctuations and fluctuation-driven transport in edge magnetic islands are not yet fully understood.
This study aims to experimentally characterize the influence of edge magnetic islands on fluctuation characteristics and transport in the medium-sized fusion device, Heliotron J [17].

Magnetic configuration
Heliotron J, a medium-sized helical-axis heliotron device, boasts a major radius (R) of 1.2 m, an average minor radius (a) ranging from 0.1 to 0.2 m, and a magnetic field strength on the magnetic axis of less than 1.5 T. It is equipped with a unique L/M = 1/4 continuous winding helical coil, where L represents the pole number and M the pitch number, along with two types of toroidal coils and three sets of vertical magnetic field coils.These components together produce a low magnetic shear configuration [18][19][20].The device's magnetic configuration is adjustable, allowing for the alteration of current ratios in each coil.This adaptability in Heliotron J enables the realization of island divertor-like SOL configurations by controlling the rotational transform.Here, the rational surface determines the last closed flux surface (LCFS) in Heliotron J. Figure 1 illustrates the connection length distribution in configurations with and without an edge magnetic island, while figure 2 displays the rotational transform profiles for each configuration.The chosen configuration, devoid of an edge magnetic island, is the low bumpiness configuration [21,22], where the rotational transform at the LCFS is approximately 4/7.This configuration allows the probe to traverse the typical SOL in Heliotron J.In contrast, the island configuration features a rational surface with a rotational transform ι/2π = 4/8 at the plasma's periphery, resulting in an island structure beyond the LCFS.Consequently, part of the magnetic island formed on this rational surface intersects with the vacuum vessel.The island exhibits a nested flux surface structure with a lengthy connection length (over 1000 m), akin to the core plasma region in vacuum conditions.

Multipin Langmuir probe
In this study, a Langmuir probe is employed to measure plasma parameters and their fluctuations in the peripheral region.Figures 3(a) and (b) illustrates the probe path, depicted as a green line, which traverses the O-point of the island in the island configuration and a simpler SOL in the configuration without the island.Figure 3(c) displays the connection length L c along the probe path.The horizontal axis represents the distance ∆r from the LCFS, with the observation region lying in the SOL outside the LCFS.The red and black lines in figure 3(c) represent L c in the island and non-island configurations, respectively.In the island configuration, a long L c region (1000 m) is flanked by areas with shorter L c (200 m), whereas L c remains consistently short in the configuration without the island.The probe head, designed specifically for measuring plasma fluctuations as well as plasma parameters, is depicted in figure 4. Constructed from boron nitride, the probe head features a 5-pin poloidal array organized in five columns with alternating poloidal radial positions.The cylindrical pins are tungsten, each with a diameter and length of 1 mm protruding from the probe head.Adjacent pins are spaced 2.5 mm apart in the poloidal direction and 3 mm radially.This setup enables triple probe operation to measure electron density n e , temperature T e and space potential V s from the ion saturation current I s2 , floating potential V f2 and probe bias V p .The radial electric field E r can be determined by calculating the radial gradient of V s .In addition, the probe can assess radial fluctuation-driven particle flux Γ e from the poloidal electric field E θ , measured by the poloidally separated floating potential (V f1 , V f2 ) signals, and the ion saturation current I s2 signal.The green lines in figures 3(a) and (b) correspond to the center of the probe head.
The experiment was conducted in two magnetic configurations: with and without the edge magnetic island.The aim was to compare the impact of the magnetic island on turbulence fluctuation and turbulence-driven transport.Electron cyclotron heating (ECH) of 250 kW was applied.The probe underwent radial scans on a shot-by-shot basis to acquire radial profiles under fixed conditions.The shot set for the island configuration is #79880-#79909, and for the configuration without the island is #82989-#83017.

Heat pulse propagation experiment in the island configuration
The presence of magnetic islands in plasmas is significantly influenced by plasma current and beta values, even in cases where a magnetic island exists in a vacuum [23].Therefore, heating modulation experiments serve as an effective method for experimentally confirming the presence of magnetic islands.A magnetic island alters heat propagation, characterized by rapid propagation of heat pulses at the island's boundaries and relatively slower decay towards the O-point.This heating modulation technique has been previously utilized to investigate the island's impact on heat transport in core plasmas [24,25].In this study, a modulational ECH with a frequency of 100 Hz and a 30% power modulation was applied to the island configuration.This approach was intended to confirm the existence of the edge magnetic island during discharge, which in turn revealed the edge plasma's response reflecting the island's structure.Measurements were conducted under conditions with an average electron density of 0.8 − 1.0 × 10 19 m −3 .The magnetic field intensity was adjusted to centralize ECH heating.The averaged electron temperature (T e ) profile, the modulated T e amplitude profile, and the phase difference ∆ϕ between the modulational ECH and T e are presented in figure 5.In the island region of ∆r = 20 − 50 mm, (b) a slight peak in the T e profile, (c) a local drop in the modulated T e amplitude profile, and (d) a larger ∆ϕ value indicating delayed heat penetration into the island region were observed.These results suggest that heat transport is substantially affected by the island at the edge region, possibly due to heat propagation along the island's outer surface, aligning with past observations in the confined region [24,25].A comparison of heat pulse propagation between open field regions and magnetic island regions has not yet been conducted.It would be beneficial to compare the results of the heating modulation experiment between the island configuration and the configuration without an island in future work.The actual position of the magnetic island, as revealed by this experiment, remained largely consistent with its position in the vacuum state, indicating that the impact of plasma current and beta on the edge magnetic field structure is not significant in this experiment.
Furthermore, we take the calculation error of about 5 mm in defining the magnetic island location into consideration, which is estimated from coil current control precisions.Additionally, there may be an uncertainty of approximately 1-2 mm in the probe radial localization, taking into account the size and shape of a set of triple probe electrodes.Therefore, we assume that the position of the island boundary has an uncertainty of ±5 mm based on the field tracing calculation in this study.This is represented as a hatched area in all relevant figures.

Radial profiles of steady-state plasma parameters
Under the same experimental conditions as the heat modulation experiment, this study also includes fluctuation measurements within the magnetic island.The edge plasma parameter profiles exhibit distinct characteristics in the configurations with and without the island.Figure 6 compares the profiles of electron density n e , electron temperature T e , spatial potential V s and radial electric field E r .The black and red lines in figure 6 represent the results for the configurations without and with the island, respectively.The edge n e in the island configuration is more than twice that in the configuration without the island.This elevated n e in the SOL is attributed to the presence of an island with a long connection length relative to the confinement region.The n e within the island remains nearly constant.The T e inside the island is lower on the wall side, and its profile is relatively flat, albeit not completely, differing from the flat T e profile observed inside core plasma islands in other studies [23,26,27].
If parallel transport predominates over perpendicular transport, the temperature within the island should be uniform, a result of rapid parallel heat transport along magnetic field lines, as documented in core plasma experiments [26,28].However, this uniformity is not observed, indicating that transport within the magnetic island, located at the peripheral region of the confined area, is complex.The magnetic field structure of the island is inherently three-dimensional, and resultantly, heat sources from the core plasma and sinks to the divertor are localized in specific regions due to the configuration's three-dimensionality.These conditions may realize the situation that perpendicular transport would also play a significant role, as well as parallel transport, inside the island localized in the edge region, indicating the observed parameter nonuniformity along the magnetic field line.The T e difference between the inner and outer island boundaries can be understood in the context described above.However, further experimental investigation and numerical study would be beneficial.This is beyond the scope of the present manuscript and will be a part of future work.
One should note that a temperature reduction at ∆r = 5 mm in the island configuration is observed, and there are a few factors that should be considered, although it is difficult to conclude the reason.Firstly, the operation range of the triple probe measurement should be considered.Generally, the triple probe needs to be biased more than ∼ 3T e , and in this experiment, 200 V was applied.However, the temperature at ∆r = 10 mm is already at the maximum measurable temperature of 70-80 eV.As the probe approaches the core plasma, the electron temperature is expected to increase and hence the triple probe measurement might not be reliable when the temperature at ∆r = 5 mm is higher than at 10 mm.Additionally, we must consider the interaction between plasma and probe material, which may reduce the temperature at the measurement position due to sputtering.Both factors are likely to contribute to the electron temperature reduction at the closest position to LCFS.
Moreover, the island region exhibits a notable impact on the electric field.In the configuration without the island, V s decreases monotonically as the probe moves away from the LCFS.Conversely, in the island configuration, variations in both V s and E r profiles are observed inside the island.These differences could potentially generate poloidal flow and influence transport within the island.In magnetic islands located in the confined region, a reversal of the radial electric field has been observed, along with a structure where the poloidal flow is reversed around the O-point of the magnetic island [6,26].These findings, however, do not align with the current observations.The exact mechanisms remain unclear, but one hypothesis is that the magnetic island may be influenced by parallel flows in the open magnetic field line region surrounding it [29].

Influence of magnetic island on broadband fluctuation
characteristics.The presence of a magnetic island notably impacts broadband turbulence in the edge region.Figure 7 presents typical frequency spectra of the ion saturation current (I s ) and floating potential (V f ) fluctuations.These results, obtained at ∆r = 20, indicate distinct differences between the two configurations.In the I s spectrum, the island configuration exhibits stronger fluctuations around 10 kHz compared to the non-island configuration and displays a notable peak at 250 kHz.The V f spectrum in the island configuration shows increased fluctuations across a broader frequency band than in the configuration without the island.The low coherence between I s , V f and the magnetic probe signal, as shown in figure 7, suggests that the magnetohydrodynamic instability component of these fluctuations is not significant in this analysis.
The presence of a magnetic island influences the spatial structure of the fluctuation characteristics.Figure 8 illustrates  the spatial distribution of I s and V f power spectrum density for configurations with and without a magnetic island.In the configuration without a magnetic island, I s and V f fluctuations decrease radially outward.Conversely, in the magnetic island configuration, I s fluctuations around 10 kHz are pronounced near the magnetic island region, and V f fluctuations below 10 kHz are elevated in parts of the island.Figure 9 shows the normalized fluctuation intensity profiles for each configuration, including frequencies ranging from 1 kHz to 100 kHz.The angular brackets ⟨. ..⟩ here mean ensemble average over a time interval of 20 ms.In the non-island configuration, the normalized fluctuation intensities, Ĩs / ⟨I s ⟩ and Ṽf / ⟨T e ⟩ , remain constant in the SOL region.However, in the island configuration, Ĩs / ⟨I s ⟩ significantly increases from the center to the outer region of the magnetic island, and Ṽf / ⟨T e ⟩ locally intensifies in parts of the island.Despite a flat profile and small gradient within the island's inner region, as depicted in figure 6, fluctuations are not locally suppressed, differing from previous findings where fluctuation profiles in magnetic islands within the confinement region were locally diminished [30].This observation suggests that the fluctuations are not solely driven by local gradients-induced turbulence but may also be influenced by other factors, such as turbulence spreading.

Impact of magnetic islands on intermittent transport.
Differences in statistical characteristics of the fluctuations are observed in the comparison between configurations with and without an island.The intermittency can be characterized by using the probability density function (PDF) and by computing the higher central moments of the fluctuating quantities, i.e.
where N is the number of data points in the time series of the variable X, the summation is over all data points.X = N −1 X j is the mean and σ X = N −1 (X j − X) 2 is the standard deviation of X.The skewness S = F 3 measures the positive-negative asymmetry of the PDF, and the kurtosis K = F 4 − 3 measures 'flatness' of the PDF, i.e. whether the distribution is more peaked or flatter than a normal distribution.Large K implies a long tail in the distribution.Gaussian turbulence has S = 0 = K, whereas S and K are positive in the SOL when blobs are present [31].Figure 10 compares the distributions of S and K of I s with and without an island.In the configuration without an island, both S and K are positive, suggesting that intermittent, outward transport, like plasma blobs, could occur in the SOL region, as observed in many tokamaks and stellarators [31][32][33].However, in the island configuration, both S and K are close to zero inside the island, i.e. the PDF is close to Gaussian.Outside the island region, these values drop at the outer boundary and become larger, suggesting blob-like and hole-like behavior around ∆r = 50, with more hole-like behavior inside and more blob-like behavior outside.This indicates that intermittent transport is suppressed inside the island, while it is enhanced outside the island.

Coexistence of different turbulence mechanisms in a
magnetic island.The analysis of the driving mechanism of density fluctuation within the magnetic island reveals that both gradient-induced driving and turbulent spreading contribute to these fluctuations.Figure 11 displays the profile of I s , its gradient −dI s /dr, fluctuation intensity Ĩ2 s , and the spread of the fluctuation Ĩ2 s Ẽθ .Here, E θ is calculated under the assumption of negligible electron temperature fluctuation since they are difficult to evaluate with the Heliotron J probe system.The validity of this assumption is discussed in section 4. Ĩ2 s Ẽθ serves as an indicator of the radial direction in which the fluctuation spreads, with positive values indicating outward radial spreading and negative values indicating inward radial spreading.In the non-magnetic island configuration (represented by the black line), the profiles of Ĩ2 s and Ĩ2 s Ẽθ structures are largely monotonic, although there are regions where −dI s /dr is almost zero.In contrast, the magnetic island configuration (represented by the red line) shows a symmetric profile of −dI s /dr about the magnetic island, with a large value at the outer edge and a minimal value near the center.The intensity of fluctuations is enhanced at the outer edges but remains consistent at the center without a clear minimum.The profile of Ĩ2 s Ẽθ suggests outward spreading from the magnetic island and inward spreading towards its interior.
To identify the driving mechanism of particle flux within the magnetic island, the turbulence drive ω D and spreading ω S terms are evaluated, based on the methodology outlined in the literature [34,35] (figures 12(a) and (b)).According to these studies, the time evolution of free turbulent energy ñ2 is given by: 1 2 where ñ = n − ⟨n⟩.The first term on the RHS of this equation is associated with local turbulence drive due to the background gradient, and the second term is a nonlocal nonlinear term related to turbulence spreading.By normalizing with the local turbulence amplitude ñ2 , the rate of turbulence drive ω D and spreading ω S are defined as: Here, assuming n ∝ I s and neglecting electron temperature fluctuation, we obtain: The angular brackets ⟨. ..⟩ here mean ensemble average over a time interval of 2 ms.
In the configuration without the island, both the turbulence drive rate (ω D ) and the turbulence spreading rate (ω S ) are nearly constant across the SOL region.However, in the island configuration, ω D remains constant within the island but is significantly higher at its outer boundary.Conversely, ω S turns negative at both boundaries of the island and peaks at the center.The contributions of turbulence spreading are assessed using ω S / (ω D + ω S ) (figure 12(c)).In the island configuration, the influence of turbulence spreading increases both within and at locations radially distant from the magnetic island.These findings indicate that the edge magnetic island substantially affects the behavior of turbulence driving and spreading, with various turbulence mechanisms coexisting and displaying distinct spatial structures in the SOL region.

Turbulence driven particle flux
Figure 13 summarizes the profiles of the fluctuation amplitudes of ion saturation current ( Ĩs ), poloidal electric field ( Ẽθ ), and the electron particle flux (Γ e ∝ Ĩs Ẽθ ), evaluated in the frequency range from 1 kHz to 100 kHz.In the configuration without the island, all fluctuation amplitudes decrease monotonically as the probe moves radially outward from the LCFS.In the island configuration, Ĩs is consistent within the island but peaks at its outer boundary.Meanwhile, Ẽθ peaks inside the island.The differing peak positions of Ĩs and Ẽθ result in two peaks in Γ e at two distinct locations: the island's central region and outer boundary.This observation suggests that fluctuation characteristics within the edge magnetic island are not uniform, leading to a spatial structure in the fluctuationdriven particle flux inside the island, even though the profile shape remains relatively flat within the magnetic island.

Discussion
Here, we examine the structure of turbulent fluctuations within the magnetic island in Heliotron J. Key observations in the magnetic island include: -The presence of small gradients.
-An approximately equal contribution from turbulence driving and spreading at the center of the magnetic island.-A decrease in turbulence spreading towards the outer edge, with values becoming negative.-A peak in Ẽθ at the center, aligning with the peak of the turbulence-driven particle flux.
Despite small gradients at the center of the edge magnetic island, fluctuations are more pronounced compared to the configuration without a magnetic island.The sources of these fluctuations appear to be a different spatial structure towards the boundary of the magnetic island.While turbulence driving and spreading have similar values in the inner part of the edge magnetic island, there are distinct driving mechanisms for fluctuations within and near the magnetic island, each characterized by non-uniform spatial features.The long connection length, akin to that of the confinement region, may facilitate the coexistence of multiple mechanisms driving these fluctuations.Our interpretation is that there are two types of turbulence: turbulence spreading, which originates and spreads from other radial regions (likely from the core plasma inside LCFS), and turbulence driven by local gradients within the island.Moreover, the detection of poloidal electric field fluctuations at the center of the magnetic island, as illustrated in figure 13, indicates the presence of a driving factor for these fluctuations, resulting in a central peak.This suggests that density fluctuation and poloidal electric field fluctuation within the magnetic island are not directly proportional but are instead decoupled.
The driving mechanism behind these poloidal electric field fluctuations cannot be fully understood using current methods of analyzing turbulence driving and spreading.As a preliminary conclusion, it appears that at least three distinct types of fluctuation mechanisms may coexist within the island, resulting in subdominant perpendicular transport in addition to dominant parallel transport.However, further experiments are necessary to confirm this hypothesis and to measure the effects at multiple toroidal/poloidal positions.At the outer boundary of the magnetic island: -Large gradients are evident.
-Density fluctuations are significant, indicating the potential for inward and outward spreading of these fluctuations.
-There is a possibility of observing hole-like features inside and blob-like features outside the island.-The influence of turbulence driving is more pronounced.
-The turbulence-driven particle flux is considerably high.
At the outer boundary, turbulence is believed to be driven by the steep gradient resulting from varying connection lengths.Similar to phenomena observed around the LCFS of other confinement devices, particles might be transported into the magnetic island as 'holes' and expelled outward as 'blobs.'The proximity of the pressure gradient's position to the peak of the radial electric field aligns with the theoretical prediction [34] that blobs occur at the maximum value of the radial electric field.It has been suggested that fluctuations initiated by the gradient at the boundary of the magnetic island could propagate through the X-point towards the O-point [36].This study's results imply that fluctuations beginning at the outer boundary of the magnetic island might spread into the island.However, elucidating this phenomenon is challenging with the current probe measurement system, which is onedimensional.Therefore, it is still necessary to use multidimensional measurements to comprehend the spatial structure of these fluctuations.
In this study, E θ is calculated under the assumption of negligible electron temperature fluctuations since they are difficult to evaluate with the Heliotron J probe system.This assumption is supported by the observation in other devices, showing that the electron temperature fluctuations are usually small and are approximately in phase with the potential fluctuations to the degree of spatial precision of the probe head [16,30,34].Furthermore, even if electron temperature fluctuation was significant, this would not affect the observation of the non-uniformity of fluctuation properties and transport inside the magnetic island, which is the main claim of this study, for the following reasons.Firstly, ion saturation current fluctuation (density fluctuation) is not substantially affected by temperature fluctuation, suggesting that temperature fluctuation is unlikely to contribute significantly to the observed non-uniformity of density fluctuation inside the island.Additionally, while temperature fluctuation could contribute more significantly to floating potential fluctuation, even if the potential fluctuation is uniform and the non-uniformity is attributed to temperature fluctuation, the non-uniform temperature fluctuation would induce non-uniform transport inside the island.
While the precise physical mechanisms are not fully explained at this stage, these observations affirm the presence of various non-uniformities in and around the magnetic islands, even with one-dimensional probe measurements.Given the three-dimensionality introduced by magnetic islands, future research necessitates two-dimensional, and ideally, three-dimensional measurements.These approaches are crucial for comprehending heat and particle transport in the SOL and divertor regions, which exhibit strong threedimensional characteristics.These findings are significant for understanding heat transport and control in the divertor region, a critical aspect for the realization of fusion reactors.

Summary
In this study, we investigated the impact of magnetic islands on fluctuation characteristics and transport within a mediumsized helical device, Heliotron J.We utilized modulational ECH to examine the edge plasma response in a magnetic island configuration.The results revealed a slight peak in the averaged electron temperature (T e ) profile, a localized drop in the amplitude profile, and an increased value of the phase difference (∆ϕ ), indicating heat deflection by the magnetic island structure.Comparing edge plasma parameter profiles in configurations with and without a magnetic island, we observed higher and constant electron density (n e ) in the island configuration.The T e inside the island was lower on the wall side.Variations in spatial potential (V s ) and radial electric field (E r ) were also observed within the island, potentially influencing poloidal flow and transport.
The presence of magnetic islands distinctly affects the turbulence mechanism, resulting in varying behaviors in fluctuation intensity, statistical properties, fluctuation spreading, and fluctuation-driven transport.The normalized density fluctuation intensity increases from the inner to the outer region of the magnetic island, while the normalized potential fluctuation intensity is enhanced in parts of the island.Intermittent transport, as indicated by skewness and kurtosis values, is suppressed within the island, where PDFs are close to Gaussian.However, outside the island region, intermittent transport is enhanced, and the PDF deviates from Gaussian.The density fluctuation is more pronounced at the outer boundary, with the direction of fluctuation spreading reversed at the boundary of the magnetic island.The turbulence driving term remains constant within the island but increases significantly at the outer boundary.In contrast, the turbulent spreading term is negative at both boundaries, peaking at the center of the island.The poloidal electric field fluctuation peaks inside the magnetic island, and the fluctuation-driven particle flux shows peaks in both the center and the outer boundary of the island.These findings suggest that various fluctuation mechanisms coexist and generate spatially modulated transport even within the structure of an edge magnetic island.

Figure 1 .
Figure 1.Connection length distribution in different configurations.Upper row shows the connection length in the island configuration, and lower row illustrates the connection length in the configuration without an island.

Figure 2 .
Figure 2. Rotational transform profiles.The black line shows the rotational transform profile for the configuration without magnetic islands, while the red line shows the rotational transform profile for the island configuration.The horizontal axis <r> corresponds to the average minor radius.

Figure 3 .
Figure 3. Connection length distribution of (a) the island configuration and (b) the configuration without an island around the probe path.Green line indicates the probe path.(c) Connection lengths on the probe path.∆r indicates the distance from the LCFS.

Figure 4 .
Figure 4. Side view of the probe head and its channel setup.

Figure 5 .
Figure 5. Profiles of (a) connection length distribution, (b) time averaged Te, (c) amplitude, and (d) phase delay.The two vertical grey hatched area indicate the boundaries of the magnetic island.∆r indicates the distance from the LCFS.

Figure 6 .
Figure 6.Radial profiles of (a) electron density, (b) electron temperature, (c) space potential, and (d) radial electric field.Black line represents the configuration without magnetic islands, while the red line represents the island configuration.∆r indicates the distance from the LCFS.

Figure 7 .
Figure 7.Typical PSD of Is and coherence between Is and a magnetic probe.Typical PSD of V f and coherence between V f and a magnetic probe.

Figure 8 .
Figure 8. Spatial distribution of Is and V f spectra.The upper row shows the radial power spectrum density profile of Is, and the lower row shows V f .Here, the left column corresponds to the configuration without a magnetic island, and the right column corresponds to the island configuration.∆r indicates the distance from the LCFS.

Figure 10 .
Figure 10.Radial profiles of (a) skewness and (b) kurtosis of Is. ∆r indicates the distance from the LCFS.

Figure 11 .
Figure 11.Radial profiles of Is, −dIs/dr, ⟨ Ĩ2 s ⟩, and ⟨ Ĩ2 s Ẽθ ⟩.The black line represents the configuration without a magnetic island, while the red line represents the island configuration.∆r indicates the distance from the LCFS.

Figure 12 .
Figure 12.Radial profiles of (a) turbulence driven term ω D and (b) turbulence spreading term ω S .(c) Radial profiles of ω S / (ω D + ω S ).∆r indicates the distance from the LCFS.