A study of turbulent filaments in the edge plasma of the Wendelstein 7-X stellarator

Filaments are studied by examining fast camera images on the Wendelstein 7-X stellarator. Fast cameras offer a unique perspective, revealing the complex 3D structure of filaments in the entire poloidal cross-section of the plasma. By correlating individual pixels, their location, shape, and movement are analyzed in standard and high-ι configurations. The presence of filaments is not uniform poloidally around. The number of active areas matches the number of magnetic islands in both configurations. Filaments are found to extend to multiple toroidal turns in standard configuration. No time delay is observed between the different toroidal sections. Such behavior is not seen in high-ι configuration. Filaments are observed within and without the edge shear layer, indicated by the direction of their poloidal rotation. Inside the shear layer, their velocity scatters around 1.25 km s−1, accompanied by a lifetime between 80 and 120 µs. Outside, their velocity shows greater absolute values and variance, but still in a few km s−1 range. The similarities and differences between the two configurations are discussed and compared to previous results.


Introduction
Filaments, or blobs as they are often referred to due to their appearance in Langmuir probe data, are a common sight in a See Sunn Pedersen et al 2022 (https://doi.org/10.1088/1741-4326/ac2cf5)for the W7-X Team.* Author to whom any correspondence should be addressed.
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toroidal fusion devices [1][2][3][4][5][6].They are typically observed in the edge and scrape-off layer (SOL) regions of magnetically confined plasmas and are a major contributor to crossfield particle and energy transport.Their formation is generally linked to interchange instability, which occurs in the presence of curved field lines and strong pressure gradients.Such are the conditions close to the last closed flux surface (LCFS) at the plasma edge.They begin as field-aligned density perturbations, hence the name 'filament'.Curvature and ∇B drifts cause charge separation within the perturbation.The induced electric field then propels the filaments against the gradient of the magnetic field by E × B drift [1].They travel from regions of high density and long connection length (inertial regime) to regions of short connection length and low collisionality, where they connect to material surfaces (sheathlimited regime).Currents running through the filaments are closing on these surfaces, thus reducing charge separation, size, and velocity.The transition between these two regimes is linked to the formation of a 'density shoulder' and the shaping of SOL density profiles [7].
Filaments were first observed on the Wendelstein 7-X stellarator (W7-X) by fast cameras [8].Since then, they have been studied by reciprocating probes [9] and alkali beam emission spectroscopy (ABES) [10,11].All those studies found that the role of filaments in SOL transport is smaller in W7-X than in tokamaks due to the short radial distance they travel in their lifetime.Zoletnik et al argue, however, that their importance lies in transporting density to the magnetic islands, thus affecting the operating parameters of the island divertors [10].
A shared limitation of previous studies is that the diagnostics they used are basically one-dimensional, only gaining some toroidal and poloidal range by correlating with diagnostics at other positions.However, the intricate 3D geometry of W7-X [12] and the complex magnetic topology of the island divertors [13] require a three-dimensional treatment [14].Fast cameras have been proven effective in the past [15] for studying filaments in complex magnetic geometries [16].They can directly observe filaments for a wide toroidal range in the entire poloidal cross-section of the device.
This paper presents an analysis of filaments on fast camera images in standard and high-ι 5 configurations [17].Correlation techniques are used to reveal their location, structure, and movement in the context of the magnetic geometry.The paper is organized in the following manner: section 2 describes the diagnostic setup and data processing methods used to analyze the fast camera images; section 3 presents the results gained from standard and high-ι configuration; section 4 interprets these results in the context of other research; and section 5 gives a summary and an outlook on future research.

Experimental setup and data processing
The data analyzed for this paper was acquired by the W7-X fast camera system [18].It consists of multiple types of cameras that fulfill various functions.As described in [19], the EDICAM cameras can record with varying framerates over multiple user-defined range-of-interests (ROI), thanks to the non-destructive readout technology.Their primary use is for hot-spot detection and divertor monitoring.For tasks that require a higher framerate, such as observing filaments 5 ι, the rotational transform is defined as ι/2π = dψ/dϕ, where ψ is the poloidal, and ϕ is the toroidal magnetic flux.In layman's terms, it gives the number of poloidal turns per one toroidal turn of the magnetic field lines on a given flux surface.
or pellet ablation [20], we use commercial Photron SA5 fast cameras.They are capable of framerates up to 1 MHz (albeit with strongly reduced ROI).For a detailed schematic of the camera setup at the time, refer to [21].

Data acquisition
The Photron camera used to study filament activity was located in a shielded box and connected to the AEQ21 port by a 500 × 700 optical fiber bundle [8].This setup provided a tangential view of the vacuum chamber.Figure 1(a) shows the fast camera view of the vacuum chamber interior.Depending on the framerate, the entire poloidal cross-section of the plasma could be observed.For filament observation, usually, 45-90 kHz was used.However, above 45 kHz, the top of the vacuum chamber was out of the ROI.The typical length of the recordings was a few hundred ms, the typical ROI was 512 × 488 pixels.
For wavelength selection, the camera was equipped with a filter wheel containing various interference filters.For most of the shots presented here, we chose a 465 nm filter.This way, the gathered light is limited to the C III emission line (including Zeeman and Doppler effects [22]).Carbon is a common contaminant in the edge plasma due to the graphite divertors.C 2+ ions have a relatively long lifetime and an intensive emission line.Even in attached plasmas, there is usually enough C III radiation from the edge so that filaments can be observed.However, during detachment, C III intensity peaks around the LCFS [23].This results in high-quality frames where filaments are quite visible.Figure 1(b) shows how filaments appear in a fast camera image using a C III filter.Apart from a slight gamma correction to even out the brightness, no further processing is applied.A H α filter (656 nm) was also equipped, however, it was not particularly useful for the purpose of this paper.H α radiation is characteristic of the far SOL [24].Consequently, quite intense light originates from the divertor (to the point of overexposure), and far less from other parts of the machine.Most of that is either scattered light or coming from radial position filaments that do not reach.Consequently, filaments are significantly less visible with a H α filter than with a C III filter and most of the activity is centered around the divertor region of the images.However, during radiation collapse, filamentary structures do appear as the plasma shrinks, even with a H α filter, quite faintly though, as seen in discharge 20181018.027.
Visible emissions form a radiation belt around the plasma.The camera sees filaments within this belt.Filaments that do not enter this region are invisible to the camera.To get an estimate of the radial position of the observed filaments, the size of the radiation belt must be known.The size of the radiation belt is estimated by calculating its effective radius (r eff ) using videos from the EDICAM system.A method based on similar principles is presented in [25].It must be noted that the EDICAMs record all visible light, not just C III.However, in standard configuration, in the divertor region, during detachment, the visible spectrum in the edge is dominated by C III emission [23].Its intensity peaks at the LCFS, while other emission profiles remain mostly flat and peak at the divertor plates.Matching the shape of filaments with field lines belonging to flux surfaces with similar r eff as estimated for the radiation belt also indicates that these estimations are rather accurate.The width of the radiation belt is unknown, however, based on the observed lifetime of filaments and their reported radial velocities [9][10][11], it must be between 1 and 5 cm.

Data analysis
After recording, the images are processed pixel-wise.First, socalled binning is applied, which means that pixels are averaged over 3-by-3 grids to reduce noise and processing time.The mean of the time series of the resulting pixels is subtracted, then they are filtered between 2 and 11 kHz.This is the frequency range expected for filament activity [10].It also helps to filter out the effects of other phenomena, such as 1-2 kHz low-frequency modes [26], and 10-30 kHz high-frequency quasi-coherent modes [10].
After pre-processing, pixel-wise correlations are calculated.The reference points are usually chosen as the projections of points with known 3D coordinates from a given flux surface.The magnetic geometry is reconstructed by field line tracing from the vacuum magnetic field.The field lines and their Poincaré plots at a given toroidal angle can be connected and projected to the image for visual reference (black dotted and solid lines in figure 2 and henceforth).It is a static representation that does not include perturbations that might be caused by the plasma or happen during an experiment, nor is it absent of numerical error.Therefore, while useful for visual reference, it should not be considered 100% accurate.
Displaying various aspects of pixel-wise correlations can reveal the location, structure, and poloidal rotation of filaments.For example, the correlations at zero time lag highlight the pixels that are active at the same time as the reference point.See figure 2 for an example.It can reveal whether the correlated area shows a filamentary structure, and if so, its shape, toroidal and poloidal extent, and if it matches the field lines well.Displaying correlation at different time lags can reveal how the correlated structure moves.
It is more efficient, however, to plot the maxima of these correlations.It highlights all areas with a significant correlation to the reference point, regardless of time lag, revealing the toroidal extent of filaments and the range of their poloidal movement.It is a more general view that helps to identify the pixels that filaments affect during their lifetime.Comparing the correlated areas to magnetic field lines of a particular flux  2, this plot highlights all pixels that correlate positively to the reference point at any time.Thus, the entire range that filaments travel over becomes visible.The red curve shows the shape of the flux surface the reference point is taken from at that toroidal position.
surface can also help pinpoint the radial positions of filament activity.See figure 3 for an example.Here, the red line is the flux surface from which the reference point is chosen.The green dotted line is the field line on that surface that passes through the reference point and its elongation by one toroidal turn in each direction.
It can be even more informative to display the time lag of the maximal correlation of each pixel.This combines information about location and movement in the same image.Areas of zero time lag show the location and shape of filaments, while areas that belong to different time lags show the direction and range of their movement.In figure 4, blue represents the areas, where the maximal correlation is at a negative time lag with respect to the reference point.This means that maximal correlation happens there before it happens at the reference point.White areas belong to zero time lag, meaning simultaneous peak activity, while reds represent positive time lag.Bluewhite-red transition indicates movement.Areas with time lags so great that they are unlikely to be significant are greyed out.Comparison with the corresponding maximal correlations (see figure 3) justifies this by showing that the grey areas have no meaningful correlation.It also makes interpreting these plots somewhat easier.Figure 3 together with figure 4 combines all the information about filament location, structure, and movement that would only be accessible by comparing momentary correlations at different time lags otherwise.
Physical properties of the filaments, such as velocity or lifetime, can be estimated by plotting the time lags along a flux surface.Figure 5    Values of maximal correlation (black curve) and its time lag (red stars) over the section highlighted in figure 4. The x-axis is the poloidal distance along the flux surface.The pink lines show the approximate position of the field line that passes through the reference point (blue star at 0 distance, 0 time lag, and 1 correlation) after one toroidal turn in both directions.The reciprocal of the slope of the red stars at the center gives the average poloidal velocity of filaments.In this figure, it corresponds to 1.23 km s −1 .The width of the correlation peak gives the poloidal range of filaments, while the difference in time lag gives their lifetime.moving through the reference point.The width of the correlated area (estimated by fitting a Gaussian) gives the average poloidal distance filaments travel, while the difference in time lag over that range gives their lifetime.
The plots introduced so far describe filaments locally, around a single reference point.To display filament activity around the entire poloidal cross-section without looking at hundreds of separate figures, plots like figure 5 can be joined together.They form two contour plots that combine the information of all reference points along a flux surface.One for maximal correlation and one for its time lags.They simultaneously give an overview of filament activity on the entire poloidal cross-section and make comparing different discharges more straightforward.For an example, please refer to figure 8 in section 3.In these plots, the x-axis is the location of the reference point on the flux surface.Distance along the surface is measured from an arbitrary point on it.The y-axis is the distance from that reference point along the same surface.In fact, figure 5  Various factors can make interpreting these results challenging.Most of them originate in the local magnetic geometry.Most perturbations (filaments or otherwise) align with field lines.Therefore, parts of the image where field lines are parallel with the line-of-sight are brighter than parts where they are perpendicular.Finer details of the changes in light intensity can be lost, especially if the increased light leads to overexposure.Such is the case at the bottom of the images, where the area of the divertor is, which is the most radiating part of the plasma by design.Also, at the bottom and the top, the projection of field lines intersect and often loop over themselves.Thus, a single filament can cause a wide area of increased, simultaneous correlation.It makes it impossible to see how filaments move there or approximate their poloidal velocity.On a plot, such as figure 5 or 8(a), it becomes more difficult to differentiate between filaments returning after a toroidal turn and those that loop over the projected flux surface.Filaments that pass right in front of the camera can also interfere with the results.It may cause a correlation between quite remote parts of the images and mask the movement of filaments behind them.Figure 6 shows how filaments passing in front of the camera can cause a smear in correlation patterns.It may hide filaments and make measuring poloidal velocity impossible since pixels there are active at the same time.

Results
In this section, we present the results of the aforementioned techniques.Most of the recorded discharges that were suitable for the purposes of this review (high enough framerate, C III filter, and enough light to analyze) were in standard configuration (EIM+252262).Only two shots were in high-ι (FTM+262).In the standard configuration, the ι at the island o-points is one, meaning there are five separate islands closing on themselves after one toroidal turn.The ι at the LCFS is somewhat lower than 1, therefore, field lines return a few cm away from their original position.In the high-ι configuration, the rotational transform is 5/4 at the islands.This means there is only one island appearing four times and closing on itself after four toroidal turns.The ι at the LCFS is around 1.2, which means that field lines return almost a fifth of a poloidal turn away from their original position.Filament activity in the standard configuration shots was generally similar.Differences were either the result of the amount of light gathered by the camera, which is a consequence of plasma density, or whether the plasma was in detachment, which affects the position and intensity of the radiation belt.Our findings about the standard configuration are presented via shots 20181016.015and 20181018.023.All other standard configuration discharges that we analyzed yielded similar results; therefore, this review focuses on these two.For a high-ι configuration, the two discharges that met the criteria are 20180904.017and 20180904.018.Both are highdensity discharges.Table 1 summarizes the parameters of the discharges whose results are presented in this section.
20181016.015 is an ideal discharge, as it was recorded at 45 kHz with a C III filter.The radiation belt was close to the LCFS, and the entire poloidal cross-section of the plasma was in view.The density was quite high, so there was plenty of light, and filaments were quite visible.The plasma also went through attached and detached phases6 .To map filament activity poloidally in 20181016.015,reference points were chosen poloidally around a flux surface at a given toroidal angle.This reference surface is just inside the LCFS.The reason for this selection is that r eff during this shot matched the effective radius of that particular surface.Comparing the shape of correlation patterns with the shape of projected field lines gave the best match for this surface as well.
Figure 7 shows filament activity around a single reference point.Figures 7(a)-(c) show the plasma in detachment.Figure 7(d) is made from the same discharge when the plasma was attached and is added for comparison.During detachment, filaments rotated poloidally counterclockwise, as the succession of colors in figure 7(b) and the slope of time lags in figure 7(c) show.In he attachment, they moved clockwise, as indicated by the reversed color succession around the reference point in figure 7(d).The differences between the attached and detached plasmas will be discussed in more detail later.

Toroidal extension of filaments
Filaments loop around the device toroidally multiple times in a standard configuration.In figure 7, there is an increased correlation along the field line that crosses the reference point, even after a toroidal turn in both directions.This is more apparent in figure 7(c).It shows an increased correlation at the position of the returning field lines with zero time lag and a similar slope as at the origo.These correlation values are much higher than at any other position.Figures 7(b) and (d) also show zero time lag along the returning field lines, indicating simultaneous correlation.There are similar patterns around the reference points at other poloidal positions.Increased correlation is present at the position of the retuning field lines at multiple locations in 8(a).Figure 8(b) shows that the time lag, which belongs to these areas, is zero.Moreover, the same succession of colors is present over them, indicating similar rotation.
Though other lines are emerging in figure 7(b), those areas are not significantly correlated to the reference point (see figure 7(a)).The pixels in those areas correlate to each other, which is why the time lags of their maximal correlations to the reference point, however small those may be, are similar.Hence the appearance of similar colors over extended but uncorrelated regions.
Parallel transport in the filaments was not observed.The time lag along the returning filaments is mostly zero.(Deviations occur, but not consistently.Most of such instances can be explained by the interference of other filaments passing in front of the camera or other effects caused by the complexity of the projected magnetic geometry.)Based on this data, it is unclear whether filaments enter the radiation belt toroidally fully extended or still spreading.If they do, it happens in less time than one timestep, which, at the highest used framerate, is ∼11 µs.In that case, the speed of toroidal spreading must be above 3300 km s −1 .A study on Alcator C-Mod found that the parallel propagation of filaments in the SOL roughly scales with the Alfvén velocity and the electron thermal velocity [29].Depending on the actual profile and the radial position of the filaments, both velocities range from a couple of 1000 to above 10 000 km s −1 in the studied discharges.These magnitudes are consistent with the observations.

Poloidal asymmetry in filament activity
Figure 8 shows a poloidal asymmetry in filament activity.There are five sections which loosely align with the five magnetic islands.Filaments move poloidally counterclockwise in them.They are separated by regions where no filament activity is observed.This pattern is, however, obscured by several circumstances.It is caused mainly by the projection of the complex 3D geometry, as described at the end of the previous section.The region from about 20-100 cm in figure 8(a) is the bottom of the camera image, where the divertor is.It is the most luminous part of the picture.Moreover, the projected field lines are quite entangled here, so even one filament can illuminate a wide poloidal range simultaneously.This is supported by 8(b), where most of that region is just plain white without any color transition.The same situation happens between 220 and 250 cm as well, which is at the top of the image.Both regions are also affected by filaments, which pass right in front of the camera.There is also a strong toroidal flow in the lower divertor region and at the tip of the bottom left island, starting around 320 cm.Also, the center (155-200 cm) belongs to the top of the image, which is blocked out by the edge of the port, unfortunately.The same thing happens later in figure 12, which is about the high-ι configuration.In both configurations, however, this area lies exactly between two islands.The inactive regions can be clearly observed on the actual recordings as well.Figure 9 shows a single (preprocessed) frame from a movie.The succession of active and inactive regions is quite apparent.
This pattern of active and inactive regions does not change, even as the radiation belt moves outward.In the attached phase of 20181016.015,there is of course less light, but filaments are still visible.This is to be expected since detachment on W7-X is brought on by an increase in impurity radiation [28].r eff of the radiation belt here is around the same as the LCFS.Filaments appear in the same regions.There is only one notable difference: the poloidal rotation of filaments changes direction at the left mid-plane island (see figures 7(b) and (d)).

Filaments in attached plasma
All other plasmas where detachment was not achieved were quite similar to each other.We chose 20181018.023as an example because, by the end of the discharge, the radiation belt shrunk closer to the LCFS.In that segment, the radiation intensity increased as well.During the discharge, filaments are still present in the same regions as in detached plasmas, only less visible (the density here was also half as much, further reducing visibility).Their correlation patterns are also similar but not as intensive.Figure 10(a) shows the change in intensity by integrating the maximal correlation along the flux surface for each reference point.The detached part of 20181016.015 is added for comparison by integrating figure 8(a) over the y-axis.The active regions are similar in both cases.As the radiation belt shrinks, the intensity (represented by the integral) increases but does not reach the level of detachment.The main difference to detached cases is that filaments move in the opposite direction at the two mid-plane islands.In figure 10(b), the framed parts show the reversal of colors, signifying clockwise rotation.There are also white patches a few cm before and after the reference points, indicating the toroidal turnaround of filaments.
The direction of poloidal rotation at the different islands is summarized in table 2 for each discharge presented here.Discharges in the same parameter range as 20181018.023,such as 20181018.035,yielded similar results.In that discharge, the radiation collapse was also recorded.During the collapse, filaments were seen poloidally all around, rotating counterclockwise.

Filaments in high-ι configuration
In the high-ι configuration, there are four islands, and four regions of activity as well.It is shown in figure 12 (from 80 to 140 cm, from 180 to 195 cm, from 215 to 290 cm, and from 300 to 70 cm).Though these regions are not aligned perfectly with the approximate positions of the islands here either, the Table 2.The direction of poloidal rotation of filaments at each magnetic island.Numbering of the islands starts with the bottom left island in EIM (figure 7(a)) and the bottom island in the FTM configuration (figure 11(a)).'+' signifies clockwise, while '−' counterclockwise rotation.The last two columns are if the plasma was detached and normalized effective radius of the radiation belt.match in number in both configurations supports the assumption, that there is a connection between the presence of magnetic islands and filament formation.Filaments rotate clockwise poloidally all around in 20180904.018.Figure 11(b) also shows the succession of colors clearly reversed.The few instances in figure 12(b) where it seems otherwise are artefacts of the 2D projection.Interestingly, in 20180904.017,it was not the case, as regions of clockwise and counterclockwise rotation were both present, though mostly it was counterclockwise.In both cases, the reference points were chosen from a flux surface that matches the radiation belt well.

Island
There was no sign of filaments looping around the device whatsoever in any high-ι shots.There is no increased correlation at the position of the returning field lines in figure 11(c).There is no increased correlation along the returning field lines in figure 12(a) either, nor are there white regions around them in 12(b).However, there are other filaments that cross the reference point in figures 11(a) and (b).They are projected to the same pixel as they curve behind the inner wall.As such, they cause similar patterns as returning filaments, even though they are not physically related.They are responsible for the second peaks at the center in figure 11(c).They also cause  the third as they cross the reference surface once more (as seen in figure 11(a)).Putting the reference point to that second crossing gives only one stripe of correlation, proving that they are indeed caused by separate events (see figure 11(d)).This serves as further evidence that the patterns seen in figure 7 are caused by the same filaments.As seen in figure 11(d), different filaments closely following each other do not correlate.5. Areas, where the results are considered realistic, are plotted with solid lines for the red and blue curves.

Physical properties of filaments
As described in the previous section, it is possible to infer the poloidal velocity of filaments by plotting the time lag of maximal correlation against the poloidal distance along a flux surface (see figure 5).However, this is only possible where the projected field lines are not entangled and the filaments are not masked by other phenomena.Such regions, for example, are the ones where there is a clear blue-whitered transition around the center in figure 8(b).Even there, the time lag around the reference point is zero for a few steps quite often (as seen in figure 5).This can be caused by the physical width of the filaments, projection, over-exposure, or other filaments passing over the region closer to the camera.To avoid this effect, these few steps were linearly interpolated over so that the fitting would give a more realistic estimate.These estimates scatter around 1.25 km s −1 in the regions where filaments could be seen clearly for all standard configuration shots and 20180904.017.In 20180904.018,the values scatter so much it is impossible to give a reasonable estimate.The results are shown in figure 13.The poloidal ranges where the results are considered realistic are plotted with solid lines for 20181016.015and 20180904.017.
To estimate the poloidal distance that filaments travel over, we fitted a Gaussian around the reference point on the correlation maxima along the flux surface.Four times the standard deviation of the fit is taken as the estimate of the width of the correlated range.It is a rather generous estimate, but it was found to match the distance along which the correlation generally falls to the level of the background.The results vary mostly between 10 and 15 cm.The corresponding time lags give a lifetime of around 80-120 µs.In 20180904.018,the lifetimes were shorter, ranging between 30-90 µs.
The poloidal width of filaments can be estimated similarly, except the Gaussian is fitted to the correlation at 0 time lag instead of the maximal correlation.Alternatively, it can also be estimated by the width of the range where the time lag of the maximal correlation is 0 or by multiplying the width of the autocorrelation of the reference point by the local poloidal velocity (as in [9]).All methods gave similar results, and all are highly sensitive to the projected angle of the filaments and the flux surface, other filaments passing over closer to the camera, or all the other issues mentioned before.Consequently, it is difficult to give a reliable estimate.The results fall between 4 and 8 cm.This seems to be an overestimation compared to [9].The possible reasons are discussed in the next section.

Discussion
As presented in the previous section, filament activity is not uniform poloidally around in the studied discharges.Section where no filaments are visible separate active areas.At this point, it is not clear whether filaments are not present in these sections or just not visible.
Filaments have been observed to form in the presence of high-density gradients [1].It has also been demonstrated that the local magnetic geometry affects density profiles [30] and turbulence [31].ABES studies found that radial shape and propagation of filaments differ in standard and high-ι configurations [11].Both simulation [32] and experiment [10] show that the radial velocity of filaments scales with connection length (indicating a possible transition between the inertial and sheath-limited regimes).Their poloidal rotation is propelled by the E × B drift, fueled by the radial electric field (E r ).In [33], the electron temperature (T e ) profile is shown to determine E r in the SOL (at least in attached plasmas, E r, SOL ∝ T e /λ q , where λ q is the exponential decay length of the divertor heat flux).The paper also claims that sheared flows in the edge caused by the sign flip of E r can cause a moderate reduction in turbulence.Poloidal non-uniformity of density and temperature profiles have also been reported [34,35].Based on the findings cited here, it is reasonable to expect that as magnetic geometry changes, so do edge profiles.Consequently, at certain poloidal positions, conditions might become unfavorable for filament formation.
On the other hand, it might just be the case that those regions of absence are simply not luminous enough for perturbations to be perceived.The brightest part of the image is, of course, the divertor since that is where most of the energy transported to the SOL is radiated away.Intensity also depends on the density profile, the alignment of field lines to the line-ofsight, and C 2+ density.The poloidal variation of C III emission has been demonstrated by simulation [36] and measurement [37] alike.
All-in-all, there are multiple possible explanations for why filaments are seen in one region and not in another.However, it is beyond the scope of this paper to decide which one is correct.What is certain, though, is that in standard and high-ι configurations, the number of active regions seems to match the number of magnetic islands and that during radiation collapse, filaments are seen poloidally all around.Therefore, it stands to reason that this pattern is somehow caused by the presence of magnetic islands.
As for the differences between the two configurations, the change in the direction of the poloidal rotation can be explained by the position of filaments relative to the shear layer.The shear layer is a narrow radial region where E r , and thus E × B driven flows, change sign.It creates a region of strong velocity shear, hence the name, and is linked to the formation of radial transport barriers [38], and H-mode [39].The interaction between filaments and shear flows is rather complex.Shear flows are an important factor in filament formation, as they shear off radially elongated density perturbations born of interchange waves [1,4,40,41].E × B flows have been shown to radially slow down filaments and distort their shape poloidally [42].Externally induced shear flows can affect blobs similarly or even break them apart [43].The interaction between E × B shear and the internal spin of filaments can also have a stabilizing effect on their structure and add a perturbation to their poloidal velocity [44].However, all these phenomena are below the resolution of the present diagnostics, therefore, we focus our discussion on the direction of the poloidal rotation of filaments.Though other effects might play a role in setting the actual velocity of the rotation, its direction is most likely a consequence of the sign of the E r experienced at the site of observation.
In [45], the E r profile is measured for multiple configurations.According to the paper, right inside the shear layer, E r is negative.This causes counterclockwise rotation.Outside it, E r is positive, therefore, the rotation is clockwise.Even though the position of the shear layer (ρ shear ) is usually associated with the LCFS, it can be a few cm off, depending on the magnetic configuration, density, and heating power.In high-ι, for example, ρ shear decreases as the density increases (though densities as high as in the shots presented here were not examined).|E r | and its change at ρ shear (∆E r ) are also higher, compared to standard configuration [45].In 20180904.018,the filaments must be outside ρ shear .Their increased velocity is also consistent with the higher ∆E r reported for the high-ι configuration.The varying direction in 20180904.017indicates that the radiation belt overlaps with the shear layer.This is supported by the smaller estimate for r eff .
In the standard configuration, ρ shear increases with density up to the separatrix in shots with similar density and heating as 20181016.015,then it decreases again.It also recedes during detachment [45].The estimates for r eff were also higher than the effective radius of the LCFS in attached cases and smaller in detachment.This is consistent with the observation of filaments moving clockwise at the mid-plane islands in attached plasmas and counterclockwise in detached ones.
Regarding the lack of toroidal turnaround in high-ι configuration, the obvious answer would be that those filaments are in the SOL.They end on the divertors before they could return after a toroidal turn.Compared to the standard configuration, in high-ι, the separatrix is at a lower radial position, and the connection length in the SOL is much smaller and drops faster [30,46].However, it only drops below twice the toroidal circumference of the device in the far SOL, while the radiation belt was estimated to be inside the LCFS.This suggests there may be a different explanation for not seeing returning filaments.It must be noted, though, that this argument about radial positions is based on the comparison of the effective radii of two things that are decidedly not circular.Neither are those values perfectly accurate (though it is argued that the error in LCFS position should be minimal [10,45]).Either way, the evidence is not conclusive to either side.
Finally, let us consider the properties of the filaments themselves.The values discussed from here on are all drawn from the poloidal regions, where the projection of the magnetic geometry allowed a reasonable estimate (as described in section 3).The velocities estimated in standard configuration and 20180904.017agree remarkably well with results gained by a similar method [9].They used poloidally displaced reciprocating probes in the SOL in low-ι configuration.The results from 20180904.018scatter more and reach significantly higher absolute values.Yet, these are still within the same order of magnitude (a couple of km s −1 ) that was measured elsewhere for poloidal flows [30,[47][48][49].The lifetimes of filaments observed by the camera are similar to the decorrelation times measured by ABES [10,11].Shorter decorrelation times for high-ι were also observed [11].Estimates for the poloidal width of filaments were higher than in [9], which found them to be under 3 cm.The spatial resolution of the camera is about 1 cm, so smaller sizes cannot be distinguished.Also, depending on the framerate and the actual poloidal velocity, filaments can move 1-3 cm during exposition time.This is added to their perceived width.The distortion of the projection, caused by the angles between the reference surface, the filament, and the line of sight, can also cause a smear.These factors combined can explain why this method overestimates the poloidal width compared to [9].

Conclusions
In this paper, plasma filaments were analyzed using fast camera images on the Wendelstein 7-X stellarator in standard and high-ι configurations.By calculating pixel-wise correlations, the location, structure, and movement of filaments are revealed.It is found that filaments are not present poloidally all around.The number of areas where they are present matches the number of magnetic islands in both configurations.The position of these active areas relative to the island o-points, however, is not uniform poloidally around.
The shape of filaments matches projected field lines well.In the standard configuration, they can loop around the device toroidally two times, matching the field lines.Toroidal spreading of filaments along the field lines was not observed.If it happens, it does under 11 µs, which corresponds to about 3300 km s −1 .Toroidal turn-around was not seen in high-ι configuration.
Filaments were observed inside and outside the edge shear layer.Their relative position was inferred by the direction of their E × B driven poloidal rotation.Their velocity inside the shear layer was about 1.25 km s −1 in both configurations.Outside the shear layer, it varied greatly but remained in the expected range (a few km s −1 ).The lifetime of filaments within the shear layer was around 80-120 µs, traveling over a 10-15 cm poloidal range.Filaments outside the shear layer in high-ι were more short-lived, about 30-90 µs.In both cases, estimates for the poloidal width of filaments vary between 4 and 8 cm, however, this is considered to be an overestimation.
Fast cameras are powerful tools in the study of plasma filaments.They can directly observe the structure and movement of plasma filaments in the context of the magnetic geometry on a much wider range than any other diagnostic.These benefits, however, come at the cost of radial accuracy.This can be compensated for in future studies by including data from other diagnostics that measure in a more localized manner such as ABES, gas-puff imaging, or reflectometry, to add the radial dimension.That way, cameras can live up to their potential for truly 3D analysis.

Figure 1 .
Figure 1.Fast camera images before preprocessing.Apart from a slight γ correction to even out brightness, no further processing is applied.(a) The inside of the W7-X vacuum chamber, as seen by the camera without interference filters.(b) Filaments in W7-X in standard configuration, using C III filter.

Figure 2 .
Figure 2. Correlation of each pixel to the reference point at zero time lag, highlighted by the green star.Black dotted lines represent the field lines that belong to the LCFS.Connected Poincaré plots representing different flux surfaces are added to provide further detail about the magnetic geometry.Green dots highlight the field line passing through the reference point and its elongation by one toroidal turn in each direction.

Figure 3 .
Figure 3. Maximal correlation of each pixel to the reference point (green star).Unlike figure2, this plot highlights all pixels that correlate positively to the reference point at any time.Thus, the entire range that filaments travel over becomes visible.The red curve shows the shape of the flux surface the reference point is taken from at that toroidal position.
plots the section of figure 4 highlighted by the green line.The green line follows a flux surface at the toroidal angle it crosses the reference point.The red stars are the time lags plotted figure 4. The black curve shows the corresponding maximal correlation values.By fitting a linear function to the red starts around the center of the plot, the reciprocal of the slope gives the average poloidal velocity of perturbations

Figure 4 .
Figure 4. Time lag of maximal correlation to the reference point (green star).Areas of simultaneous correlation match field lines.A section of the flux surface that crosses the reference point at its toroidal position is also highlighted in green.

Figure 5 .
Figure 5.Values of maximal correlation (black curve) and its time lag (red stars) over the section highlighted in figure4.The x-axis is the poloidal distance along the flux surface.The pink lines show the approximate position of the field line that passes through the reference point (blue star at 0 distance, 0 time lag, and 1 correlation) after one toroidal turn in both directions.The reciprocal of the slope of the red stars at the center gives the average poloidal velocity of filaments.In this figure, it corresponds to 1.23 km s −1 .The width of the correlation peak gives the poloidal range of filaments, while the difference in time lag gives their lifetime.

Figure 6 .
Figure 6.A smear in correlation patterns over the reference point (green star) caused by filaments passing in front of the camera.The pattern matches field lines that enter the view at the top of the image.
matches the vertical sections of figures 8(a) and (b) at x = 352.5 cm.As such, along the y-axis, the reference points are always at 0. In figure 8(a), the colors represent the maximal correlation to a reference point; in figure 8(b), the time lag of that correlation.At y = 0, the correlation values are always 1, and the time lags are always 0.

Figure 7 .
Figure 7. Correlation patterns show filaments looping around toroidally in standard configuration.(a) Maximal correlation to the reference point (green star).The green dotted line is the field line crossing the reference point followed over one toroidal turn in both directions.The red line is the reference surface, the red star is x = 0 in figure 8. (b) shows the corresponding time lags of (a).(c) shows a section of (a) and (b) along the red line in (a).It also matches the vertical section of figure 8 at x = 304.29.The black line is the maximal correlation, the red stars are its time lags.The vertical lines show the positions of the returning field lines.(d) Time lags of the same discharge in attachment.

Figure 8 .
Figure 8. Plots like figure 7(c) joined together to form contour plots in a standard configuration.The green curves indicate the position of the field line crossing the reference point after one toroidal turn.(a) shows the poloidal evolution of maximal correlation around each reference point along the flux surface indicated by red and measured from the red star in the counterclockwise direction in figure 7(a).The vertical lines show the approximate poloidal positions of the island o-points.(b) shows the time lags belonging to the correlation values of (a).

Figure 9 .
Figure 9. Poloidal asymmetry of filament activity in the actual video.This is a single (preprocessed) camera image from a standard configuration shot.It shows how filaments are observed only at certain poloidal regions, loosely aligned with magnetic islands.

Figure 10 .
Figure 10.Differences during attachment.(a) shows the change in activity as the radiation belt moves from the far SOL closer to the LCFS and when the plasma is in detachment.Activity is represented by the integral of the maximal correlation along the flux surface (the yellow curve, for example, is figure 8(a) integrated over the y-axis).(b) shows the reversal of poloidal rotation at the mid-plane islands (in the black rectangles).

Figure 11 .
Figure 11.No sign of returning filaments in high-ι configuration.(a) shows maximal correlation.(b) shows the corresponding time lags.(c) A section of them along the red line in (a) (also x = 235 in figure12).(d) shows that there is no correlation between the two stripes in (a) by moving the reference point.

Figure 12 .
Figure 12.No indication of filaments looping around toroidally in the high-ι configuration.(a) show the poloidal evolution of maximal correlation around each reference point along the flux surface indicated by red and from the red star in the counterclockwise direction in figure 12(a).The vertical lines show the approximate positions of the island o-points.(b) shows the time lags belonging to the correlation values of (a).

Figure 13 .
Figure 13.Poloidal velocity along the flux surface indicated by red in figures 7(a) and 11(a) as estimated by the method depicted in figure 5. Areas, where the results are considered realistic, are plotted with solid lines for the red and blue curves.

Table 1 .
The parameters of the discharges discussed in section 3. The columns: discharge number, magnetic configuration, electron density, heating power, framerate, length of the recording.