Proceedings of ITC/ISHW2007

On impurity retention eﬀect in the edge ergodic layer of LHD
Masahiro KOBAYASHI1) , Yuehe FENG2) , Sigeru MORITA1) , Kuninori SATO1) ,Malay Bikas CHOWDHURI3) , Suguru MASUZAKI1) , Mamoru SHOJI1) , Yukio NAKAMURA1) ,Masayuki TOKITANI1) , Nobuyoshi OHYABU1) , Motoshi GOTO1) , Tomohiro MORISAKI1) ,Ichihiro YAMADA1) , Kazumichi NARIHARA1) , Naoko ASHIKAWA1) , Hiroshi YAMADA1) ,Akio KOMORI1) , Osamu MOTOJIMA1) and the LHD experimental group1)

2)

National Institute for Fusion Science, Toki 509-5292, Japan
Max-Planck-Institute fuer Plasmaphysik, Wendelsteinstrasse 1, D-17491 Greifswald, Germany
3)
Graduate University for Advanced Studies, Toki 509-5292, Gifu, Japan

The impurity transport characteristics in the ergodic layer of LHD is analyzed using the 3D edge transport
code (EMC3-EIRENE), in comparison with the experimental data. The 3D modelling predicts the impurity
retention (screening) in the ergodic layer at high density plasma. It is found that the edge surface layer plays animportant role for the retention, where the friction force significantly dominates over the thermal force. The line
intensity measurements of CIII to CVI shows consistent behaviour with the modelling, indicating the existenceof impurity retention in the ergodic layer. The applicability of the model for high Z impurity is also discussed,
where it is found that the experimental data is, at least, consistent with the results of edge transport modelling.
Keywords: ergodic layer, impurity transport, LHD

1

Introduction
radialControl of impurity transport in a fusion device is one of
the most important issues, in order to avoid impurity contamination of core plasma, which leads to confinement
degradation by radiative cooling, as well as reduction offusion power due to fuel dilution [1]. The impurity that
released at divertor plates or the first wall, reaches first thescrape-oﬀ layer (SOL), where they experience ionizationand thereby transported as charged particles. The transport
in the SOL then determines the influx of the impurity to thecore region [2]. This paper focuses on the impurity transport in the edge region, especially the eﬀect of stochastic magnetic field. It has been reported in Tore Supra experiments that there is an indication of plasma decontamination during the ergodic divertor configuration [3], andan interpretation for this phenomena was discussed using(1D) analytical model [4, 5], as an enhanced outflux ofplasma by the stochastic field lines, that tends to exhaust
impurity. Similar explanation was given also by D. Kh.
Morozov et al. [6].
On the other hand, the Large Helical Device (LHD)in National Institute for Fusion Science, intrinsically has
ergodic layer in the edge region. It is found that even withextremely high core density operation, where the negative
radial electric field is formed, it is free from radiation collapse, suggesting no serious impurity contamination [7]. In
this paper, we try to discuss impurity transport in the edge
ergodic region of LHD using 3D numerical transport codethat takes into account all relevant terms of impurity transport model as well as precise magnetic field configuration
author’s e-mail: kobayashi.masahiro@lhd.nifs.ac.jp

Edge surface
LayersStochastic
Regioninboardpoloidaloutboard

inboardFig. 1 Connection length (LC ) profile in ergodic layer of LHD,
superposed with Poincare plot of field lines. LC is resolved up to 100 km.

(i.e. braiding magnetic field). This enable us to directlycompare the impurity transport model with experimental
results and thus gives us clearer interpretation of the impurity transport process in the ergodic layer.

2

Magnetic field structure of ergodic
layer in LHD

LHD is a heliotron type device with steady state magnetic
field sustained by superconducting helical coils of l = 2.
The major and averaged minor radii are 3.9 m and ∼ 1.0 m,
respectively [8]. The helical coils’ winding creates magnetic field structure of 10 field periods in toroidal direction.
The radial magnetic field coming from the helical coilswith many diﬀerent modes, produces magnetic islands atthe edge region, and they overlap to create ergodic fieldstructure there.

Proceedings of ITC/ISHW2007
The connection length profile of the ergodic layer isplotted in Fig.1, together with Poincare map. In this paper, the ergodic layer is divided into three regions, following the terminology of ref.[8], which is defined based on
the magnetic field topology that aﬀects thereby the transport properties of plasma (impurity), as shown later. The
region with m=8 magnetic islands are considered as confinement region because of the clear island structure andthe long connection length ( > 100 km ). The stochastic region starts from m=7 islands, where they are overlappingwith neighbouring islands and the separatrix is no longer
clear. From the mode of m=4, it is called the edge surface layer, where short and long field lines are mixed. This
structure is an unique feature of of heliotron divertor configuration, which is created by strong magnetic shear thatstretches and bends the flux tubes, and thus mixes up thelong and short flux tubes. The outside of the edge surface
layer is divertor legs, which connects to divertor plate inseveral metes, which is, however, not shown in Fig.1.

+

Parallel flow velocity-(b) plasma flow(c) Impurity flow
(4e19 m-3)(a) Impurity flow
(2e19 m-3)

Fig. 2 (a) Parallel impurity flow velocity at nLCFS = 2×1019 m−3 ,(b) parallel flow velocity of bulk plasma, (c) same as (a)but for nLCFS = 4 × 1019 m−3 . The yellow and blue indicate positive and negative flow in toroidal direction. The
dashed lines are located at the same radial position foreye guide.

10.0

3

Impurity transport analysis in the ergodic layer

2e19 m-3
1.0

The impurity transport analysis has been carried out by using the edge transport code EMC3 [9] - EIRENE [10], inorder to take into account the magnetic field structure of
the ergodic layer. The code solves the fluid equations ofmass, momentum and energy as well as impurity in a realistic 3D geometry. The details of the model are describedin ref.[9]. EIRENE solves a kinetic equation for neutralgas, which recycles at the divertor plates or first wall.
The impurity transport along the field lines is considered to be governed by the momentum equation,

mz

∂Vzk
Vik − Vzk
1 ∂T i nz=−+ mz+ ZeEk
∂t
nz ∂s
τs
∂T e
∂T i
+ Ce
+ Ci
,
∂s
∂s

(1)

where the subscript z and i denote the impurity with charge
state Z and the bulk plasma ion, respectively. The s isthe coordinate along magnetic field line and it is assumed
that T z ≈ T i . τ s , Ek and Vk are the impurity-ion collisiontime, parallel electric field and parallel flow velocity, respectively. Ci ≈ 2.6Z 2 and Ce ≈ 0.71Z 2 . The first term on
the right hand side is pressure gradient force of impurity.
The second term, friction force, and the third term, parallel
electric field, are usually directed to the divertor, while theforth and fifth terms on the right hand side, electron andion thermal force, are pulling impurity upstream becauseof the parallel temperature drop to the divertor plate. It iseasily shown that the dominating terms in the equation are
the ion thermal force and the friction force [11] [12]. In

3e19 m-3
4e19 m-3
stochasticedge surface

0.1
0.60

0.65
reff (m)0.70

Fig. 3 Radial profiles of carbon density summed up over all
charge states, for diﬀerent density, nLCFS = 2, 3, 4 ×
1019 m−3 normalized with the downstream density. re f f isdefined by cylindrical approximation of the volume enclosed by the radial surface of computational mesh.

force balance, eq.(1), therefore, reads,
Vzk = Vik + Ciτ s ∂T i
mz ∂s

(2)

i
Since Vik flows towards divertor plate, while ∂T∂s directs upstream, when the friction dominates over the thermal force,the impurity flows to the divertor. The ratio of the friction
and the thermal force in eq.(1) is given by [13] [14],f riction f orce 5/2ni T i Vik
ni |M|∼,∝
thermal f orce κi0 T i2.5 ∇k T i T i ∇k T i(3)with M being Mach number. The numerator represents
convective energy flux while the denominator does conductive one.
Eq.(3) shows that as the plasma becomes dense andcold with substantial flow acceleration, the friction forceProceedings of ITC/ISHW2007
dominates over the thermal force, resulting in impurity retention at the divertor. In the present analysis, carbon is
selected as the impurity species, which is released at thedivertor plate, with source rate being proportional to thedivertor flux, and traced according to eq.(1), also in perpendicular to field lines as diﬀusive process. Plotted in
Fig.2 are the parallel impurity flow velocity as well as
the bulk plasma flow obtained by the 3D modelling, fordiﬀerent density with fixed input power, where the yellow and black colours mean flows in positive and negative toroidal directions, respectively. In this figure, it isclearly observed that at nLCFS = 2 × 1019 m−3 , the impurity flow direction is opposite to the bulk plasma flow,
i.e. thermal force pushes the impurity upstream, while atnLCFS = 4 × 1019 m−3 the direction of impurity flow becomes same phase as the bulk plasma flow due to the friction force. The resulting total impurity density (summed
up over all charge states) profiles are plotted in Fig.3, inradial coordinate re f f for the diﬀerent plasma density. re f f
is defined by cylindrical approximation of the volume enclosed by the radial surface of computational mesh. At the
low density, nLCFS = 2 × 1019 m−3 , the thermal force is so
eﬀective that the impurity is drawn to LCFS, and accumulates there. With increasing density, the upstream impurity
density gradually decreases, and at nLCFS = 4 × 1019 m−3 ,the impurity is driven towards divertor by the friction force,
resulting in divertor retention as seen in Fig.3.
As the retention eﬀect is switched on, the profile become flat in the stochastic region and lower than the downstream, where the density gradient is formed especially inthe edge surface layer. The profile indicates that the friction force to push the impurity outward is eﬀective only inthe edge surface layer. Plotted in Fig.4 (c) is eq.(3), theratio of friction and thermal force, as well as (a) electron
temperature and density, (b) Mach number and ionization
source of bulk plasma. In the edge surface layer, there
appears substantial acceleration of Mach number, whichis considered caused by the hydrogen ionization source
there and also the particle sink due to the short connection length flux tubes that are embedded in-between thelong ones. The temperature decreases towards the edge.
These parameter change results in the significant increaseof the friction-thermal force ratio in the edge surface layer,
as observed in Fig.4 (c).

4Comparison with experiments

Figure 5 (a) shows radial profiles of carbon density in different charge states at nLCFS = 4 × 1019 m−3 , where the impurity retention is eﬀective as discussed above. For comparison, the profiles at nLCFS = 2 × 1019 m−3 is plotted in
Fig.5 (b), in which case the impurity accumulates around
LCFS because of the dominant thermal force. Due to thelarge jump in the ionization potential between C +3 (=64.5eV) and C +4 (=392 eV), there appears clear separation of

4

200

3
2

100

1
0
0.8

0.6

(a)
0

(b)

6

0.4

4

0.2

2

0

0

103
stochastic

102
101
100
10-1

E
0.60

0.65
reff (m)edge surface
0.70

Fig. 4 Radial profiles of (a) ne and T i , (b) Mach number andionization source, (c) eq.(3), as a function of re f f , fornLCFS = 4 × 1019 m−3 .

the location of peak positions between the low and highcharge states groups, i.e. lower charge states C +1 , C +2
and C +3 are mainly located at re f f > 0.67m, while higher
ones C +4 , C +5 and C +6 have peaks at re f f < 0.67m. At
nLCFS = 4 × 1019 m−3 , it is seen that the lower charge states
increases due to the retention eﬀect at the outer radius,
at the same time the density of higher charge group near
LCFS is suppressed. In the case of nLCFS = 2 × 1019 m−3 ,on the other hand, the higher charge group increases significantly in the inner radius, with reduced lower charge
group at outer radius. The diﬀerence of the profiles are reflected on the radiation intensity, which are shown in Fig.6(a). The radiation from lower charge states, CII, CIII and
CIV, increases monotonically with increasing bulk plasma
density. This is due both to the increase of carbon yield,
which is proportional to divertor flux, and to the retention eﬀect. On the other hand, the radiation from higher
charge states, CV and CVI, remains almost constant. Thisis mainly due to the reduction of the density caused by theretention at higher density, also partly because of the temperature change caused by density scan, where the CIV
and CV are still sensitive to the temperature in the rangeof 100 to 200 eV. In order to illustrate the impact of friction exerted by bulk plasma flow, Vik is set to be zero ineq.(1), keeping all other parameters unchanged. The results are plotted in Fig.6. In this case, because of no outward component of impurity flow, the absolute content of
impurity increases, and thus the radiation intensity is relatively higher than Fig.6 (a). One should also note the quali-

Proceedings of ITC/ISHW2007
1012

C YHTKEVKQP

C

CIII

C+1
C(all)

2 104

C+2
CII

11

10

C+4
C+5

C+3

CIV

1 104

C+6
1010

CV
CVI
0
4 104

109
1012

radiation_nup
CV

D YQHTKEVKQP

D

CIII
3 104

C(all)

CVI
CIV

C+6
1011
C+4

C+1

C+5

2 104

C+2
CII

1010

C+3

1 104

0

109

0.60

0.65
reff (m)0.70

Fig. 5 Radial profiles of carbon density at diﬀerent charge
states, black : C+1 , yellow : C+2 , red: C+3 , green : C+4 ,blue : C+5 , grey : C+6 , dashed lines : total density of carbon. (a) nLCFS = 4 × 1019 m−3 , (b) nLCFS = 2 × 1019 m−3 .

tatively diﬀerent behavior of CV and CVI, i.e. the radiationfrom higher charge states (CV and CVI) monotonically increases with increasing density. This is attributed to thelarge increase of C +4 and C +5 density at the inner radius ofergodic layer because of the lack of flushing eﬀect by thebulk plasma flow.
The radiation intensity is measured in the experiments, using VUV monochromators and EUV spectrometer. It is found that the CII radiation is negligibly small
in the experiments, while it has substantial intensity in themodelling. This is probably because in the modelling thedivertor legs are neglected, which then allows the C +1 toreach the ergodic layer, while in experiments they are ionized much earlier downstream in the legs. The obtained
line integrated intensity for diﬀerent charge stages are plotted in Fig.7 as a function of density. In this plot, the sumof CIII (977 Å) & CIV (1548 Å) and CV (40.27 Å) & CVI(33.73 Å) are plotted rather than each. The radiation ofindividual charge states shows similar behavior as Fig.7.
The CIII + CIV increases monotonically with increasing

2

34<ne> (e19 m-3)

5

6

Fig. 6 (a) Radiation intensity from diﬀerent charge states as afunction of density. (b) Same as (a) but with Vik = 0 in
impurity transport. black : CII, yellow : CIII, red : CIV,
green : CV, blue : CVI.

density, on the other hand the CV + CVI stays almost constant against density scan. These results are in qualitative
agreement with the modelling with friction force, Fig.6 (a),and can be interpreted as a clear experimental evidence of
impurity retention in the ergodic layer.
It should be noted that the eﬀective impurity retention is also due to the geometrical advantage of the ergodic
layer in LHD, where the edge surface layer surrounds theplasma in all poloidal and toroidal direction, and thus it canprotect the plasma from the impurity neutrals coming fromall direction, e.g. impurity released at the divertor plate byplasma flux or at the first wall by charge exchanged neutrals.

5 Implication for high Z impurity
From eq.(2), one sees that the balance between the first andsecond terms on the right hand side is independent of thecharge Z, because τ s ∝ 1/Z 2 , which then cancels with theZ 2 at the numerator.
In order for the friction force to drive the impurity

Proceedings of ITC/ISHW2007
100

H
10-1

C 50eV-210

Fe 100eV
C 10eVC

Fe 10eV10-3(ne=1e19 m-3)
101

102

103

Te (eV)

Fig. 8 Estimated neutral penetration length for hydrogen, carbon and iron, indicated with H, C and Fe, respectively.

D

Fig. 7 Radiation intensity from diﬀerent charge states as a function of density, measured by the VUV monochromatorsand EUV spectrometer. (a) CIII (977 Å) + CIV (1548
Å), (b) CV (40.27 Å) + CVI (33.73 Å).

to the downstream, the ionization location of impurity
species, in the present case C 0 , should be far downstreamof that of the bulk plasma. The larger the separation between the source locations of impurity and bulk plasmais, the stronger the retention eﬀect. Because of the lower
ionization potential of carbon than that of hydrogen, this is
usually the case unless the carbon is injected with very highenergy. Figure 8 shows the estimated penetration length ofneutral hydrogen, carbon and iron as a function of electron
temperature. Due to the very low ionization potential of
Fe0 , 7.9 eV, the penetration length of Fe is even shallower
than carbon, indicating that the impurity retention model
presented in section 3 could also apply.
Figure 9 shows the time trace of line radiation intensity of FeXX (132.85 Å) + FeXXIII (132.87 Å) measured by VUV spectrometer, for diﬀerent plasma density,
being normalized with ne at the centre of plasma. Fromt = 1.0 s to 2.0 s, the plasma density and temperature
was kept constant for each shot. The input power was
fixed at ∼ 8 MW. As the density increases, the normalized intensity decreases gradually, while the intensity at
nLCFS = 3 × 1019 m−3 shows strong increase in spite of

the constant plasma parameters during flat top. The increase seems to continue further after t = 2 s, although
the discharge was terminated just after 2 s. This increaseindicates impurity accumulation at the core region. The
similar behavior was observed in the low power discharge
with ∼ 1 MW [15]. Nevertheless, at the higher density ofnLCFS = 4 × 1019 m−3 , the intensity is significantly suppressed and no such accumulation is observed. Comparedto the low density case, the reduction is a factor of 5. With
the increase of the density, the electron temperature at thecentre of the plasma decreases from ∼ 2 keV to ∼ 1 keV, i.e.
by a factor of 2, due to the fixed input power. However, taking into account the temperature dependence of the line intensity of FeXX (132.85 Å) + FeXXIII (132.87 Å), whichis almost saturated around 1 to 2 keV, the reduction of themeasured radiation (normalized by density) indicates reduction of Fe+19 and Fe+22 at the centre of plasma. Although in order to consistently analyze the transport of thehigh charge states of the iron we need to address the core
impurity transport, the behavior is consistent with the prediction of the edge model in the section 3.

6

Summary

The impurity transport properties in the ergodic layer of
LHD has been analyzed, using the edge transport code
(EMC3-EIRENE) in comparison with experimental data.
The 1D impurity transport model along field lines predicts
the impurity retention (screening) when the plasma becomes dense and cold with substantial flow acceleration.
This is demonstrated in the ergodic layer of LHD by the3D numerical simulations. It is found that the edge surface
layer plays an important role for the retention, where theratio of friction force and the thermal force (eq.(3)) significantly increases due to the flow acceleration and theProceedings of ITC/ISHW2007
6 102
5 102

P.%(5 GO 

4 102

GO 

3 102
2 102

GO 

1 102
0
1.0

1.2

1.4

1.6

1.8

2.0

time (s)Fig. 9 Time traces of line intensity of FeXX (132.85 Å) +FeXXIII (132.87 Å) measured by VUV spectrometer for
diﬀerent density, at flat top discharge during t = 1 to 2
sec. The intensity is normalized with electron density at
the centre of plasma.

temperature decrease. The carbon line radiation measurements is compared with the simulation results, where thegood qualitative agreement is obtained with the modelling
results with friction force, indicating the existence of impurity retention in the experiments. It should be noted that theretention eﬀect is also due to the geometrical advantage ofthe magnetic field structure of ergodic layer in LHD, where
the edge surface layer surrounds the plasma in all poloidal
and toroidal directions. This structure eﬃciently stops theimpurity originating from any locations, i.e. divertor or
first wall.
Applicability of the model for the high Z impurity was
discussed with respect to the charge dependence and theneutral impurity penetration distance. The brief estimation
implies the mechanism could also apply for the high Z impurity. The behavior of measured line intensity of FeXX
+ FeXXIII against density change is consistent with theprediction of edge modelling. It is, however, necessary toaddress the core impurity transport properties in order tounderstand the behavior of high Z impurity, for which we
still need further experimental as well as theoretical work.
Acknowledgements
The authors are grateful for the support for computational resource, AMD Opteron-InfiniBand Cluster Machine, by Grant-in-Aid for Science Research on Priority
Areas (Area 465, No.18070005) from Ministry of Education, Culture, Sports, Science and Technology, Japan.
The part of the computational work is also financially supported by the budget code NIFS07ULPP538. One of theauthors, M.K., is grateful to N. Yamamoto for the fruitful
discussion and the calculation for temperature dependenceof line intensity of Fe.

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