Turbulent transport in the scrape-off layer of Wendelstein 7-X

Turbulent transport is widely considered to be the main driver for cross-field transport in the scrape-off layer (SOL) of toroidal magnetized plasmas. Here, reciprocating Langmuir probes are employed to measure both the plasma profiles and the turbulent particle transport in the SOL of the Wendelstein 7-X stellarator. The relation between turbulent radial particle flux Γ r and the local pressure gradient is often approximately linear across the entire SOL width, indicating that radial turbulence spreading is absent. This observation holds across a wide range of magnetic configurations and different plasma heating and density scenarios. The magnitude of the turbulent transport for a given gradient reveals a dependence on the magnetic configuration and the position in the SOL, which we relate to the cross-spectral characteristics of multi-tip floating potential measurements. Magnetic islands can add further complexity due to non-monotonic SOL profiles and the breaking of the transport-gradient relation. Finally, anomalous diffusion coefficients are determined from the probe measurements.


Introduction
The width of the scrape-off layer (SOL) is a fundamental control parameter for the distribution of heat loads onto plasma-facing components in magnetic fusion devices [1,2].In general, a wider SOL is considered to be favourable as it distributes heat loads to targets over larger areas.Ideally, the SOL is tailored such that it is wide enough to reduce peak heat loads to acceptable levels while still ensuring that heat loads end up on the 'right' components, i.e. typically the divertor.
Assuming in a simplified picture that the sole source of energy and particles for the SOL is the last closed flux surface (LCFS), the SOL profiles follow from the competition of * Author to whom any correspondence should be addressed.a See Klinger et al 2019 (https://doi.org/10.1088/1741-4326/ab03a7)for the W7-X Team.
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.parallel transport to the divertor vs perpendicular transport across the SOL.The latter process is widely assumed to be dominated by turbulent transport [3][4][5].The origin of the turbulence in the SOL, the major mechanisms being the interchange mode and the drift wave, however, is not always clear.Both mechanisms depend on the pressure gradients that are intrinsically present in the SOL.However, numerous investigations report on turbulence activities in regions of the SOL that do not correlate to the local gradients, also called turbulence spreading: in tokamaks, turbulent blob-filaments appear to travel quasi-ballistically from their birth region at the separatrix into the far SOL, where they cause much higher intermittent fluctuation levels than expected from the far SOL plasma conditions [6][7][8][9].In stellarators, (poloidal) turbulence spreading has also been reported, where turbulence spreads poloidally from (interchange) unstable to stable regions [10,11].Turbulent transport arising from turbulence spreading is sometimes also called non-local turbulent transport [12].
In the optimized stellarator Wendelstein 7-X (W7-X), plasma filaments have been observed to span long parallel elongation lengths through regions of strongly varying magnetic curvature [13,14].Moreover, due to the 3D nature of the W7-X SOL imposed by the island divertor [15], also the local perpendicular gradients can vary significantly along a field line.In previous investigations, no indications for tokamaklike intermittent transport of blob filaments or radial turbulence spreading have been observed outside of magnetic islands: the probe investigations in Killer et al [14] indicate that the SOL turbulence is local, i.e. turbulent structures do not emerge radially from their birth region, as the radial velocities of not more than a few 100 m s −1 in conjunction with their lifetime do not allow for a considerable radial turbulence spreading.Consequently, density fluctuations closely resemble normal distributions across the SOL in W7-X [13,14], which again is in contrast to tokamaks [16,17].Agreement of the W7-X observations with modelling indicates that the slow filament velocities in W7-X are mostly due to the smaller magnetic curvature that follows from the large major radius (R major ≈ 5.5 m) of W7-X.
The indications for the local character of turbulence observed in the W7-X SOL [14] imply that the magnitude of turbulent transport is expected to scale with the radial plasma pressure gradient that drives the instabilities, i.e.Γ r ∼ ∇p [8,18].Here, this hypothesis is tested using reciprocating Langmuir probes mounted on the multi-purpose manipulator (MPM) [19,20] of W7-X.Exploiting spatially distributed arrangements of multiple probes, profiles of T e , n (and therefore the pressure gradient) as well as an estimate of radial fluctuating particle transport via Γ r = ñ ṽr = ñ Ẽ pol /B are obtained.After the experimental setup has been introduced in section 2, the scaling of Γ r vs ∇p will be assessed across multiple magnetic configurations and a wide range of plasma conditions in section 3. Finally, we briefly consider the description of turbulent transport as a diffusive process which allows to estimate anomalous diffusion coefficients in section 4.

Experimental setup
On the low field side of W7-X, the MPM [19] allows to plunge fast reciprocating probes across the SOL.Here, a probe head containing an array of 22 cylindrical Langmuir probe tips is employed, which are arranged such that the array is approximately tangential to the LCFS [20].The multiple probe tips allow to operate triple probe setups, constant ion saturation current and floating potential measurements as well as classic swept Langmuir probes simultaneously.

Probe location in the magnetic field of W7-X
While the position of the MPM is fixed, the topology of the magnetic field along the probe path can change as a function of the different magnetic configurations in W7-X.Particularly relevant for the SOL, the chain of magnetic islands forming the island divertor concept [21] varies as a function of the rotational transform ι.The location of the probe path w.r.t. the island chain is presented in figure 1 for the three major island divertor configurations (ι edge = 5/5, 5/4, 5/6, respectively).In the standard and high iota configuration, the probe scans through one of the magnetic islands, slightly above the O point.In the low iota configuration, the probe path barely intersects the island, slightly above an X point.In addition to these situations, so-called limited configurations can be created by setting ι edge such that there is no island chain at the edge, so that nested closed flux surfaces extend up to the divertor targets, which then act as limiters [22].The bottom row in figure 1 shows the local vicinity of the reciprocating probe with the connection lengths to the targets being color-coded.

T e and n profiles
To increase confidence about the Langmuir probe results, both classic swept Langmuir probes as well as triple probe arrangements have been employed to determine T e and n [23,24].The swept Langmuir probe has the advantage of a more accurate model (measuring the entire I -V curve), to the expense of a low temporal resolution (and therefore low spatial resolution as the probe moves) due to the limited sweeping frequency.The triple probe, in contrast, operates faster (at the speed of data acquisition) but uses a rougher simplification of the I -V curve model.
Typical results of both techniques in two measurements in the magnetic standard configuration are presented in figure 2. Both probe methods usually agree qualitatively, although the swept probe mostly provides higher T e and smaller n compared to the triple probe.As the swept probe has a stronger scatter and unreasonably high temperatures in the far SOL at d LCFS > 7 cm (due to high fluctuation levels in the raw data that make it difficult to identify the transition between electron and ion branch of the I -V curve), we use the triple probe for all further computations in this work.The swept probe results are considered as a qualitative confirmation of the triple probe scheme.
Finally, the T e and n profiles are approximated by an 8th order polynomial for further processing (gradient calculation) and better handling of large amounts of experiments in a data base.The relatively high order of the polynomial is required to accurately reflect fine structures of the profiles that are associated with the magnetic islands, see e.g. the characteristic T e peak at d LCFS ≈ 4 cm in figure 2 top left panel.

Fluctuation measurements, estimation of perpendicular fluctuating transport
The reciprocating electric probes have further been used to measure plasma fluctuations with a sampling rate of typically 2 MHz.In particular, several pins on the poloidal array [14,20] have been operated in floating potential (V fl ) mode or at a constant negative bias voltage (collecting ion saturation current I i,sat ).Considering a set of three pins with the I i,sat pin in the centre and V fl pins above and below it, density (via I i,sat pin) and V fl fluctuations can be obtained simultaneously.The fluctuating poloidal electric field across the position of the density measurement is estimated by E pol = (V fl,upper − V fl,lower )/d pins with the sign convention such that a positive E pol points downwards, resulting in a radially outwards E pol × B drift at the LFS with the usually ccw magnetic field direction of W7-X.The probe pins have a diameter of 2 mm and a (poloidal) spacing of 5 mm between adjacent pins, which is both much larger than typical dispersion scales/ion gyro-radii of 200-300 μm.
T e fluctuations have been neglected here, as previous experiments have shown that they are usually small and to the degree of the spatial accuracy of the probe head approximately in phase with the potential fluctuations, legitimizing this simplification [14].The radial velocity follows directly by v r = (E pol × B)/B 2 and the fluctuating radial particle For these calculations, only the spectral range of 5 kHz to 50 kHz was considered by applying band-pass Butterworth filters to the raw data.This decision is motivated by the spectral characteristics of the raw data that is exemplarily presented in figure 3. The power density spectra (PSD) of I i,sat and V fl data in figure 3(a)) show an increase of the PSD towards higher frequencies starting at 30-50 kHz and typically peak in the region between 150 kHz and 300 kHz.Such a behaviour is not expected from purely turbulent fluctuations and is presumably due to (possibly Alfvenic []) mode activity.On the lower frequency end of the spectrum, the influence of the nearby swept probe operating at 1 kHz (including harmonics) is clearly seen and can thus perturb the fluctuations measurements.Therefore, both the low (typically <5 kHz, which also encompasses diamagnetic and E r × B frequencies) and high (typically >50 kHz) frequency range is excluded from further analysis.
The cross-phase is particularly relevant for the particle transport from density and v r fluctuations and for the identification of the underlying instabilities.It is presented in figure 3(c)) for the relevant spectral range only for visual clarity.In the frequency range of a few 10 kHz, the crossphase between I i,sat (∼n) and E pol (∼ v r ) is ≈0, maximizing  the outwards particle transport for given I i,sat and E pol fluctuation amplitudes.In the same spectral range, the cross-phase between I i,sat and V fl is roughly in the region of π/2, revealing an interchange-type character of the observed fluctuations.While the PSD and CSD are qualitatively representative for the vast majority of the available data, the cross-phase and cross-coherence can change significantly as a function of magnetic configuration and measurement position, which will be discussed in section 3.2.The paramount role of the cross phase for the resulting particle transport is further showcased in the exemplary time traces of the fluctuating density ñ and fluctuating ṽr as well as their product Γ r = ñ ṽr in figure 4(a)).While ñ and ṽr show similar levels of positive and negative fluctuations, Γ r features much more positive events, indicating a bias towards outwards directed particle transport.This observation is further solidified in the probability distribution functions of these three quantities presented in figure 4(b)) and the associated statistical moments listed in table 1.While ñ and ṽr closely resemble normal distributions (in agreement with earlier investigations in the W7-X SOL [13,14]), Γ r is characterized by positive skewness and positive (excess) kurtosis.This is due to the cross phase between ñ and ṽr and indicates a tendency towards positive (outwards) particle transport with an increased occurrence of large transport events.

Turbulent transport vs local gradients
Due to the absence of turbulence spreading in the SOL of W7-X in [14], the magnitude of turbulent transport is expected to directly depend on the local plasma gradients.Without specifying the underlying instabilities, we first consider the plasma pressure gradient, i.e. test the relation Γ r ∼ ∇p.In figure 5, the turbulent particle transport Γ r is presented as a function of ∇p.The data from more than 200 reciprocating probe measurements is distinguished by magnetic configuration and each data point represents the averaged transport over a 5 ms interval, in which the probe does not move more than 2 mm.The data points cover a wide range of (ECR) heating powers ([1-6] MW) and line integrated densities ([2-12] ×10 19 m −2 ) and are taken over the SOL from the LCFS (if the probe moved that far) up to 5 cm outside the LCFS.
In general, a linear relation Γ r ∼ ∇p is seen in most configurations, particularly in the high mirror, high iota, low iota configurations, supporting the hypothesis of local turbulent transport.In these three configurations, the high mirror and low iota cases feature a much larger slope of the linear relation compared to the high iota configuration, implying a systematic configuration dependence of the turbulent transport for a given pressure gradient.The limiter configurations [22] in the rightmost panel also indicate a configuration dependence, with stronger scatter towards higher transport levels for the ι < 1 configurations.
Finally, the standard configuration results in the leftmost panel display a more complex picture.The data is by colour further distinguished into experiments with 'regular' sized magnetic islands (without using the island control coils, i.e.I cc = 0, blue) and enlarged islands (I cc = +[1-2.5]kA, red).For the I cc > 0 data, again a roughly linear relation Γ r ∼ ∇p is observed.The I cc = 0 data, however, reveals a much larger scatter.While still mostly positive (outwards) transport is observed, the quantitative relation to the (sometimes even negative) pressure gradients is not clear.It is interesting to note that particularly in the standard configuration with I cc = 0 differences in the SOL profiles across the magnetic islands have been reported.Observations include nonmonotonic T e profiles [15,20,25,26], a poloidal plasma rotation around the islands due to an 'island radial electric field' [20,27], and a still unexplained fast correlation of plasma fluctuations between inboard and outboard side of an island [13].The large scatter in the I cc = 0 data in figure 5 further emphasizes the additional complexity that magnetic islands can entail.
In the following subsections, a few possible reasons for the unclear flux-gradient relation in the standard configuration at I cc = 0 and for the configuration dependence of the linear slopes in the other configurations in figure 5 will be discussed.

Magnetic field characteristics
Assuming interchange-type turbulence, magnetic field characteristics affect both the origin of the turbulence (normal curvature) and the dissipation of turbulent fluctuations (connection length to target) [8].
While the normal curvature in W7-X has strong, fine-scale variations along a magnetic flux tube [14,28], previous work has indicated that due to the fast dynamics parallel to the ambient magnetic field, the averaged normal curvature along a field line dominates the formation and behaviour of turbulent filaments [14,29].Since the magnetic configurations of W7-X considered here mostly differ with respect to the rotational transform, the magnetic curvature profile along a field line starting from the probe does not change more than a few % between configurations.Assuming that indeed the averaged curvature determines the SOL turbulence, no configurationdependent effect is expected for the growth of interchange-type turbulence in our measurements.
The connection length to the targets L c varies quite significantly between different W7-X configurations (see figure 1) and is important as it affects the radial velocity (v r ∼ L c in sheath-limited regime) and dissipation of turbulent filaments [8].
To investigate the systematic differences between turbulent transport levels in different magnetic configurations, the role of L c is investigated in figure 6. There, the same data as in figure 5 is shown (in smaller axis limits) with the connection length for each data point colour coded.Since the connection length can be determined in both parallel directions, along and against the magnetic field, the upper row represents the shorter connection length and the lower row the longer one.Intuitively, one would expect the shorter connection length to play the more important role for the behaviour of turbulent structures as this determines the current closure and therefore propagation of a turbulent filament.
However, the connection length does not offer a clear insight into the systematic differences between configurations.Comparing the high iota case with smaller transport per pressure gradient to the high mirror and low iota cases with larger transport per pressure gradient, no clear relation to the connection length is seen.If at all, the high iota case has (for the shorter direction) longer connection lengths.Similarly, the connection length does not relate to the large spread of transport levels for the different limiter configurations, which all show generally small connection lengths.
In the standard configuration, however, the connection length appears to at least correlate to the rather confusing Γ r ∼ ∇p relation: for short L c in both directions, i.e. in the shadowed region of the island and the private flux region outside the island (see figure 1), a roughly linear relation Γ r ∼ ∇p similar to the other configurations is seen.For data points just inside the main island SOL with very long connection lengths (>200 m in the long direction), significant Γ r levels are observed even at low pressure gradients <10 Pa cm −1 .As  indicated in figures 2, 7 and 9 (and [15,20,25,26]), the plasma profiles taken by the reciprocating probe in the standard configuration often feature a local maximum of T e and a flattening of n at the transition region between the shadowed region with short L c and the main island SOL with long L c , resulting in small (or even slightly negative) pressure gradients.This observation might indicate poloidal turbulence spreading in the magnetic islands [13], which, however, cannot be verified without improved diagnostic coverage in upcoming operation phases of W7-X.

Turbulence characteristics
As discussed in section 2.3, the turbulent particle transport Γ r depends both on the fluctuation amplitudes and on the cross phase between the individual quantities.The radial profiles of plasma conditions and fluctuation amplitudes/cross phases for five representative experiments in different magnetic configurations in figure 7 will give further insight into the different transport levels between configurations and probe positions.
Starting with the centre column in low iota configuration, the fluctuation amplitudes of n, V fl and E pol all increase towards the LCFS.As the phase between n and E pol is generally ≈ 0 in all configurations (see figure 3), the turbulent particle transport is maximized given the observed fluctuation levels (compare to the high Γ r in low iota configuration in figure 5).
In the high iota configuration, the fluctuation amplitudes of n and V fl also increase towards the LCFS.However, the E pol amplitude is here much smaller since the two floating potential pins (from which E pol is deduced) are almost perfectly in phase, with a high coherence.Consequently, the turbulent particle transport will be small, see high iota panel in figure 5. Radial profiles of key quantities along the MPM path (cf figure 1) for five measurements representing different magnetic configurations.All experiments were performed in ECR heated hydrogen plasmas with heating powers between 4 MW and 5.5 MW.The fluctuation amplitudes σ, cross-phase and coherence are evaluated in the frequency range between 3 kHz and 30 kHz.The turbulent particle transport from these experiments is highlighted by star symbols in figure 5.
A similar observation can be made in the limiter configuration in the rightmost panel.Moving closer towards the LCFS, the relative magnitude of E pol fluctuations compared to V fl fluctuations decreases due to an increasingly coherent, in-phase behaviour of the two floating potential measurements.Again, this behaviour results in reduced turbulent transport levels even at stronger pressure gradients, see the star symbols in the rightmost panel in figure 5.
Considering finally the more complicated standard configuration, again the importance of the island size manipulation with control coils is evident.For the enlarged island case in the second column, T e increases monotonically towards the LCFS and σ n /n ≈ 0.1 throughout the entire SOL.Again, while the V fl fluctuation amplitudes increase similarly to n fluctuations towards the LCFS, the E pol fluctuations show a much smaller increase due to highly coherent in-phase fluctuations of both V fl pins towards the LCFS.For the case with regular magnetic islands in the leftmost panel, again the well-known T e peak at the L c transition between shadowed SOL and main SOL is seen.In the main island SOL (left of that peak), the relative density fluctuations decrease while the V fl fluctuations increase quite strongly.However, again due to the highly coherent in-phase fluctuation of the V fl pins, E pol fluctuations become particularly small here.
Concluding, in most situations the fluctuation amplitudes of n and V fl increase towards the LCFS, whereas E pol (which drives the turbulent particle transport) does not increase as strongly and furthermore shows a dependence on the magnetic configuration and the position in the SOL.

Diagnostic limitations
The probe array of poloidally aligned probe tips with a finite distance has intrinsic uncertainties: the alignment of the probe array to the magnetic field was chosen such that the array is tangential to the LCFS.While the flux surface shape varies slightly between configurations, the alignment error is not more than 2 • for the configurations considered here.In the magnetic islands, which have their own flux surfaces, however, the alignment of the probe array breaks down.In the worst case, close to the island O point, the definition of radial (from probe movement) and poloidal (from probe array) switch places in the island's own magnetic geometry.Therefore, the particle transport measured by the probe (following section 2.3) would not be radial but rather poloidal on an island flux surface.However, this issue is restricted to only a narrow part (<1 cm) of the probe path close to the island centre and is not reflected in the data (see e.g.leftmost column of figure 7).
Similarly to the poloidal array potentially loosing its meaning in the magnetic island, the radial pressure gradients obtained from the reciprocating movement of the probe might not show the major directions of the pressure gradients in the magnetic island SOL [15,20,25,26].Finally, the analysis of plasma fluctuations with a probe array is only sensitive to typical structure sizes of the order of magnitude of the pin separation.A possible interpretation of the increasingly coherent in-phase fluctuations of V fl pins close to the LCFS is that the turbulent structures become much larger (in the poloidal direction) than the distance between probes.Indeed, using other V fl pins with a larger poloidal distance to the central I i,sat pin yields somewhat larger E pol results in those situations.This observation might, however, also be explained by the slightly decreasing coherence between more distant pin pairs, as the phase remains still very close to 0 in these cases.For further insight into this phenomenon, experiments with larger poloidal probe arrays are planned for the upcoming operation phase of W7-X.Summarizing the quantifiable uncertainties in determining Γ r (and therefore also D in section 4), we find that the choice of different spectral bandpass filter ranges (see section 2.3) and the choice of the pin combination on the probe head [14] can change Γ r (and D) by up to 50%.This is not a general systematic error as the magnitude and even direction of the error varies between different magnetic configurations and plasma scenarios.

Turbulent transport as a diffusive process
The nature of turbulent transport in the SOL can be described as either convective, diffusive, or a combinations of both [30,31].While the convective character applies to individual turbulent filaments/blobs, a purely diffusive description is often employed (for modelling purposes) when sufficiently long time series are considered, such that individual convective events are just part of the total time-averaged transport [4,32].As an example for modelling applications, the anomalous diffusion coefficient is an integral input parameter into global simulations such as EMC3-EIRENE [33][34][35][36].
In figure 8, the same data from figures 5 and 6 is presented in terms of a generalized Fick's law with both convective and diffusive contributions Γ r = nv 0 − D∇n, with the convective velocity v 0 and the anomalous diffusion coefficient D. In this representation, the intersection of a linear fit with the vertical axis would indicate a convective transport contribution v 0 .As no clear indication of a significant convective velocity v 0 is seen here, (but also in tokamaks, this flux-gradient relation is often not very clear [30,31]), we now simply determine diffusion coefficients via D = Γ r /∇n for comparison with EMC3-EIRENE modelling.
Radial profiles of D along with fundamental properties T e , n, ∇T e , ∇n, Γ r are presented in figure 9 for different magnetic configurations/plasma scenarios.For visual clarity, only one data set is shown per scenario.Since not all data sets were at similar experimental conditions (heating, fuelling), the further analysis focuses on qualitative rather than quantitative differences.
Similar to the results in section 3, the standard configuration results appear to behave differently from the other configurations.While all other experiments show a monotonic increase of T e , n towards the LCFS, the red (and to a smaller degree the blue) curve feature a distinct local peak/profile flattening close to the transition between long and short connection length region (see figure 1) at d LCFS = 4 cm, which is not affecting the transport levels.In general, diffusion coefficients obtained via D = Γ r /∇n with Γ r due to turbulent transport are not larger than a few 0.1 m 2 s −1 .

Summary and conclusion
Reciprocating probe measurements in the SOL of W7-X have been performed such that both the stationary T e , n profiles as well as an estimate for the turbulent radial particle flux Γ r were obtained.The underlying density and potential fluctuations follow approximately a normal distribution, while the cross phase between n and v r is ≈0, maximizing Γ r and implying an interchange-type character of fluctuations.However, in some situations the magnitude of v r becomes small compared to individual potential fluctuations as multiple potential measurements can show highly coherent, in-phase fluctuations, which are not consistent with interchange-type turbulence.
Still, over a wide range of magnetic configurations and plasma conditions, a roughly linear relation of Γ r ∼ ∇p was found, agreeing with the hypothesis that the turbulent transport in the W7-X SOL originates locally due to the SOL gradients.In detail, systematic quantitative differences regarding the strength of the Γ r ∼ ∇p scaling are observed between different magnetic configurations, which we associate to the different v r levels following the relation of fluctuations in different potential pins.A prominent exception from the Γ r ∼ ∇p relation occurs in the main island SOL in the standard configuration, where even for very flat local gradients a significant turbulent particle transport is seen.While different potential explanations for this behaviour are discussed, more solid insight will require additional experiments in the upcoming operation phase 2 of W7-X.
Finally, describing the SOL turbulent particle transport as a diffusive process, anomalous diffusion coefficients D of typically a few 0.1 m 2 s −1 have been determined.Even within uncertainties of up to 50% due to spectral filter choices and probe pin configurations, these values are smaller than typical tokamak experimental results or modelling assumptions [30,32,35,37].In EMC3-EIRENE modelling of W7-X, D is typically assumed between 0.5 m 2 s −1 -1.5 m 2 s −1 to obtain plausible modelling results [36,38,39].Therefore, the level of turbulent transport observed here advocates to use 0.5 m 2 s −1 or less in EMC3-EIRENE simulations.

Figure 1 .
Figure 1.Upper row: Poincaré cross section of different W7-X magnetic configuration in the MPM plane.The major resonant magnetic islands forming the island divertor are highlighted in colours.The probe path is indicated by a dashed green line.Bottom row: Poincare cross section and color-coded connection length (sum of L c along and against the field) in the vicinity of the MPM.

Figure 2 .
Figure 2. Comparison of T e and n profiles from triple probe (blue) and swept probe (orange).The smoothed data is lowpass-filtered and the fitted data is represented by an 8th order polynomial.The vertical dashed line indicates the L c transition in the standard configuration with regular islands.

Figure 3 .
Figure 3. Spectral characteristics of typical I i,sat and V fl data in a 1000 ms measurement with a constant probe position in the low iota configuration.(a) Power spectral density, (b) cross spectral density, (c) cross-phase.

Figure 4 .
Figure 4. Example time traces of (a) fluctuating n, v r , and (b) Γ r .(c) Histogram of ñ (red), ṽr (green) and Γ r (blue) fluctuations.A normal distribution is shown in black for comparison.

Figure 5 .
Figure 5. Scatter plot of turbulent radial particle flux as a function of radial plasma pressure gradient distinguished by magnetic configuration.Each dot represents a 5 ms time slice of probe data, covering a wide range of heating and fuelling scenarios and 0 < d LCFS < 5 cm.The star symbols represent data points belonging to the experiments presented in figure 7.

Figure 6 .
Figure 6.Same data as in figure 5 in different axis limits with connection lengths to the targets color-coded.The upper (lower) row shows the shorter (longer) connection lengths to the target.

Figure 7 .
Figure 7. Radial profiles of key quantities along the MPM path (cf figure 1) for five measurements representing different magnetic configurations.All experiments were performed in ECR heated hydrogen plasmas with heating powers between 4 MW and 5.5 MW.The fluctuation amplitudes σ, cross-phase and coherence are evaluated in the frequency range between 3 kHz and 30 kHz.The turbulent particle transport from these experiments is highlighted by star symbols in figure 5.

Figure 8 .
Figure 8. Same data as figures 5 and 6 presented as a function of the generalized Fick's law Γ r /n = v 0 − D∇n/n with λ n = n/∇n.

Figure 9 .
Figure 9. Radial profiles of anomalous diffusion coefficient D and relevant key plasma quantities along probe path for various magnetic configurations.