The fine structure of ELMs in the scrape-off layer

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INSTITUTE OF PHYSICS PUBLISHING PLASMA PHYSICS AND CONTROLLED FUSION

Plasma Phys. Control. Fusion 47 (2005) 219–240 doi:10.1088/0741-3335/47/2/002

The fine structure of ELMs in the scrape-off layer

M Endler1, I Garcıa-Cortes2, C Hidalgo2, G F Matthews3,ASDEX Team1,4 and JET Team5

1 Max-Planck-Institut fur Plasmaphysik, EURATOM Association, D-17491 Greifswald, Germany2 Asociacion EURATOM-CIEMAT, Madrid, Spain3 EURATOM/UKAEA Fusion Association, Culham Science Centre, Abingdon, Oxfordshire,OX14 3DB, UK4 Max-Planck-Institut fur Plasmaphysik, EURATOM Association, D-85748 Garching, Germany5 JET Joint Undertaking, Abingdon, Oxfordshire, OX14 3EA, UK

E-mail: endler@ipp.mpg.de

Received 13 August 2004, in final form 1 November 2004Published 11 January 2005Online at stacks.iop.org/PPCF/47/219

AbstractEdge-localized modes (ELMs) have been observed by diagnostic systems withhigh spatial and temporal resolution in the ASDEX and JET tokamaks. Duringthe ELMs, substructures exist in the scrape-off layer (SOL) with sizes of 2–5 cmand lifetimes of the order of 20–50 µs. Their poloidal–temporal evolution isdirectly observed, and the radial transport due to turbulent E × B drift in thesesubstructures is estimated. A comparison is made between ‘normal’ fluctuationsbetween ELMs and these substructures in terms of poloidal size and velocity andrelated radial transport. The increased radial transport during ELMs is shownto be mainly due to these substructures. The observed fluctuation amplitudesand velocities of the substructures are found to be compatible with the modelof radial transport by plasma ‘blobs’ and plasma potential gradients generatedby the sheath boundary conditions. The transport due to turbulent radial E ×B

flows is compared during and between ELMs, and the observation of ELMsubstructures in the main plasma SOL is put into context with the observationof substructures on the target plates.

(Some figures in this article are in colour only in the electronic version)

1. Introduction

Since the discovery of the state of improved confinement called H-mode in the ASDEXtokamak [1, 2], many investigations of the phenomenon called edge-localized modes (ELMs)have been conducted (for an overview, see [3–5]). ELMs are an instability associated with arapid loss of particles and energy from the edge plasma onto the target plates and possibly thewall of the device. It was soon realized that a high temporal resolution in the microsecond rangeis necessary to resolve the fast changes during an ELM, which are observed, e.g. by Mirnov

0741-3335/05/020219+22$30.00 © 2005 IOP Publishing Ltd Printed in the UK 219

220 M Endler et al

coils or reflectometry. Until recently, however, hardly any investigation existed of the spatialfine structure (on the scale of a few millimetres) of ELMs. It was then noted that a temporalsubstructure exists in the ion saturation current (Isat) signals of Langmuir probes during ELMsin the main plasma scrape-off layer (SOL) of the JET and MAST tokamaks, i.e. in the signalsof spatially highly localized measurements [6–9]. The same was noted in a comparativeanalysis of Isat, electron temperature (Te) and floating potential (�fl) fluctuations during theL-mode and the ELM-free H-mode and during ELMs in DIII-D, where also the turbulentradial E × B particle and energy transport was investigated [10]. Te fluctuations were alsotaken into account in a recent analysis of particle and electron energy transport during ELMsto the JET main chamber wall [11]. In measurements with multiple Langmuir probes with0.5–1 cm separation it could be demonstrated that the temporal ELM substructures are indeedrelated to spatial substructures on the scale of 1–2 cm [8, 9]. Such spatial substructures arealso visible in poloidally resolved Hα emission measurements in the ‘old’ ASDEX [9]. Theanalysis of JET Langmuir probe measurements was then extended to the calculation of theradial E × B velocity during ELMs [8, 9], and to a detailed statistical analysis of the relationbetween local radial gradients, radial and poloidal electric fields and effective radial transportvelocity during ELMs [12]. It was soon realized that the spatial structures observed in the SOLduring ELMs resemble the fluctuation ‘events’ or ‘blobs’ initially suggested by Krasheninnikovet al [13, 14] in order to explain the radial particle transport in the SOL due to ‘ordinary’fluctuations, without regarding ELMs. The observed properties of the ELM substructures or‘plasmoids’ were compared with the predictions of this blob model in [9, 10] and, in detail,on a broad statistical basis and extending the model to the case of hot ions, in [15]. Recently,toroidally non-symmetric substructures in the divertor plate power load were found 5–10 cmoutside the strike line during type I ELMs in ASDEX Upgrade with a fast infrared camera [16],toroidal asymmetries in the net electric current to target tiles were observed in DIII-D [17],and the filamentary structure of an ELM in the Dα light was made visible with a fast cameraon MAST [18].

In this paper, we report on measurements during ELMs with a dedicated Hα/Dα fluctuationdiagnostic (HFD) system in the edge and SOL of the old ASDEX and with Langmuir probes inthe SOL of JET. After a description of the diagnostic systems in section 2, we shall present theresults of the ASDEX Hα measurements, where the poloidal size and propagation velocity ofthe ELM substructures are directly visible, in addition to the temporal substructure (togetherwith a comparison with divertor signals), in section 3. In section 4, we shall estimate theradial E ×B transport from the JET Langmuir probe measurements and compare the transportduring and in between type I ELMs. We shall then in section 5 briefly recall the mechanismsgenerating electric potential gradients in the SOL, including the radial propagation mechanismin the model of SOL fluctuations as high-pressure ‘blobs’ in a low-pressure background plasma,which was introduced in [13, 14]. In our discussion in section 6, we shall use these models toestimate propagation velocities for ELM substructures and ‘normal’ fluctuations and comparethem with the observations in order to find a unified picture of ELM substructures and normalfluctuations. In addition, we shall compare the measured increase in radial transport with thevalues from transport modelling. Our conclusions will be presented in section 7.

2. Diagnostic systems used for ELM observation

2.1. Hα/Dα diagnostics in ASDEX

An HFD was used in the midplane of ASDEX, which allowed recording of the Hα/Dα radiationfrom the plasma edge with photomultipliers at 16 positions, which were spaced poloidally in

Structure of ELMs in the scrape-off layer 221

vacuum vessel

H /D fluctuationdiagnostic

α

FDKO photodiodeviewing position

gas valve

α

plasma

separatrix

lens

poloidal arrayof fibresto PMTs

z

emittinglayer

[m]

0.500

–0.045

0.0450.000

R [m]1.25 1.65 2.05

B It p,

Figure 1. Arrangement of the HFD in the midplane and of the FDKO photodiode in the divertorof the ASDEX tokamak. The two diagnostics, shown here at the same poloidal cross section, werenot located at the same toroidal position. The direction of the toroidal magnetic field, Bt , and ofthe plasma current, Ip, as shown here is valid for the data presented in figures 4 and 5.

steps of 6 mm [19]. The signals were sampled at 1 MHz after applying a low-pass filter witha smooth cut-off at 300 kHz (−3 dB frequency). In order to increase the light intensity andto obtain a well-defined and constant influx of neutral gas, hydrogen or deuterium was puffedthrough a gas valve into the observed edge region. EIRENE calculations showed that forthe typical plasma parameters in the edge of fusion experiments, the Hα radiation originatesmostly from a narrow radial layer of 1–2 cm width centred slightly outside the last closedmagnetic surface (LCMS). In this region, during the H-mode, densities were in the range(0.5–1.0) × 1019 m−3 and electron temperatures in the range (20–100) eV [2].

Whereas the n = 3 state excitation coefficient is only a weak function of Te for theseconditions and depends linearly on the neutral gas density and almost linearly on the electrondensity [20], recent detailed simulations using a Monte Carlo neutral transport code andincluding the behaviour of D2 molecules have revealed a certain Te dependence of the emissivityof Hα/Dα photons for ne � 1018 m−3 [21].

In contrast to the common belief that, in a radial observation geometry, the Hα intensityis a direct measure of the neutral gas influx only and is independent of the electron density,which is true in the stationary case, it has been shown that for electron densities fluctuatingsufficiently fast, corresponding fluctuations of the Hα radiation do ensue, and these fluctuationsreflect fluctuations of the local electron density, which has been confirmed by comparison offluctuation measurements between the HFD and Langmuir probe and collective scatteringmeasurements [19, 22]. We shall in the following interpret the light fluctuations observed bythe HFD as mainly due to density fluctuations, while a certain sensitivity to Te fluctuationswill not alter the conclusions we draw.

In addition to the HFD, we use data from a photodiode observing the upper outer divertorplate with low spatial resolution. This ‘FDKO’ signal was one of the standard monitor signalsfor L–H transitions and ELMs on ASDEX. The arrangement of both detector systems is shownin figure 1.

2.2. Langmuir probes in JET

A reciprocating Langmuir probe (RLP) system at the top of the plasma [23] was used for ELMinvestigations (see figure 2) in the JET tokamak. The probe head was inserted into the edgeplasma with a vertical velocity below 0.6 m s−1, corresponding to 0.45 m s−1 in minor radius

222 M Endler et al

probehead

flux surface

z [m]

2

1

0

R [m]1.8 3.25 3.9

B It p,

Figure 2. Arrangement of the RLP system on JET. The direction of Bt and Ip as shown here isvalid for the discharges analysed in section 4. The design of the probe head is shown in detail infigure 3.

13

z

θ

φR

probetips

z

θ

φ

R

z φ

R

10˚

1.95.9

5.51.5

3.96.

48.9

7.254.75

2.25

B

perspective view tangential view vertical view

Figure 3. Probe head used for fluctuation measurements on a reciprocating drive in the JETtokamak. Two groups of three probe tips were arranged at two radial positions. The tips of eachtriple were approximately at the same radial position and at different poloidal positions. They werearranged in triangles to avoid shadowing. The tips were cylindrical and fabricated from graphitewith 1.5 mm diameter. All lengths in this figure are given in millimetres.

or 0.3 m s−1 in midplane minor radius. It was fitted with a head comprising six carbon tipsof 1.5 mm diameter, arranged in two triples with 4.1 and 2.3 mm poloidal separation betweenthe tip centres within each triple, measuring �fl fluctuations with the two outer tips and Isat

fluctuations with the central tip (see figure 3). The three tips of each triple were placed on thesame flux surface, and the centres of the triples were separated by 1.3 cm in the radial directionand 2.3 cm in the poloidal direction [24,25]. The signals of the probes were digitized at a rateof 250 kHz.

The arrangement on the RLP system of two poloidally displaced Langmuir probe tips,measuring �fl, and a third tip in between, measuring Isat, can be used to calculate the fluctuation-induced radial E×B transport if the probe tips are close enough to each other to allow a reliablecalculation of the poloidal gradient of �fl at the position of the intermediate probe tip and if oneneglects the effect of temperature fluctuations on the quantities �fl and Isat. Even if electrontemperature fluctuations exist, their influence on the result is minimized if they are in phasewith the plasma density fluctuations [26].

Structure of ELMs in the scrape-off layer 223

0 50 100 150 200 250 300time [�s]

5.806.006.20

Hα intensity [arb. units]

Fluctuations between ELMs

0

4.5po

l. po

s.z

[cm

]

−4.5

Figure 4. Grey scale image of the 16 poloidally displaced channels of the HFD at ASDEX fora time interval between ELMs, showing the normal fluctuations and their typical poloidal size,lifetime and poloidal propagation (bottom). The time trace from one of the 16 channels is depictedin the top panel.

3. Spatial fine structure of ELMs in Hα/Dα light in ASDEX

3.1. Midplane

The HFD described in section 2.1 was used to investigate the spatio-temporal properties ofthe normal density fluctuations in the SOL of ASDEX [19]. In figure 4, an example for thisnormal turbulence, which is always present, is given. The fluctuations can be characterizedby certain parameters like amplitude, spatial and temporal scales and poloidal velocity. Theseparameters vary for different discharge conditions. Note in particular that the poloidal velocityof the structures, as visible from their inclination in the poloidal–temporal representation of theraw data in figure 4, is rather constant for stationary discharge conditions—in the case depictedhere, a poloidal velocity of (−1100 ± 300) m s−1 can be calculated from the inclination of thestructures.

Note that the velocity of structures observed with a one-dimensional (in this case poloidal)array of detectors will always be a projection of the true velocity onto the direction defined bythe array. Therefore, the observed poloidal velocity may contain components due to a radialvelocity, if the observed structures are inclined in the radial–poloidal plane. This effect wasdemonstrated in the Wendelstein 7-AS stellarator [27] (in that case, a dominantly poloidalvelocity was projected onto a radial array of Langmuir probes). From the similarity of thefluctuations in Wendelstein 7-AS and ASDEX, it seems probable that in the ASDEX caseshown here also the true poloidal velocity of the structures dominates the observed poloidalprojection.

In contrast to the uniformity of the structures of normal fluctuations, each ELM displaysa different spatio-temporal structure when viewed with the same resolution as the normalfluctuations, which is demonstrated by three examples in figure 5. The spatial scale of thesubstructures seems to be comparable with that of normal fluctuations. However, the poloidalvelocity of the substructures is in general much higher during ELMs and exhibits a much largerscatter; often even structures with opposite poloidal velocity occur during a single ELM. Inour examples, poloidal velocities between +14 000 and −7500 m s−1 occur (‘−’ denoting theion diamagnetic drift direction, which is, due to the radial electric field and the resultingdominating E × B drift, the usual direction of propagation for the SOL fluctuations, seesection 5). Due to the high poloidal velocity of these substructures, it is difficult to give valuesfor their lifetime since the baselength of the array of observation is insufficient for followingthem for a sufficiently long time. Only a lower estimate of 10–20 µs can be given.

224 M Endler et al

−4.5

µs]

0

4.5

pol.

pos.

z[c

m]

−4.5

−4.5

0 50 100 150 200 250 300time [

5.806.006.20

0 50 100 150 200 250 300

Examples for ELMs

0 50 100 150 200 250 300

5.806.006.20

5.806.006.20 Hα intensity [arb. units]example 1

example 2

example 3

0

4.5

pol.

pos.

z[c

m]

0

4.5po

l. po

s.z

[cm

]

Figure 5. Same as in figure 4, but during three ELMs. The ELMs exhibit substructures on atimescale of 20 µs, and their poloidal velocity is much higher than for normal fluctuations. Inaddition, not all the substructures move in the same direction.

3.2. Comparison with divertor signals

Why have the strong and very short peaks in Hα/Dα intensity not been noted in one of thoseHα/Dα signals often used as monitors for ELM activity? For comparison, we display in figure 6several ELMs recorded by the HFD together with the ‘FDKO’ signal, an Hα/Dα monitor signalfrom a photodiode observing the upper outer divertor plate with low spatial resolution (seesection 2.1 and figure 1). An averaging over eight channels of the HFD, corresponding to apoloidal average over 9 cm (displayed in light grey: blue), hardly reduces the strong peaks andstill bears much more similarity to the signal of a single channel (displayed in black) than tothe FDKO signal (displayed in dark grey: red). The fast initial rise of the FDKO intensitydemonstrates that this diagnostic should be able to resolve peaks of 10–20 µs duration. Theprincipal difference between the two positions of observation is that the neutral gas in thedivertor is exclusively due to recycling. During an ELM, the plasma flux onto the targetplates and hence the neutral gas density increase strongly, whereas the neutral gas density inthe observation region of the HFD is dominated by the constant gas puffing and stays almostconstant. This can also explain why the peak intensity of the FDKO signal during an ELM ishigher by a factor of 3–6 than between ELMs in these examples, whereas the increase during

Structure of ELMs in the scrape-off layer 225

0 200 400 600 800 1000( −1.0290 s) [�s]

3.5

4.0

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5.5H

α si

gnal

(m

ain

cham

ber)

[ar

b. u

nits

]

0.2

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FDK

O H

α si

gnal

[ar

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]

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5

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7

8

Hα

sign

al (

mai

n ch

ambe

r) [

arb.

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KO

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sign

al [

arb.

uni

ts]

0 200 400 600 800 1000 1200( −1.0778 s) [�s]

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al (

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0 200 400 600 800 100012001400( −1.1050 s) [�s]

4

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8

Hα

sign

al (

mai

n ch

ambe

r) [

arb.

uni

ts]

0.5

1.0

1.5

FDK

O H

α si

gnal

[ar

b. u

nits

]

tt

t t

Figure 6. Comparison between signals of the HFD in the midplane of ASDEX (black: singlechannel; light grey (blue): average over eight channels, corresponding to a poloidal region of 9 cm)and the ‘FDKO’ Hα /Dα monitor in the upper divertor (dark grey: red) for four different ELMs inone discharge.

the sharp peaks in the HFD signals is only by a factor of 1.3–2. The substructure on top ofthe FDKO ELM signals, with an amplitude of only 15–30% of the total ELM amplitude and atimescale of 50–100 µs, could then be due to peaks like those dominating the signal of the HFD.

3.3. With/without gas puffing

As in the divertor Hα/Dα signals, the fast substructures of an ELM are hardly visible in the HFDsignals if we do not puff gas into the observed region. In this case, the light intensity from theobserved region of the main chamber SOL decays back to its inter-ELM level even slower thandoes the FDKO signal (see figure 7). The increase in light intensity may now be dominatedby emission from the torus inboard side, where the HFD is out of focus and cannot resolvespatio-temporal fine structures anyway, and by reflections. The slow decay may be caused byincreased recycling from the main chamber wall, which dominates the neutral density in theabsence of the gas puff.

4. Langmuir probe measurements of ELMs and related E × B transport in JET

4.1. Spatial fine structure in the SOL of the main plasma

During many ELMs, the tips of the RLP system described in section 2.2 started to emit due tothe high heat loads. A full analysis of the data from these probes was therefore only possible

226 M Endler et al

0 500 1000 1500(t−1.2869 s) [�s]

0.6

0.8

1.0

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Hα

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al (

mai

n ch

ambe

r) [

arb.

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0.2

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FDK

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gnal

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b. u

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0 500 1000 1500 2000(t−1.3032 s) [�s]

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r) [

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0 500 1000 1500 2000 2500 3000(t−1.3975 s) [�s]

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sign

al (

mai

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r) [

arb.

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0 500 1000 1500(t−1.4586 s) [�s]

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ts]

0.5

1.0

1.5

2.0

2.5

FDK

O H

α si

gnal

[ar

b. u

nits

]

Figure 7. Comparison between signals of the HFD in the midplane of ASDEX without puffing ingas into the observed region (black) and the FDKO Hα /Dα monitor in the upper divertor (grey: red)for four different ELMs in one discharge. Without the constant gas puffing, fast substructures likethose visible in figure 6 are hardly discernible in the midplane signal.

for a small number of ELMs, especially for ELMs with smaller amplitude, for probe positionsfarther out in the SOL, and for the outermost rather than the innermost triple of probe tips.

The results of the RLP system for one such ELM are displayed in figure 8. As in theHFD signals from the main chamber of ASDEX, strong peaks in the Isat signals occur with aduration of 10–50 µs. When comparing the signals on the two Isat tips, which are separated by2.7 cm perpendicular to the magnetic field, most strong peaks can be identified in both signals;however, their amplitude and the time lag between the two tips vary (even for substructureswithin the same ELM): it is not always the innermost tip (the one closer to the separatrix) whichdetects the higher amplitude or the one on which a peak occurs first. This indicates a spatialstructure perpendicular to the magnetic field on a scale smaller than the probe tip separation of2.7 cm. (For limiter probes with a larger radial separation of several centimetres, a statisticaldelay of the ELM signal on the probes farther out in the limiter shadow with respect to theprobes closer to the limiter edge was found and used to determine a radial propagation velocityof the substructures [15, figure 12].)

4.2. Radial E × B transport during ELMs

The arrangement of the probe tip triples on the RLP system measuring �fl and Isat fluctuationsallows us to calculate the fluctuation-induced radial transport due to fluctuating radial E × B

drifts (see section 2.2). As the neglect of temperature fluctuations in the case of ELMs may

Structure of ELMs in the scrape-off layer 227

innermost probe tipsoutermost probe tips

0 500 1000 1500 2000 2500(t−55.12150 s) [�s]

050

100150200250

I sat [

mA

]

−2000

−1000

0

1000

2000v r

[m

s-1]

−2×1022−1×1022

01×10222×10223×1022

Γ r [

m-2

s-1]

0

4×1017

8×1017

∫ Γr dt

[m

-2]

(a)

(b)

(c)

(d)

Figure 8. Measurements of the two Langmuir probe tip triples on the RLP system during one ELMin a JET 12 MW NBI discharge. (a) Isat ; (b) radial E × B velocity (calculated from the poloidaldifference in floating potential, neglecting temperature fluctuations); (c) resulting fluctuating radialparticle transport, �r (assuming Ti ≡ Te ≡ 10 eV for the calculation of n from Isat); (d) time integralof �r . The vertical grey (and rose) bars are intended to help relate the behaviour of the differentquantities for the strongest radial transport events. The innermost probe tips are approximately3.5 midplane cm outside the LCMS, the outermost probe tips 0.7 midplane cm farther out.

appear to be a very bold assumption, we shall interpret the results of our analysis only as arough estimate of the true radial E × B transport during an ELM.

In the three lower panels of figure 8, the fluctuating radial E×B velocity, vr , the fluctuatingradial particle flux, �r , and the integrated radial E×B particle flux are depicted. The latter twoquantities are only known up to a factor

√Ti + Te from the transformation of Isat into plasma

density—here, we assume an average temperature of 10 eV. 6 Whereas the traces of vr and �r

only display strongly increased fluctuation amplitudes, the trace of∫

�r dt demonstrates that

6 The value of 10 eV was extrapolated from inter-ELM target plate profiles and converted to the upstream position ofthe RLP at the middle position during its reciprocation. There exist strong indications that Ti can exceed Te by factorsof up to 5–10 in JET H-modes, in particular in a narrow layer outside the separatrix [28]. Furthermore, Te exhibitsstrong peaks during ELMs at the same time as the Isat peaks in JET [11]. This results in a tendency to overestimatethe particle flux when neglecting temperature fluctuations. These caveats must be kept in mind when trying to drawconclusions based on the absolute values of �r calculated in this paper.

228 M Endler et al

050

100150200250 innermost probe tips

outermost probe tips

0 50 100 150(t−55.12172 s) [�s]

I sat [

mA

]

20

0

20

40

Φfl [

V]

−2×1022−1×1022

01×10222×10223×1022

Γ r [

m-2

s-1]

−2000

−1000

0

1000

v r [

ms-1

]

innermost probe tipsoutermost probe tips

Figure 9. Enlarged view of the first peaks in figure 8. In contrast to figure 8, the �fl signals aredisplayed in the second panel, and

∫�r dt is omitted. The sequence of probe tips in the poloidal

E ×B drift direction is as follows: �fl (grey solid), Isat (grey), �fl (grey dashed); �fl (black solid),Isat (black), �fl (black dashed) (orange, red, magenta, green, black, cyan online).

the net radial flux is indeed directed outwards, and the distinct steps show that the dominatingcontributions to this transport happen during those very brief intervals of 10–50 µs, which aremarked by the peaks in the Isat signals. The radial E × B velocity during these intervals canreach 1000–2000 m s−1, with the largest amplitudes at the beginning of the ELM and the vr

amplitude then decaying to its inter-ELM value, as noted in [11]. Since we cannot followindividual peaks longer than they are registered on a single probe tip, the duration of 10–50 µsis a lower estimate of their lifetime, and together with the radial E × B velocity we obtain alower estimate of 1–10 cm for the radial movement of plasma within these structures. Fromfigure 8(d) it is evident that, locally, the radial transport in an ELM occurs mainly concentratedwithin a few (typically 1–3) short intervals of 10–50 µs, coinciding with the strong peaks inthe Isat signals.

A closer inspection of these short intervals reveals that the peaks in �r are even shorterthan in Isat: typically, a �fl event is slightly phase shifted with respect to the Isat peak. Thisis visible in the close-up view (figure 9) of the first peaks of figure 8, in particular around

Structure of ELMs in the scrape-off layer 229

t = 55.121 72 s + 90 µs. The spatial phase shift is transformed into a temporal shift as thestructure passes the probe tips due to the poloidal E×B drift. vr displays a nicely antisymmetricbehaviour as a result of the poloidal �fl gradients. However, since the Isat peak is delayed withrespect to the �fl peak, the outward component of �r is larger than the inward component, andthe duration of the �r peak is shorter than that of the Isat peak7.

4.3. Comparison of the radial transport during and between ELMs

If it is true that, during ELMs, ‘blobs’ (or filaments extended ‖ B) of high density andtemperature move radially through the SOL, it is interesting to calculate by what factor the localradial particle and heat fluxes during type I ELMs increase in comparison with their valuesbetween ELMs. This is also of interest for estimating the local fluxes onto wall componentswhich are close (of the order of 10 cm) to the LCMS. ELM substructures (and also fluctuationevents during the L-mode) have indeed been observed to reach the radial position of the mainchamber wall in DIII-D [29]. Here, we shall restrict ourselves to estimating the particle fluxes.

A second question of interest is whether the turbulent radial E × B transport is sufficientto account for the increased radial transport inferred from transport modelling of ELMs.

In order to answer the above questions, we have subdivided the measurement intervalsof the RLP system during three JET discharges into ‘ELM’ time intervals and ‘inter-ELM’time intervals. We analysed 28 ELM intervals of 0.3–4.5 ms length (using either one or bothprobe tip triples) and 108 inter-ELM intervals of 2–20 ms length (using both the innermostand outermost probe tip triples). The end of the ELM intervals was chosen such that either theprobe signals had returned to their inter-ELM behaviour or a new ELM started. The lengthof the inter-ELM intervals is restricted by the requirement that the probes should only move afew millimetres radially within one analysis interval.

For our comparison we use averages over time intervals T of the radial particle flux�r = nEθ /B (where n is estimated from Isat by neglecting temperature fluctuations andassuming Ti ≡ Te ≡ 10 eV and Eθ is calculated from two tips measuring �fl, as described insection 2.2),

〈�r〉T ≡∫ t+T/2

t−T/2�r dt ′

and the ‘effective radial velocity’,

(vreff)T ≡∫ t+T/2t−T/2 IsatEθ/B dt ′∫ t+T/2

t−T/2 Isat dt ′, (1)

which has the advantage of being independent of the average temperature [19].As a measure for the turbulent radial E ×B transport between ELMs, we use the averages

over the entire analysis intervals (denoted by the subscript ‘tot’), 〈�r〉tot and (vreff)tot. Inaddition, we calculate running averages over 50 and 500 µs both for ELM and inter-ELMintervals, 50 µs being the typical timescale of the individual peaks during an ELM and 500 µsbeing a timescale comparable with the duration of ELMs themselves, as observed on otherdivertor diagnostics (see, e.g. the ASDEX FDKO signals in section 3). From each analysisinterval, we use the maxima of the running averages, max(〈�r〉50/500 µs), max((vreff)50/500 µs)

and the corresponding minima. These values are represented in figure 10 together with 〈�r〉tot

and (vreff)tot for the analysis intervals in between ELMs. The radial probe position in this

7 Even if the Isat peak and the vr peak were of equal size, the equivalent width of the product peak would be reducedby a factor depending on the precise shape of the peaks.

230 M Endler et al

min

(

) [

m

s ]

Γ r–2

–1

max

(

) [

m

s ]

Γ r–2

–1 1022

1020

1018

–1018

–1020

–1022

max

(

) [

ms-1

]v r

eff

min

(

) [

ms-1

]v r

eff

1000

100

10

–10

–100

–1000

0 40 60[midplane-mm]r rsep–

8020 0 40 60[midplane-mm]r rsep–

8020

Figure 10. Maximum and minimum values for running averages of the radial particle transport,〈�r 〉T (left), and the effective radial velocity, (vreff )T , as defined in equation (1) (right) during ELMsand between ELMs as a function of the probe position in the JET SOL (the separatrix location and itsuncertainty are indicated by the grey bar). The symbols/colours are for the following: ×/red—ELMintervals and 50 µs averages; +/orange—ELM intervals and 500 µs averages; ♦/blue—inter-ELMintervals and 50 µs averages; �/cyan—inter-ELM intervals and 500 µs averages; ◦/grey—inter-ELM intervals, entire analysis interval (i.e. 2–20 ms averages, corresponding to a maximum radialmovement of the probe of 4 midplane-mm).

figure is expressed as the distance from the separatrix which the corresponding field line hasin the torus midplane.

In order to perform a direct comparison between ELM and inter-ELM intervals, wenormalize the maxima and minima of the running averages to the averages of the entireinterval (for inter-ELM intervals) or to the average of an adjacent inter-ELM interval (forELM intervals), 〈�r〉tot and (vreff)tot. In this manner we obtain ‘enhancement factors’

F� 50+ ≡ max(〈�r〉50 µs)

〈�r〉tot

, (2)

F� 50− ≡ min(〈�r〉50 µs)

〈�r〉tot

, (3)

Fv 50+ ≡ max((vreff)50 µs)

(vreff)tot, (4)

Fv 50− ≡ min((vreff)50 µs)

(vreff)tot(5)

and, likewise, F� 500+, F� 500−, Fv 500+ and Fv 500− for the 500 µs averages (see figure 11).We find that, between ELMs, the maximum outward particle transport in 500 µs intervals ishigher by a factor of O(10) than on the average and in 50 µs intervals by a factor of O(50). Incontrast, during ELMs, we find maximum enhancements of O(300) for the 500 µs intervalsand of O(2000) for the 50 µs intervals (the factors stated here in the text are geometric averagesfor the corresponding sets of intervals for reducing the impact of outliers). Hence the peakradial particle fluxes during ELMs are, on a geometric average, higher by factors of 30–40than the corresponding peak values between ELMs.

The enhancement factors of the effective radial velocity during ELMs are lower than forthe particle flux. This indicates that the high radial particle fluxes during ELMs are not only due

Structure of ELMs in the scrape-off layer 231

F ΓT

+F Γ

T–

10000

1000

100

10

1–1

–10

–100

–1000

–10000

1000

100

10

1

–1

–10

–100

–1000

FT

–v

FT

+v

0 40 60[midplane-mm]r rsep–

8020 0 40 60[midplane-mm]r rsep–

8020

Figure 11. ‘Enhancement factors’ F� T ± (left) and Fv T ± (right) with T = 50 and 500 µs, asdefined in equations (2)–(5). The factors indicate how much larger the maximum values of turbulentradial particle flux, �r , or effective radial velocity, vreff , averaged over 50 or 500 µs intervals, arecompared with averages over longer inter-ELM time intervals (2–20 ms) at the same probe position.The symbols/colours are (as in figure 10) for ×/red—ELM intervals, 50 µs averages; +/orange—ELM intervals, 500 µs averages; ♦/blue—inter-ELM intervals, 50 µs averages; �/cyan—inter-ELM intervals, 500 µs averages.

to higher turbulent radial E×B velocities but also due to peaks in the local density (which werealready visible in the Isat raw data, see figure 8). This is consistent with the observation in [11]that in larger ELMs (in the sense that 〈Isat〉 is larger) also higher effective radial velocities aremeasured.

5. Plasma potential and behaviour of ‘blobs’ in the SOL

In this section we shall briefly recall the mechanisms of generating electric fields ⊥ B in theSOL in order to discuss in section 6.1 the observed floating potential fluctuation amplitudesand velocities of ELM substructures and normal fluctuation events.

In the SOL, the plasma potential in a flux tube can be largely determined by the sheathboundary conditions at the target plates at the ends of that flux tube. The current density ontoa target plate can be modelled, in a simple sheath model, as

j‖ = en

(cs − ce

4(1 − δ) exp

(− e�pl

kBTe

))(6)

(see, e.g. [30]). Here, cs is the ion sound velocity, cs = √kB(Ti + Te)/mi, ce is the electron

thermal velocity, ce = √8kBTe/(πme) and δ is the secondary electron emission coefficient.

The target plate potential, as the common reference for all flux tubes, is set = 0. If wecalculate the plasma potential from equation (6), we obtain

�pl = −kB

eTe ln

4(cs − j‖/(en))

ce(1 − δ). (7)

We shall not discuss the range of validity of equation (6), which is at least limited by theconditions �pl > 0 and j‖ < encs. For j‖ = 0, the target is at floating potential, i.e.

�pl = −kB

e

1

2

(ln

Ti + Te

Te+ ln

2πme

mi− 2 ln(1 − δ)

)Te ≡ αTe (8)

232 M Endler et al

with α ≈ 2.8kB/e for deuterium and under the assumption that Ti = Te and δ = 0. This valuemay be corrected by an additional term (0.5–1)(kB/e)Te, depending on the presheath model.The dependence on the ratio Ti/Te is comparatively weak, with Ti = 10Te only reducing thenumerical factor in α from 2.8 to 2. An electron temperature gradient ∇Te ⊥ B in the SOLtherefore generates an electric field (−α∇Te), which is pointing radially outwards for the usualtemperature gradient in the plasma edge and hence generates a poloidal E × B drift.

If we now consider fluctuations which are elongated ‖ B, the above sheath mechanismstill links Te and �pl, which would be in phase, such that (without, for the moment, regardingdensity fluctuations) no net energy transport results when averaging over the fluctuationstructures. However, in addition, the fluctuations cause current densities ⊥ B like polarizationcurrents and fluctuating diamagnetic currents. For illustration, we consider the perturbationsof the diamagnetic current, j⊥, due to pressure perturbations p:

j⊥ = −∇p × BB2

.

In a non-uniform magnetic field, the divergence of j⊥ does not vanish:

∇ · j⊥ = ∇p ·(

∇(

1

B2

)× B

)

if the local current density is sufficiently low for ∇ ×B to be neglected. Hence, ∇ · j⊥ dependson the component of ∇p which is perpendicular to the magnetic field and to its gradient. In atokamak magnetic field, |B| ∝∼ 1/R, where R is the major radius. Therefore,

∇ · j⊥ ≈ ∂p

∂y

2

BR, (9)

where y = ∇R × B/B is the direction perpendicular to the major radius and the magneticfield8.

In the SOL, ∇ · j⊥ must be balanced by a current density between the plasma and targetplates. If we assume symmetric current densities onto the target plates j‖ at both ends, weobtain

−2j‖ =∫

∇ · j⊥ds, (10)

where the integration is ‖ B from one target plate to the other. Using the observation that theSOL fluctuations are highly correlated and of almost constant amplitude along the magneticfield ( [31] and references therein and [27, 32]), and restricting ourselves to a region where∇ · j⊥ does not vary too much along the magnetic field, like the torus outboard side in a doublenull divertor configuration, we can set∫

∇ · j⊥ds ≈ ∂p

∂y

2

BRL,

where L is the length of the flux tube ‖ B. With j‖ from equation (10) in (7), we obtain

�pl =(

α − kB

eln

(1 +

L

encsRB

∂p

∂y

))Te.

If, for the moment, we assume T ≡ const, the potential perturbation is out of phase by π/2 withrespect to the pressure perturbation (�pl is largest where ∂p/∂y is largest). This mechanism cantherefore generate instability in the region of unfavourable magnetic curvature, as was pointed

8 Note that equation (9) is the same expression which results from ∇B and curvature drifts in a single particle picture.

Structure of ELMs in the scrape-off layer 233

out in [33–36] and, in comparison with experimental data, in [19]. In those investigations,small fluctuations were assumed in order to perform a linear stability analysis.

In contrast, even normal SOL fluctuations exhibit considerable relative fluctuation levels,typically >20–40%. In many observations, the ‘spikiness’ of SOL fluctuations has beennoted. They seem to consist of individual ‘events’ [37] or ‘blobs’. This is particularly notablein Langmuir probe measurements of the radial E × B transport, where it has been shownthat most of the transport occurs within a comparatively small fraction of time, i.e. due toconcentrated ‘transport events’ (see, e.g. [8,19,38]), which are also spatially localized [39,40].

In addition, very flat density profiles have been observed several centimetres outside theLCMS in several tokamaks [41,42], which would imply huge radial transport coefficients in adiffusive ansatz.

Krasheninnikov has pointed out that a blob of plasma with higher pressure than itssurroundings and elongated along the magnetic field would indeed start moving radiallyoutwards, once it is placed in the SOL in a region of unfavourable magnetic curvature [13]because, as outlined earlier, the poloidal pressure gradients generate a plasma potentialperturbation and hence a radial E × B drift in the centre of the blob.

This model was then extended to include electron temperature [14] and ion temperatureperturbations [15], and a detailed comparison between several model predictions andthe observed amplitude and radial propagation velocity of ELM substructures for a largesample of ELMs was performed [15]. Here we shall give only a brief estimate for the potentialperturbation related to the diamagnetic current perturbation in the SOL and the correspondingE × B velocity. We assume a high-pressure blob in a low-pressure background plasma ofdensity nbg and temperature Tbg, with nblob and Tblob in the centre of the blob, and a blobsize ⊥ B of dblob, and evaluate �pl at the edges of the blob, using n = (nbg + nblob)/2,T = (Tbg + Tblob)/2 and ∂p/∂θ = ±(pblob − pbg)/dblob.

This yields

|�pl| ≈ kB

eTe ln

1 + a

1 − a(11)

with a = (pblob − pbg)L/(encsRBdblob). We shall use estimate (11) for an approximatecomparison of the relations between the SOL plasma parameters and potential fluctuationamplitude between this model and the observation in section 6.1.

6. Discussion

6.1. Origin of the fine structure and comparison with normal SOL fluctuations

The use of diagnostics with a resolution of a few millimetres ⊥ B has revealed that ELMsindeed display substructures on this scale in the SOL of tokamaks. As long as observationswith similar spatial resolution are not available for the edge gradient region inside the LCMS,where ELMs are believed to originate, it is difficult to say whether the observed fine structureis inherent to the instability underlying an ELM or if it is generated as a secondary effect onceplasma from the confinement region is injected into the SOL.

If we compare these substructures with the events observed in Ohmic or L-mode plasmas orin the H-mode between ELMs, the lifetime and poloidal size are rather similar (see section 3.1).The phase shift between the �fl and Isat substructures, as described in section 4.2, is alsoreminiscent of that in normal SOL fluctuations [19], and the result that the duration of the�r peaks is shorter than that of the Isat peaks has already been found in the SOL of ASDEXand Wendelstein 7-AS [43, 44] (in these investigations with poloidal arrays of probe tips

234 M Endler et al

it was shown that also the poloidal size of �r events is smaller than that of Isat and �fl

events).What differs from normal SOL turbulence certainly is the amplitude of the substructures

relative to the average values of density and temperature: the relative fluctuation level of Isat

in normal turbulence usually does not exceed 20–40% (normalized standard deviation) in thefirst few centimetres outside the LCMS. In this respect, the ELM substructures appear to bea prime example for the blobs of high-pressure plasma in a low-pressure background, whichwere suggested by Krasheninnikov et al [13,14] to explain the flat gradients in the outer SOLobserved in various tokamaks.

A further difference between the ELM substructures and normal fluctuation events is theuniformity of the poloidal propagation velocity in the latter (see section 3.1). It should be notedhere that the poloidal propagation velocity observed by the ASDEX HFD is a velocity of thestructures, integrated radially. That method cannot distinguish between a plasma drift velocityand the propagation of a structure (e.g. a wave or a blob) relative to the plasma particles. Incontrast, with the JET RLP system, only radial E ×B velocities were investigated in section 4.Nevertheless, we can discuss the differences between the two velocities for ELM substructuresand normal fluctuation events: the poloidal velocity of normal fluctuations is dominated by thepoloidal E ×B flow due to the radial electric field, which is generated in the SOL as a result ofthe radial temperature gradient. One to three centimetres outside the separatrix, where the peakintensity contributing to the Hα/Dα signals originates, the radial electron temperature gradientis typically of the order of 10 eV cm−1, which corresponds, according to section 5, to a poloidalE × B velocity of the order of 1000 m s−1 for B = 2.5 T. This is indeed the observed poloidalvelocity of normal fluctuation structures in ASDEX (see figure 4). For JET discharges, similarvalues of the poloidal phase velocity have been reported previously [45, 46], although in theH-mode and closer to the separatrix the conditions may be more complex due to the existenceof energetic ions [28].

The poloidal velocity of the ELM substructures in figure 5 is higher by a factor of 5–10,with the propagation still dominantly in the direction corresponding to a radially outwarddirected electric field during the strongest peaks of Hα/Dα emission. A tendency of the poloidalvelocity to decrease within the first 100–200 µs of the ELM is also visible in figure 5. Thisbehaviour could be explained by a layer of hotter plasma coming into contact with the targetplates and thus temporarily increasing the radial electron temperature gradient by a factor of5–10, however with poloidal inhomogeneities explaining the observed variation in poloidalvelocities of the substructures during a single ELM.

Since the signals in the HFD are the result of a radial integration, and the penetrationdepth of neutral gas may vary in particular during a non-stationary event like an ELM, thevariation of the observed poloidal velocity could also be due to the signals originating at aradial position different from that in the intervals between ELMs. However, between ELMs,at no radial position in the SOL of ASDEX were poloidal fluctuation velocities exceeding∼1500–2000 m s−1 observed in discharges of this type by Langmuir probes (granting radiallocalization). The observed high values (>5000 m s−1) are therefore specific to ELMs. Onthe other hand, the structures moving into the electron diamagnetic drift direction which areobserved at the beginning of many ELMs (see figure 5) might well originate from inside theseparatrix, beyond the velocity shear layer. They might then be identified with the currentfilaments observed by poloidal arrays of Mirnov coils at the edge of COMPASS-D duringELMs, which precede the expulsion of plasma into the SOL [47].

Before discussing radial velocities, we should note that a Langmuir probe measuring thefloating potential is not sensitive to potential perturbations �pl = αTe as long as the electrontemperature fluctuations are uniform along the magnetic field between the probe tip and target

Structure of ELMs in the scrape-off layer 235

plate, since the same potential drop, αTe, is generated in both sheaths at the probe tip and atthe target plate9. The probe tip would therefore measure only the component of �pl due tofluctuating currents parallel to the magnetic field onto the target plates:

�pr = �pl − αTe = −kB

eln

(1 − j‖

encs

)Te

(see section 5). For the case of perturbed diamagnetic currents, this corresponds toexpression (11) for the perturbed plasma potential, �pl.

If we consider the case B = 2.5 T, deuterium ions, a background density nbg =5 × 1018 m−3, background temperature Tbg = 20 eV, L = 20 m (comparable with thecorrelation length parallel to the magnetic field of normal SOL fluctuations), R = 3 m, anda blob size of 2 cm, we obtain for Ti = Te and a typical large normal fluctuation event withnblob = 2nbg, Tblob = 2Tbg a potential difference between the blob edges of ��pl ≈ 12 Vand a resulting radial E × B velocity of vr ≈ 240 m s−1. If we use these values except fornblob = 5nbg, Tblob = 5Tbg for the case of an ELM substructure, we obtain ��pl ≈ 75 V andvr ≈ 1500 m s−1. The case of nblob = 5nbg, Te,blob = 2Tbg, Ti,blob = 10Tbg yields only��pl ≈ 40 V and vr ≈ 860 m s−1, since the factor Te has a larger influence on the result thanTi in the argument of the logarithm in equation (11). Radial velocities of 1000–2000 m s−1

for ELM substructures have consistently been observed on JET by calculating the radialE × B velocity [9, 12] and the time delay between the peaks on radially displaced probetips [12, 15]. Similarly, radial propagation velocities of 500 m s−1 have been observed duringELMs in DIII-D close to the LCMS, both as the E × B velocity from Langmuir probe dataand from reflectometry [17]. This velocity was found to decrease to 120 m s−1 farther out inthe SOL.

From the similarity in the relative phase between �fl and Isat fluctuations between normalSOL fluctuations and ELM substructures (see section 4.2) and from the fact that the amplitudeof measured floating potential fluctuations can in both cases be described in the frameworkof the same model, we conclude that the same mechanism is underlying the behaviour of theELM substructures in the SOL and the normal SOL fluctuations.

The density and electron temperature fluctuations during the ELM substructures werefound to be in phase in JET [11]. Similarly, most of the peaks in density and electrontemperature signals in DIII-D occur simultaneously [29], whereas an earlier analysis of DIII-Ddata, using conditional averaging, had shown hardly any correlation between n and Te, incontrast to events during normal fluctuations [10].

Since plasmas of unusually high density and temperature are present in the SOL duringELMs, they might also serve as a ‘laboratory’ to investigate the turbulence dynamics typicalfor the SOL over a wider range of parameters than under normal SOL conditions. This couldinclude a more detailed investigation of the changes in relative phase between n, Te and �pl.

6.2. Radial transport during and between ELMs

As we have discussed in section 6.1, our computation of the turbulent radial particle flux canbe taken as a realistic estimate in spite of the neglect of temperature fluctuations by using �fl

rather than �pl to calculate vr . We then find local transport enhancement factors of O(300)

(geometric average) for 500 µs ELM intervals relative to the average inter-ELM transport,however with a large scatter between different ELMs (see section 4.3) and slightly decreasingclose to the separatrix (which could be a selection effect, since a larger fraction of ELMs hadto be excluded from the analysis due to probe tip emission when the probe head was close to

9 A further condition is that the probe tip and the target plate have similar secondary electron emission coefficientsin the sense that variations in ln(1 − δ) are small compared with 0.5 ln(2πme/mi) (see definition (8) of α).

236 M Endler et al

the LCMS). Due to the neglect of temperature fluctuations in our calculation of n from Isat,this enhancement may be slightly overestimated (see section 4.2). For transport modellingof type I ELMs in ASDEX Upgrade with the B2-EIRENE package, Coster et al [48] had toincrease the transport coefficients around the separatrix by a factor of 50 for 1 ms to describethe transport effect of an ELM. Similarly, Kallenbach et al [49] find in EDGE2D/NIMBUSmodelling of type I ELMs in JET that they have to increase the particle diffusion coefficientsby a factor of 20 for 1 ms. No transport modelling for ELMs exists for the far SOL severalcentimetres outside the separatrix to compare with. We can conclude, however, that the increasein turbulent radial E × B transport during ELMs in comparison with the inter-ELM level isat least sufficient to explain the transport increase which is modelled in transport codes byincreased transport coefficients to describe the effect of ELMs. This is also consistent withthe conclusion of Counsell et al [6] from the evolution of edge Thomson density and electrontemperature profiles that the energy loss from the pedestal region of MAST during ELMs ispurely convective.

6.3. Footprints of substructures on the divertor plates

Recently, fast infrared camera observations of the divertor plates in ASDEX Upgrade showedthe existence of a spatial substructure of the power flux onto the plates significantly outsidethe strike line marking the intersection of the separatrix with the target plate during type IELMs [16]. While two or three radial peaks had been observed in target plate power fluxmeasurements during ELMs in JT-60U previously [50], it was now demonstrated in [16] thatthe radial positions and numbers of these substructures vary between individual ELMs, andthey are not toroidally symmetric but display a pattern which would result from a blob withan approximately circular shape in the midplane due to the magnetic shear. For the caseof normal fluctuations, it has been demonstrated that magnetic shear can indeed distort thepoloidal–radial cross section (and thus also the toroidal–radial cross section) of the fluctuationstructures due to their large correlation length parallel to the magnetic field [27,51]. We wouldtherefore interpret the thermographically observed ELM substructures on target plates withlifetimes below 100 µs as the footprints of structures like those observed in the SOL of themain plasma with the ASDEX HFD and the JET RLP systems.

Models assessing the impact of ELMs on the lifetime of divertor target materials, like thatpresented in [52], should therefore consider that the ELM thermal load to the divertor platescan locally also have a temporal substructure within the total ELM duration of the order of500 µs. This can be seen on divertor Langmuir probe signals with sufficiently high samplingrates (see, e.g. [53, figure 7]). Qualitatively, the erosion threshold for tungsten and carbonplates was shown to be lowered if the duration of model ELMs consisting of a single peak witha given shape and energy deposition was reduced [52, figures 9 and 10].

7. Conclusions

We have directly observed the poloidal fine structure of ELMs in the edge and SOL of ASDEXwith a resolution of 6 mm and a baselength of 4.5 cm. An ELM usually consists of substructuresor blobs with a poloidal size of a few centimetres, like the events observed in the normalfluctuations between ELMs. However, the poloidal velocity of the ELM substructures is higherby a factor of 10–20 and less uniform than during normal SOL turbulence. Due to the possibleinfluence of projection effects it would be of interest to verify these values by analysis oftwo-dimensional (radial–poloidal) beam emission spectroscopy (BES) observations like thoseof normal fluctuations in Alcator C-Mod [54] or NSTX [55]. First such BES observations of

Structure of ELMs in the scrape-off layer 237

ELM substructures have been reported from DIII-D [56, 57] and are also available now fromNSTX [58].

The comparison of poloidal and radial propagation velocities of ELM substructuresand normal SOL fluctuations with the values of stationary and fluctuating plasma potentialsestimated from a simple sheath model and the common behaviour of relative phase betweenIsat and �fl led us to conclude that these phenomena can be described in a unified picture basedon the target plate instability/blob propagation model.

For ELMs on MAST it was shown in fast camera snapshots that the ELM substructuresare arranged parallel to the magnetic field [18]. Conducting the comparison with normalfluctuations further could include an investigation on the precision, to which this is the caseand on whether the correlation is as high as was found for the normal SOL turbulence (forASDEX, see [19]; for JET, see [32]).

We have estimated the local turbulent radial E ×B transport during type I ELMs from ionsaturation and floating potential measurements in the JET SOL. This transport is concentratedon scales of a few centimetres (derived from the differences between the signals from two setsof probe tips), i.e. on similar scales as the peaks in Isat signals and locally in time intervals of10–50 µs.

As to the radial propagation of blobs, the following observations form a consistent picture:

• From the directly measured radial E × B velocities (see also [12]), the radial distancetravelled by the plasma while such a blob is detected by the probe tips can reach 10 cm,and the lifetime of the blob may even be longer due to its propagation past the probe tips,as observed in the ASDEX Hα/Dα fluctuation data.

• The density is increased 10 cm outside the separatrix, e.g. in MAST [6] or ASDEXUpgrade [59].

• The radial profiles of peak density in DIII-D are very flat [56, 57].• Only half of the ELM energy loss is found on the targets in many discharges in JET and

ASDEX Upgrade [53, figure 4] or, for an overview, [60].• The measured radial E × B velocities agree with the values of vr expected in the context

of the target plate instability/blob model (see section 6.1 and [10,15]) and with the radialpropagation velocities derived from the average delay of the Isat peak at different radialpositions of JET limiter probes [15].

In addition, the order of magnitude of turbulent radial E×B transport increase during ELMs ascompared with inter-ELM intervals is consistent with the transport increase used in transportmodels to describe the effect of ELMs.

A comprehensive investigation of the relative phase between density and electrontemperature fluctuations during ELM substructures, including a comparison with the behaviourof normal fluctuations, would be interesting for comparing the results with SOL turbulencemodels in a parameter regime not normally found in the SOL. However, a more detailedinvestigation of Langmuir probes under non-stationary conditions may also be required forinterpreting such measurements correctly [15].

Taking into account the indications that the ion temperature may significantly exceed theelectron temperature [28], a time-resolved measurement of the ion temperature during ELMswould be important in order not to miss the major fraction of radial heat transport.

In order to decide experimentally whether the observed fine structure is based on theinstability underlying the ELM and hence already exists during the birth of ELMs or whetherthis fine structure is only generated in the SOL by those mechanisms also responsible for thenormal SOL turbulence, diagnostics with comparable spatial and temporal resolution wouldbe required for the steep gradient region inside the LCMS, where ELMs originate.

238 M Endler et al

Acknowledgments

We thank S Davies, K Erents, H Guo and R Monk for stimulating discussions and for theirhelp in running the JET RLP systems and determining probe positions and radial profiles,W Fundamenski, C Silva and T Eich for their important comments, H Niedermeyer and A Rudyjfor clarifying discussions on the interpretation of the ASDEX Hα data and H Scholz and G Neillfor their invaluable contributions to building and maintaining the diagnostic systems used inthese experiments.

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