Proceedings of ITC/ISHW2007

Investigation of the fluctuation properties of the ion saturation
current in the edge and divertor plasmas in LHD
S. Masuzaki, N. Ohno a, V.P. Budaev b, S. Sakakibara, T. Morisaki,
M. Kobayashi, N. Ohyabu, A. Komori and the LHD Experimental Group
National Institute for Fusion Science,322-6 Oroshi-cho, Toki 509-5292, JapanaEco Topia Science Institute, Nagoya University, Nagoya 464-8603, Japanb
Nuclear Fusion Institute, RRC Kurchatov Institute, 123182, Kurchatov Sq.1, Moscow, Russia(Received day month year / Accepted day month year should be centered 10-point type)
Fluctuation properties of the ion saturation current measured by using Langmuir probes in the edge and divertor
plasmas were investigated based on probability distribution function (PDF) analysis in the Large Helical Device(LHD). In the edge plasma region, both positive and negatively skewed PDFs were observed. Unlike tokamak cases,negatively skewed PDFs were found at divertor legs. On a divertor plate, sign of skewness of Isat PDF inverts frompositive to negative value during a discharge.
Keywords: Large Helical Device (LHD), edge plasma, divertor plasma, ion saturation current,fluctuation, intermittent events, probability distribution function (PDF)

1. Introduction
In magnetic fusion devices, energy and particle fluxes
crossing the last closed flux surface (LCFS) are transported
to plasma facing components conductively andconvectively in scrape-off layer (SOL). The distributions ofheat and particle loads on plasma facing components arevery important parameters for designing devices, and aredetermined by the balance between the parallel andperpendicular transports. The perpendicular transportcoefficients, such as diffusion coefficient are anomalous,and fluctuation phenomena are believed to strongly relate
to the transport [1].
In tokamaks, it is widely observed that SOL consistsof the near- and far-SOL [2]. The difference between theseregions is the density decay length. In the near-SOL, justoutside LCFS, the density profiles are usually exponential
with short (a few cm) decay length. On the other hand, thedecay length is long, and the profiles are nearly flat in thefar-SOL. Therefore plasma with substantial density exists
in front of main chamber first wall, and the particle load on
first wall cannot be ignored. The transport in the far-SOL isbelieved to be not diffusive but convective associated withintermittent events, so called ‘blob’, and the probability
distribution function (PDF) of the density fluctuations in
the far-SOL has non-Gaussian tail.
In the Large Helical Device (LHD), the world largest
superconducting helical device with heliotron-typemagnetic configuration, there is a unique edge magnetic
author’s e-mail: masuzaki@LHD.nifs.ac.jp

field lines structure. There exist an intrinsic stochastic
layer just outside of LCFS, residual islands embedded in
the stochastic layer, the edge surface layers and theintrinsic divertor structure (helical divertor), this magnetic
structure is one of the characteristics of the heliotron-type
configuration [3]. Figure 1 (a) shows a Poincare plot ofmagnetic field lines in a horizontally elongatedcross-section in LHD. Blue and red points outside LCFS
indicate open field lines striking divertor plates. Yellowlines are contours of magnetic field strength, and theyshow that the gradient of magnetic field strength largely
changed in a poloidal cross-section. For the difference ofmagnetic structure in the edge plasma region, comparison
the fluctuation properties in the edge and divertor
plasmas between tokamaks and helical devices could
make it possible to understand the physics of cross-fieldtransport.
It was reported that the intermittent properties of Isat
measured by a Langmuir probe on a divertor plate issimilar to that observed in tokamaks SOL and linear
divertor simulator [4]. It was observed that large positive
and negative bursty signals dominates the time-evolutionsof Isat measured at lower field side and striking point of
the divertor leg, respectively, and this is consistent withtheoretical prediction of blob transport [5]. In this paper,
the fluctuation properties of the ion saturation current, Isat,
measured by Langmuir probes in the edge and divertor

Proceedings of ITC/ISHW2007
torus inboard-side in the horizontally elongatedcross-section, there is a Langmuir probe array (LP array)consisting of 16 dome-type electrodes with a 2 mm ofdiameter as shown in Fig. 1(c). The distance betweenelectrodes is 6 mm, and Isat profiles along S-axis wereobtained. S-axis is along the edge of the divertor plate, andthe direction is almost toroidal. Sampling frequencies anddynamic ranges of the LP array and FSP for their dataacquisition are 500 kHz and 1 MHz, respectively.

3. Results and discussions
The fluctuation properties of Isat signals measured byLangmuir probes were analyzed based on PDF analysis.
For fully random signal, PDF has a Gaussian distribution.
The deviation of PDF from Gaussian distribution function
can be characterized by skewness, S = <x3>/<x2>3/2, andflatness, F = <x4>/<x2>2. Skewness and flatness aremeasures of asymmetry and of the tail’s weight withrespect to core of PDF, respectively, and S = 0, F = 3 forGaussian distribution.

sat(a.u.)86(a)Isatskewness

Hydrogen plasmas heated and sustained by neutralbeam injection (NBI) are investigated in this study. Figure
1 (b) and (c) show positions of the Langmuir probes. Fast
scanning Langmuir probe (FSP) moves 500 mm verticallyfrom the top wall along Z-axis as shown in Fig. 1(b) usinga pneumatic cylinder. The position of first wall is Z~1.6 m.
The maximum velocity of FSP is about 1 m/s. One
electrode made of graphite, dome-type with 2 mm ofdiameter, was provided for this study, and Isat profiles alongZ-axis were measured. On the divertor plate which locates102-10-2(b)opposite direction

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102. Experimental set-up

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plasmas in the unique edge magnetic structure areinvestigated based on PDF analysis.

3Skewness

10IFig. 1 (a) Poincare plot of magnetic field lines in ahorizontally elongated cross-section in LHD.
Blue and red points outside LCFS indicates
open field lines striking divertor plates. Yellow
lines are contours of magnetic field strength.
Poloidal cross-sections of LHD plasma andvacuum vessel at the positions of (b) FSP (fastscanning Langmuir probe) and of (c) thedivertor plate in which LP array is installed,respectively.

3.1 Result of the edge plasma measurement
Isat profiles in the edge plasma were measured by FSP
during discharges with a magnetic configuration of Rax =3.60 m, where Rax is major radius of magnetic axis. Figures
2(a) and (b) show an Isat profile during a discharge with
2×1019 m-3 of line averaged electron density and 3 MW ofNBI heating power and field lines connection length, Lc,
profile along Z-axis calculated with field lines tracing code,respectively. Smaller Z is closer to LCFS. Field lines trace

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same direction
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Fig. 2 (a) Isat profile along Z axis measured by using
FSP and skewness profile estimated using every
1000 data points. (b) Profiles of connection
length of magnetic field lines (Lc) along Z axis
calculated with field lines tracing code. Red andblue lines show Lc profiles calculated for sameand opposite directions of magnetic field
direction, respectively.

Proceedings of ITC/ISHW2007

3.2 Temporal change of PDF property in divertor
plasmaTemporal change of PDF property of Isat measured byLangmuir probe array on a torus-outboard divertor plate(see Fig. 1(c)) was observed during discharges with Rax =3.60 m and PNBI = 5.9 MW. Typical waveforms of plasma
parameters in such a discharge are shown in Figs. 3(a)-(c).
Normalized Isat profiles on the Langmuir probe array at t =1.3 s and 1.8 s are depicted in Fig. 3(d). In Fig. 3(c),time-evolution of skewness and flatness of Isat signal at thepeak of the Isat profile are depicted. Skewness increases inthe early phase of neutral beam injection, and it has peak att ~ 1.4 s. Then it decreases gradually, and it becomes

1(a)

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0.20(b)n e,bar (10 19 m -3)3(A)0n e,bar2
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0.8

normalized I

0-2

2.8(d)

1t = 1.3 st = 2.0 s
0020s (mm)4060Fig. 3 Typical time evolutions of (a) stored energy, Wp,
and neutral beam deposition power, PNBI, (b)line averaged density, ne,bar, and gas-puff, (c) Isat,skewness (S) and flatness (F) during a discharge
with magnetic configuration of Rax = 3.60 m. (d)Isat profile on the Langmuir probe array during
same dischage. Horizontal axis is probe position(see Fig. 1(c)). Blue and red lines are fittingresults.
2Skewness

was conducted for two directions. One is the same
direction as magnetic field, and another one is the opposite
direction. Two Isat peaks appear at Z = 1.0 m and 1.2 m,
and they correspond to long Lc groups positions in Fig. 2(b). The difference of positions between Isat peaks and Lc
peaks is considered to be caused by the alignment error ofFSP. These long field lines approach the vicinity of LCFS,
and they are main channel of particle and energy flow fromLCFS to divertor. On the other hand, field lines less than
100 m do not approach LCFS [6].
Skewness profile is also plotted in Fig. 2(a).
Skewness was estimated after removing DC component
from raw Isat signal using high-pass digital filter (>100Hz),
and using 1000 data points (1 ms). Therefore the spatial
resolution of this analysis is about 1 mm. In tokamaks,
negative skewness has been observed near or inside LCFS,
and skewness is positive and becomes larger with increase
the distance from LCFS [7]. In LHD Rax=3.60 m
configuration case, there are two negative peaks at thevicinity of Isat peaks (Z ~ 1.02 m and ~ 1.18 m) , that is thevicinity of Lc peaks as shown in Fig. 2. This result indicatesthat negative bursts corresponding to density drops aredominant in this region. Fig. 2(b) shows that these fieldlines at the Lc peak positions connect to divertor plates lessthan 10 m, and that means these peaks are divertor legs.
Relatively large positive skewness appears beside negative
peaks of skewness as shown in Fig. 2(a). This observationis consistent with previous observation in divertor plasma[5]. From Z ~ 1.20 m to 1.28 m, skewness decreases from
1 to 0 with decay length of 2 cm, and Isat becomes noiselevel at Z > 1.28 m. It suggests that transport becomes
diffusive in the outermost region. Assuming the positive
spikes in Isat at Z > 1.21 m region are blobs, a possible
explanation of determining the decay length of skewness islifetime of blobs. Lifetime of blob is roughly estimated as
Lc/Cs, where Cs is ion sound speed. In the case of around Z= 1.21 m, Lc ~ 10 m and Cs ~ 3×104 m/s (assuming Te =10eV), and the lifetime is ~ 0.3 ms. Assuming blob speed
to be 100 - 1000 m/s, the propagation length is 3 - 30 cm.

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ne,bar (1019m-3)

45Fig. 4 Skewness of Isat as a function of line averaged
density.
negative after t ~ 1.8 s. The negative sign of skewness iskept until the NBI termination, and then skewness andflatness become 0 and 3, respectively. To reveal the key
parameters of changing sign of skewness, electron density
and temperature dependences of skewness wereinvestigated. A series of discharges with different densities(ne,bar = 2 - 4×1019m-3 ) were conducted. In Fig. 4,300

Te, LCFS

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3Te, LCFS (eV)Proceedings of ITC/ISHW2007

Fig. 5 Time-evolutions of skewness of Isat and electron
temperature at LCFS, Te,LCFS, during the sameseries of discharge as Fig. 4.
skewness of Isat in each discharge is plotted as a function ofline averaged density, and the figure suggests that inversionof skewness sign does not depend on electron density.
Figure 5 shows time-evolutions of skewness of Isat andelectron temperature at LCFS in the same series ofdischarges as Fig. 4. Skewness increases during electrontemperature increase, and then decreases during electron
temperature is almost constant. It seems that skewness
does not depend on Te,LCFS in the later phase. In Fig. 5(a),sign of skewness becomes negative after t ~ 1.8 s. On theother hand, in Fig. 5(b), skewness becomes 0 at t ~ 2.1 s,and it is kept until t = 2.9 s. The difference between Figs.
5(a) and (b) is electron temperature at LCFS. In the former
case, Te,LCFS ~ 300 eV and ~ 200eV in the latter case. This
result suggests that skewness depend on Te,LCFS, and its
sign does not become negative when Te.LCFS is around 200eV. In Fig. 5(c), skewness increases at t ~ 2.3 s withdecrease of Te.LCFS, and decreases from t ~ 2.4 s withincrease of Te.LCFS. This result also suggests that skewness
depends on Te,LCFS.
In Fig. 4(d), two Isat profiles are shown. They are inpositive (t = 1.3 s) and negative (t = 2.0 s) skewness phases,
respectively. From the fitting results, the peak of Isat profile
shifts about 3 mm, and this shift is considered to be causedby modification of magnetic field lines structure.
Modification of magnetic field lines structure could be acause of the inversion of skewness sign. As described insection 3.1, it was observed that the negative skewness
region in divertor leg is narrow, and at the vicinity of that,
there is positive skewness rergion. Therefore, a small
movement of magnetic structure on the divertor plate due

to some reason such as a small change of rotationaltransform caused by toroidal plasma current could change
the sign of skewness.

4. Summary
Fluctuation properties of Isat in the edge and divertor
plasmas in LHD were investigated based on PDF analysis.
In the LHD edge plasma region, skewness of PDF of
Isat has both positive and negative values, and negative
region is relatively narrow. Negative peaks of skewness
appear at the positions of divertor legs. In the outermost
region of the edge plasma, skewness decrease from ~1 to 0
with the decay length of a few cm. This decay length iscomparable to the blob propagation length roughly
estimated from the lifetime of blob.
On a torus-outboard divertor plate, it was observedthat the sign of skewness inverts from positive to negativeat a probe channel during a discharge. Electron density
does not affect this behavior but electron temperature
and/or modicication of magnetic field lines structure at thedivertor plate caused by toroidal plasma current could
affect it.

Acknowledgements
This work was supported by the NIFS budget
NIFS06ULPP511.

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