J. Plasma Fusion Res. SERIES, Vol.7 (2006) 85-88

Plasma and Neutral Transport Study of Local Island Divertor
Configuration in Large Helical Device Edge Region
with 3D Monte Carlo Codes
KOBAYASHI Masahiro, REITER Detlev1 , FENG Yuehe2 , MORISAKI Tomohiro,
MASUZAKI Suguru, SARDEI Francesco2 and HAYASHI Takaya
National Institute for Fusion Science, Toki 509-5292, Japan
1 Institut fuer Plasmaphysik, Forschungszentrum Juelich GmbH, D-52425 Juelich, Germany
2 Max Planck Institut fuer Plasmaphysik, D-17491, Greifswald, Germany（Received: 4 October 2004 / Accepted: 24 May 2005）

Abstract
Edge transport physics of the Local Island Divertor (LID) configuration in Large Helical Device (LHD) isstudied with the 3D transport code package, EMC3-EIRENE [Y. Feng et al., Contrib. Plasma Phys. 44, 57(2004)] [D. Reiter, Technical Report Jul-1947, KFA Juelich, Germany (1984)]. Particularly, the behaviour ofneutrals around the divertor region was investigated, where it was found that the resulting profiles of atom andmolecular density as well as temperature are considerably diﬀerent each other. The cause of these diﬀerenceis discussed.
Keywords:edge transport, 3D modelling, Monte Carlo, application of atomic/molecular data,
Large Helical Device (LHD), Local Island Divertor (LID)
1．Introduction
Demands for edge transport modelling (plasma andneutrals) in magnetically confined devices such as tokamaks and stellarators have been increasing in order tointerpret experimental results and to also predict relevant physics of upcoming devices like ITER. Much efforts has been paid for the works in the last decades, andthe modellings, simplest in 1D along flux tubes and often in 2D in poloidal cut, have successfully applied forthese purposes [1].
An assumption of an axisymmetry accepted widely
so far in 2D tokamak computations, however, may haveto be relaxed to cope with the observed toroidally asymmetric profiles, e.g. plasma or/and impurity deposition
pattern on the divertor plates that might be attributed
to any toroidal un-uniformity caused by gas puﬀ, NBI,
toroidal coil ripple etc. Yet in devices which inherently have a 3D magnetic structure such as stellaratorsor tokamaks with special configuration, e.g. W7-AS,W7-X, TEXTOR-DED and LHD, a 3D treatment is anonly approach to an understanding of transport properties therein.
A 3D modelling of the edge transport taking into
account recycling neutrals from wall and thus relevant atomic/molecular processes was first implemented
in W7-AS with the codes, EMC3 [2] (plasma part)and EIRENE [3] (neutral part). The codes could
successfully reproduce the experimental results andhelped understanding well the transport physics that are
sometimes unique to the 3D magnetic structure. The
modelling has been extended to other machines, i.e.
TEXTOR-DED [4] and W7-X [5], to predict the edgetransport or to optimize the design.
The purpose of this paper is to implement the codes,
EMC3-EIRENE, in the Local Island Divertor (LID)
configuration [6] of LHD which also exclude any 2D
approach due to its inherent 3D magnetic structure, andto demonstrate a feasibility of the codes with the configuration. In this paper, particularly the behaviour ofneutrals is discussed.
2．Model of plasma & neutrals
EMC3 solves the standard plasma fluid equations [7]of conservation of mass, momentum and electron & ion
energy, in steady state, with a Monte Carlo scheme [8].
EIRENE solves neutral kinetic transport equations witha Monte Carlo scheme [3]. Both codes work in almost
arbitrarily complex 3D geometry of plasma and wallcomponents. The codes are iteratively coupled eachother via source/sink terms appearing in the plasma
C 2006 by The Japan Society of Plasma

Science and Nuclear Fusion Research

Corresponding author’s e-mail: masahiro@nifs.ac.jp85

Plasma and Neutral Transport Study of Local Island Divertor Configuration in Large Helical Device Edge Region with 3D Monte Carlo Codesback side of the LID head, where the collected plasma
is pumped out. The systems are movable separately inhorizontal direction in order to adjust a pumping eﬃciency (particle collection eﬃciency).

equations, i.e., particle source due to ionization, momentum and energy source/sink due to charge exchange(CX), dissociation and elastic collisions between ionsand neutrals, respectively. At material surfaces, theBohm condition is imposed for particle and heat fluxof plasma, and the deposition pattern on the surfaces isobtained taking into account the incident angle of fieldlines. Recycling neutrals from the LID head (divertorsurface) are released with weights being proportional toplasma particle deposition pattern. The released neutrals are atoms or molecules based on TRIM model assumed on the divertor surface of carbon with a recycling coeﬃcient of 1. The neutrals experience following
atomic/molecular processes [9] activated in EIRENE in
the present computations. Among those, the most important processes areAtoms(H)4．Implementation
The present computations are corresponding to theshots 41691 and 41696: major radius of magnetic axis(Rax ) is 3.60 m, PNB (input power) = 1.4 MW, rhead (LIDhead position) = −118 mm. Spatially constant crossfield particle & heat diﬀusivities (D, χe , χi ) are used in
EMC3 to simulate an anomalous perpendicular transport. The values are set to best fit the measured radial
profiles of density and temperature. For the shots inconcern, those were selected as D = 0.3 m2 /s, χe =χi = 0.8 m2 /s, respectively, which are in agreementwith the values estimated in Ref. [10]. In the present
computations, the plasma parameters in the divertor regions were, on an average, found to be T e ∼ T i ∼ 5 eVand n ∼ 1020 m−3 . The estimated ion saturation current
from these results were found in good agreement withthe probe measurements.

e + H(1s) → e + H+ + e (ionization)p + H(1s) → H(1s) + p(charge exchange + elastic component)
Molecules(H2 )5．Behaviour of neutrals
A high neutral compression in the divertor region is
expected from the closed structure of LID head and thebaﬄe. This is confirmed in Fig. 2, where atom andmolecule densities around the divertor region are plotted in logarithmic scale normalized with maximum values of 3.3 × 1019 and 2.3 × 1020 m−3 , respectively. In
the figures, one sees the densities are higher inside thedivertor than outside by at least one order. The atom
density peaks near the divertor surface where the recycling is occurring, whereas the molecule density becomes higher deep in the pump duct, where there are
more chances for atoms to recombine into molecules
in course of surface reflections. The elastic collision,p + H2 , whose cross section becomes higher in lower
temperature [11], pushes back these molecules into theduct. This is the reason why the molecule density decreases towards the divertor surface, as shown in Fig.
2(b).
Shown in Fig. 3 are the temperature profiles of atomand molecule, which were obtained by energy density(eV/m3 ) divided by particle density (m−3 ). Because of
the very low particle density outside the divertor, i.e.
the statistical error, the temperature there is not reliable,
so that we will restrict our discussion only in the divertor region. It is seen that the atom temperature is rather
high, about 4 eV almost throughout the pumping duct,
while the molecule’s is around 1 eV and decreases down
to room (wall) temperature deep in the duct (note thee + H2 → e + H+2 + e (ionization)p + H2 (elastic collision)
H+2+e + H+2 (v) → e + H+∗
2 → e + H + H(1s)(ionization).

3．LID configuration
The magnetic field configuration together with theLID head and the baﬄe are shown in Fig. 1, in a
poloidal cut at the center of the LID head. A magnetic
island of (m,n) = (1,1) is induced at the edge region, utilizing the separatrix as SOL to guide the plasma to theFig. 1 Schematics of LID head and the pump duct together with the separatrix of (m,n) = (1,1) island,at φ = 162◦ .
86

Plasma and Neutral Transport Study of Local Island Divertor Configuration in Large Helical Device Edge Region with 3D Monte Carlo Codes

Fig. 2 (a) Atom density proﬁle around the LID head, inlogarithmic scale normalized to the maximum
density of 3.3 × 1019 m–3 . The LID head is depicted with the black background.

Fig. 3 (a) Atom temperature proﬁle around LID head.

Fig. 3 (b) Molecule temperature proﬁle around LID head.
Fig. 2 (b) Same as Fig. 2 (a) but for molecule, normalized
to 2.3 × 1020 m–3 .

cated as shown in sec. 2, and there are several channelsof energy exchange that are also tightly linked with H +2 .
Although a dominant energy gain is the elastic collision which has almost same cross section as that of CX
for atoms with the present parameter range, the reactions that produce H+2 take away some of the gainedenergy, which are then mainly given back to plasma(2.2.12, 2.2.11). The obtained proportion is, a gain formolecules of 3.5 % of input power, while loss for H+2of 1.8 %, respectively. These are considered the reasons giving such diﬀerences in the temperature profiles
in atoms and molecules. As a result, the neutral pressureof 1 to 5 Pa in the duct and a neutral compression ratio,p0,div /p0,sep ∼ 30 (p0,div and p0,sep are neutral pressure
at divertor and separatrix (upstream), respectively), areobtained in the configuration, that are comparable to thenumbers achieved in various tokamaks with closed divertor configurations [12,13].
The energy loss/gain discussed above is still small
compared to that via electron (through ionization, exci-diﬀerent scale for each plot). The diﬀerence of the profiles deep in the duct is attributed to the reflection modelat the material surfaces, in which the atom carries still
significant fraction of incident energy after reflection,
whereas the molecule is first accommodated in the wallthen released with the wall temperature that is assumed
to be room temperature.
Another reason for the diﬀerence is considered due
to energy gain/loss channel with plasma. Atomsgain/loss energy through CX (plus elastic collision) andionization. In the parameter range given above, mean
free paths for the reactions are estimated as, λCX,elastic ∼a few cm, λion ∼ a few tens cm, respectively, so that CX
is a dominant process of, probably, energy gain fromplasma. The code results showed that practically theenergy exchange is a net gain for atoms of 5 % of inputpower. For molecules, the processes are more compli-87

Plasma and Neutral Transport Study of Local Island Divertor Configuration in Large Helical Device Edge Region with 3D Monte Carlo Codestation, dissociation) which is about 30 % of input power.
But the former component is directly converted to theneutral energy (momentum) and it then aﬀect neutralpressure in divertor region. This is an important process
in terms of edge density control and also helium ash removal by pumping in fusion devices [14], not only inLHD but also for forth-coming machines like ITER.
The reflection model of molecules at the wall may
have to be still improved with higher energy reflection
coeﬃcient as for atoms. Also an elastic collision between atoms and molecules would equilibrate the temperatures to some extent, which has not been taken into
account in the present runs. These are the next step
studies.

be continued.

[1]
[2]
[3]

[4]
[5]
[6]

6．SummaryThe 3D edge transport codes, EMC3-EIRENE, forplasma & neutrals, was successfully implemented in
LID configuration of LHD. We particularly investigatedneutral behaviour in this paper and found,

[7]

[8]
[9]

1. The closed divertor structure gives rise to highneutral density in the duct, giving pressure of 1 to 5 Pa
and p0,div /p0,sep ∼ 30.

[10]

2. Neutral density and temperature can diﬀer significantly depending on the species (atoms and molecules)in the divertor region. The diﬀerence is attributed to theenergy gain process from plasma and the wall reflection
model for each species.

[11]
[12]
[13]

In order to give an accurate estimation of the neutral
profile in divertor region that is important in terms of theedge density control by pumping, helium ash removal,chemical sputtering etc., the survey on the issue must

[14]

88

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