Proceedings of ITC/ISHW2007

Comparative Divertor-Transport Study for W7-AS and LHD
Y. Fenga), M. Kobayashi b), N. Ashikawa b), L. Giannone a), P. Grigull a), K. Idab), J. Kisslinger a), A.
Komori b), R. König a), LHD experimental group b), S. Masuzaki b), K. McCormick a), J. Miyazawa b), T.
Morisaki b), S. Morita b), O. Motojima b), Y. Nakamura b), K. Narihara b), N. Ohyabu b), B.J. Peterson b),
F. Sardei a), K. Sato b), M. Shoji b), N. Tamura b), H. Thomsen a), M. Tokitani b), F. Wagner a), U. Wenzela), H. Yamada b), I. Yamada b)a)

Max-Planck-Institut für Plasmaphysik, Euratom Association, Germanyb)
National Institute for Fusion Science, Toki, Japan

Using the W7-AS island divertor and the helical divertor in LHD as examples, the paper presents a comparative divertor
transport study, aiming at identifying the essential differences and similarities in divertor function between two typical helicaldevices of different size and divertor concept. Investigated are the impacts of specific field and divertor topologies on plasma,
impurity and neutral transport. Topics addressed are neutral screening, impurity retention, thermal power removal via impurity line
radiation, detachment and Marfes. Special attention is paid to the SOL screening effect on intrinsically-released impurities, aspredicted by the EMC3/EIRENE code for both divertors. The conditions for realizing the impurity-screening regime in the SOL
are analyzed and its role in achieving high-density plasmas in helical devices is assessed. Discussion is guided by EMC3/EIRENE
simulations. Key physics issues are compared with experimental results.

Keywords: W7-AS, LHD, EMC3-EIRENE, Divertor, SOL transport, Impurity screening, Detachment

1. Inroduction
Unlike the standard poloidal-field divertor intokamaks, divertor concepts presently investigated instellarators are based on specific edge magnetic fieldstructures intrinsically available in each device [1].
Typical examples are the island divertor for the advanced
low-shear stellarators W7-AS [2] and W7-X [3], and thehelical divertor for the high-shear, largest heliotron-typedevice LHD [4]. The former utilizes the divertor potential
of inherent edge magnetic islands while the latter is basedon a stochastic field resulting from island overlapping. In
view of the large differences in field and divertor
geometry among helical devices, it is interesting to see
whether there exist certain common physics issues interms of divertor transport or divertor functionality.
Recently a collaboration work between IPP and NIFS wasstarted for this purpose and the paper presents acomparative divertor transport study for the island
divertor (ID) in W7-AS and the helical divertor (HD) in
LHD. Discussion throughout this paper is guided by
EMC3[5]-EIRENE[6] simulations. Topics addressed areparticle flux enhancement, neutral screening, impurity
retention, impurity radiation and detachment, as alreadyextensively studied for the W7-AS ID (see e.g [7]). They
are also the important basic elements of a divertor whiche-mail: feng@ipp.mpg.deneed to be firstly investigated and understood especiallyfor a divertor concept based on a complex 3D fieldstructure like the ID in W7-AS and the HD in LHD. In
particular, the paper is concentrated on understanding theelementary, global transport processes associated with thespecific field topologies, aiming at forming a comparison
basis for two typical helical devices of completely
different divertor concept and geometry.
2. Divertor and field topology
W7-AS is a low-shear stellarator having a fivefold field symmetry. The low-shear in W7-AS favors
large island formation as the radial size of the islands
scales as ri ∝Rbmn / nι' where R is major radius,

bmn the resonant radial perturbation field normalized tothe toroidal field, n the poloidal mode number and ι´ theshear. Within the operational ι-range (0.3~0.7), a numberof low-order islands of different poloidal mode numbers
are available at the edge. The extensively-explored, socalled standard divertor configuration is based on the 5/9
island chain, which is shown in Figure 1. Two up/downsymmetric divertor modules are installed at the ellipticalplane of each field period, with five identical divertor
module pairs covering the whole torus. The divertor
plates are discontinuous due to technical reasons. EachProceedings of ITC/ISHW2007•••

Fig. 2 Field and divertor geometry of the helicaldivertor in LHD.

Fig.1 Standard W7-AS island divertor configuration:
Nine islands are formed at the edge of the 5/9
configuration. A divertor module pair is
up/down-symmetrically installed on theelliptical cross-section.

to behave diffusively [9]. In reality, however, thin open
surfaces have been identified to exist within the outer,strong island-overlapping region in LHD [4]. In theoutermost region close to the wall, the increased poloidal
field components of the two helical coils form a
configuration similar to the double-null configuration in
tokamaks, as shown in figure 2. Graphite targets cut thefour divertor legs at the position just before theirtermination on the wall. The large poloidal component of
the field along the divertor legs result in short connection
lengths (~2 m on average) from the X-points to thetargets [10]. Thus, the divertor legs are optically thin for
the recycling neutrals, especially for the presently-open
divertor structure.

target plate toroidally extends over 18 degrees andpoloidally cuts two islands in order to increase thedeposition area. The baffles prevent the recycling neutrals
from escaping from the divertor region towards the
midplane where the magnetic islands are radially strongly
compressed and optically thin for the recycling neutrals.
The island size and the internal field-line pitch can be
adjusted externally by ten control coils.
LHD is the largest heliotron-type device with 10
field periods. In contrast to W7-AS, LHD has a large
shear, especially at the edge. The rotational transform in
the edge region of the helical divertor configuration
covers countless resonances which overlap each other,
forming a stochastic layer of ~10 cm thickness. Unlike
the single island chain in W7-AS, the stochastic SOL in
LHD exhibits a complex field structure characterized bycoexistence of remnant magnetic islands, stochastic fields
and edge surface layers. Deep in the SOL, the moderate
shear does not destroy the low-order islands completely,
so that closed island surfaces still exist in limited regions
around the O-points. Moving outwards, the shear
increases quickly, leading to stronger island overlap. The
remnant island cores become smaller and eventuallydisappear. In this case, the Chirikov parameter [8] should
largely exceed unity and the field lines are then expected

2. Basic common transport features
Plasma transport in the island SOL of W7-AS canwell be explained in terms of regular magnetic islands [7].
In order to clarify to what extent the plasma transport
follows the complex field structure in LHD,
EMC3/EIRENE simulations have been performed [10,11]. In the following, we make a transport analysis basedon figure 3, starting with the field topology shown in thelower picture. The 10/8 island chain has a quasi-closed
island structure, which is clearly shown by the Poincareplots. Starting from the 10/7 island chain, the field lines
in the most region become irregular, with small islandcores, however, remaining in the 10/7 and 10/6 island
chains. Moving outwards, closed island cores vanish andPoincare-plots show a strong irregularity of the field lines,
thus indicating that the field is highly stochastic. On theother hand, the underlying connection length contour
plots show a strong field-line correlation even in the outerregion without remnant island cores. The connection
length contour reflects actually the basic field structure of
low-order resonances. Indeed, all the low-order modes
expected within the give ι-range can be identified. Thisstrong field-line correlation contradicts obviously the
diffusive behavior of field lines characterized by•Proceedings of ITC/ISHW2007

Thomson* EMC3-EIRENE

Inboardmidplane
10/6

10/8

poloidalRadialloutboard
midplaneFig.3 Comparison of Te-profiles between simulations
and Thomson measurements (upper) and aradially-zoomed connection length contourwith an overlying Poincare plot (lower) overhalf poloidal field period at a toroidal location
as shown in figure 2. The three dot-dashed lines
indicate the 10/6, 10/7 and 10/8 island chains
which have remnant closed island cores.
ergodicity. The upper picture of figure 3 shows thecalculated and measured (Thomson) Te-profiles along theinboard midplane at a φ-position where the long axis of
the elliptical plasma cross-section lies horizontally, as
shown in figure 2. Both the code and Thomson results
show clearly the impact of the low-order 10/7, 10/5 and10/3 magnetic islands on electron energy transport. The
10/8, 10/6 and 10/4 mode structures have a poloidallyshifted phase distribution, with the X-points being on the
midplane. This is reason why they are not reflected by the
Te-profiles. In addition, the code shows a strong
correlation of parallel plasma flows with the island
structure where positive and negative flows surround the
O-points [11]. Even for the mode structures without aclosed island core, flow channels residing on the island
chains are still identifiable. Thus, it is to conclude that theplasma transport in the stochastic layer is governed by the
low-order islands, although the relative importance of thestochastic effects can not yet be quantified.
Particle transport along field lines is governed by aclassical convective process, with the parallel flow
velocity being determined by momentum balance.
Momentum transport in both W7-AS and LHD divertor
configurations is characterized by friction between
opposite flows in different parts of the magnetic islands
which gives rise to significant momentum loss andthereby breaks up the pressure conservation along open
field lines already under low-density, high-temperature
conditions without intensive plasma-neutral interaction.
This can be understood qualitatively by the followingpressure balance equation:()

p 1 + M 2 = 2 p up − mD ∫

nVII
∆2⊥

dl

(1)

where p is the total thermal pressure of ions and electrons,
M the Mach number and the subscript ‘up’ indicates
upstream. The last term on the right side of eq. (1)represents the frictional momentum loss between
opposite flows separated by a characteristic perpendiculardistance of ∆⊥. D is the diffusivity. The integration is
performed along field lines from upstream down totargets. This term is relevant for W7-AS and LHD
because of the small ∆⊥ and the long integration(connection) length. In W7-AS, interaction between
opposite flows happens in both poloidal and radial
directions [7], while in LHD radial approach of counterflows residing on neighboring island chains is the main
reason for flow damping [10,11].
As a consequence, a high recycling regime as
observed in tokamaks does not take place in theisland/stochastic SOLs of W7-AS and LHD. Target
Langmuir probes show, in consistence with Ha-signals,
typically a roughly-linear dependence of ion saturation
currents on the upstream (defined at the LCFS in thepresented analysis) density up to a rollover point, as

Fig. 4 Ion saturation currents increase linearly withplasma density. This linear-dependence canwell be reproduced by the 3D code,
independent on the D-ansatz.

Proceedings of ITC/ISHW2007
10
Total Fe yield / a.u.

shown in figure 4 for LHD. This linear behavior can bewell reproduced by the EMC3/EIRENE code, insensitive
to the selected D-ansatz. Nevertheless, the use of aconstant D results in an ion flow slope matching betterthat of Isat from the probes. Similar results are found in
W7-AS, as shown in figure 5 where the calculated
average downstream density ned is compared with those11

to detach.

nLCMS /1019 m-3

10

Fig.7 Calculated Fe-prodution rate as a functionof nLCMS in LHD.

Fig.5 Absence of a high recycling regime in W7AS, predicted by the EMC3 code (left) andconfirmed by experiments (right).
from target probes of different peak locations. There is noevidence for a high recycling regime characterized by astrongly-nonlinear increase of ned with the upstream
density nes.
2. SOL screening effects on CX-neutrals and intrinsic
impurities
Both the ID in W7-AS and the HD in LHD have an
open divertor structure and the first wall is made ofstainless steel. High-energetic CX-neutrals hitting thewall is a potential source producing impurities by mainsofphysicalsputtering.
An
optically-thickTotal Fe production rate / 1019 /s

5
D=0.5 m2/s, peaked ne-profile
D~1/nes, peaked ne-profile
D=0.5 m2/s, flat ne-profile
D~1/nes, flat ne-profile

4

3

2

1

0

0

2

nes / 1019 m-3

4

6

Fig.6 Sensitivities of high-energetic CX-neutrals tocore profiles and cross-field transportcoefficients as well as separatrix density,
calculated by ECM3-EIRENE for W7-AS.

island/stochastic SOL can move the CX-neutrals to alower energy band in the energy spectrum and thereby

reduce the sputtering-relevant neutral flux. For a given
input power entering the SOL, the SOL temperaturedrops with increasing the SOL density, especially at thedownstream of maximum population of the recycling
neutrals. Figures 6 and 7 show respectively the total Fe
yield sputtered by CX-neutrals for W7-AS and LHD.
Because of the existing uncertainties in wall conditioning,
the Fe yield shown here should be regarded as a physics
quantity for measuring the sputtering-relevant, highenergetic CX-neutral flux, rather than an absolute ironproduction. For both W7-AS and LHD, the 3D code
simulation results show that a dense, coldisland/stochastic SOL can effectively reduce the highenergetic CX-neutral flux and thereby the related Fe
sputtering yield.
3. SOL impurity transport and retention
Although, as shown in the previous section, a highdensity SOL moderates the physical sputtering process of
CX-neutrals on plasma-facing components, high-Z
impurities like the wall-released Fe can, even with areduced source, cause significant radiation loss if theyreach the confinement core region, preventing plasma
from a high density operation. EMC3/EIRENE code has
predicted that, under enhanced recycling conditions, theedge islands in W7-AS have a retention effect on intrinsic
impurities [12]. Similar retention effect has been also
predicted for the stochastic layer in LHD. Using the
intrinsic carbon as test impurities, figures 8 and 9 show
how the carbon impurity density distribution changes
from peaked to hollow profiles with increasing the SOL
density. Parallel-force balance analysis based on the 3D
simulations shows that the net force acting on impurities
can be, with increasing the SOL density, changed fromthermal-force dominating to friction dominating, leading
to a reversal of the convective impurity flow fromProceedings of ITC/ISHW2007
inwards- to outwards-directed [7, 12]. This is the reason
for the carbon density profile change with the SOL
density, as shown in figures 8 and 9 for W7-AS and LHD.
The reduction of the dominating ion thermal force
under high SOL-density conditions are attributed to thesignificant contribution of the cross-field heat conduction
to the energy transport in the island SOLs because of thesmall divertor-relevant field-line pitch in both W7-ASa) nes = 1.5 x 1019 m-3b) nes =5.0 x 1019

Fig. 8 Island retention effect on intrinsic impurities
predicted for W7-AS.

nLCMS=2×1019 m-3

A separation between core and SOL transports of
intrinsic impurities has been recently realized
experimentally in LHD by observing the relative changes
in radiation intensity among different ionization stages of
the intrinsic carbon impurities [13]. Carbon impurities ofdifferent ionization stages are populated in different
depths of SOL and the radiation ratio between low andhigh ionization stages reflects the profile form of carbon
density. Observed was a sharp decrease in the radiation
ratio of high- to low-ionization stages at a SOL density
roughly consistent with the code-predicted one, thus
confirming the code prediction of SOL impurity retention.
4. Stability of detached plasmas
Detachment has been achieved in both devices atvery high SOL densities. However, stabilizing a detachedplasma turned out to be difficult. In W7-AS, stabledetachment is always partial and restricted to large islandand field-line pitch configurations. Configurations withsmall islands or field line pitch will drive detachedplasmas immediately into an unstable stable, with an
unstable, Marfe-like radiation inside the LCFS. In LHD, astable partial detachment remains still a challenge and aquasi-stable complete detachment leads always to astrong degradation of the global energy confinement due
to the location of a rotating radiation belt inside the LCFS.
These experimental observations motivated detailed
numerical studies in order to understand the underlying
mechanisms driving instability. It is found numericallythat the radiation distribution is highly sensitive to the

4×1019 m-3

Fig. 9 Similar impurity retention effect predictedalso for the stochastic layer of LHD.
and LHD. Because of the high sensitivity of the parallel
heat conductivity to the ion temperature, it can be shown
that, for a given input power, there exists a threshold SOL
density above which the ion thermal force can beswitched off and friction becomes dominating [7]. This isconsistent with the experimental observations in bothdevices where Fe-radiation originating from core drops
sharply once the plasma density is raised above athreshold density. It should be mentioned that here, apossible, still-unknown core transport mechanism setting
in at high collisionallities to flush impurities could not yet
be completely excluded.

Fig. 10 Inboard side radiation (left) or divertor
rediation (right), depending on the island
geometry.
island geometry. For the island configurations in whichstable detachment is established in W7-AS experiments,

Proceedings of ITC/ISHW2007
the 3D code shows a radiation belt formed on the inboard

Fig. 11 Radiation prefers remnant island cores.
side (see figure 10). For small islands or field line pitch,radiation is located at the X-point in the recycling region,
as shown in figure 10, leading to a strong reduction of theisland neutral screening efficiency in comparison to theinboard side radiation case. A linear stability analysis
shows that the loss of neutral screening could be thereason for the detachment instability observed inexperiments [14]. For the stochastic layer in LHD, the 3D
code predicts that remnant island cores attract radiation.
Converged numerical solution is found when theradiation layer touches the 10/6 and 10/7 island chains
which have small closed island cores, as shown in figure
11. Till to now, such radiation patterns could not yet bestabilized in LHD experiments. One of the possible
reasons for the discrepancy, as for the divertor radiation
pattern in W7-AS, is that the SOL power, which is fixedin simulations, should decrease in experiments due to theincreased code density resulting from recycling neutrals
after the detachment transition. The stability analysis
made for W7-AS [14] should also be valid for the LHD
case. More detailed analysis is left for further.

flows cause significant momentum loss of the streaming
ions, being the reason for the absence of a high recycling
regime in both devices. It is numerically shown that adense, cold island SOL shifts the CX-neutrals to low
energy range and reduces the physical sputtering yield on
plasma facing components. Benefiting from geometricadvantage of the small effective field-line pitch in theislands, the parallel ion heat conductive flux can be,
under high density, low temperature conditions, strongly
reduced by the perpendicular one, resulting in a strong
reduction of the related thermal force. Conditions forachieving a purely friction-dominated impurity transport
regime are predicted by the 3D code for both W7-AS and
LHD. Consistent with the code predictions, both W7-AS
and LHD experiments show a sharp drop in Fe radiationfrom core when plasma density exceeds a threshold value.
The correlation and relevance of the observations to thepredicted impurity retention effect of the SOL will bechecked further by isolating the SOL transport from coreeffects. The strong reduction of high-Z impurity
concentration in the core extends the plasma to rather
high densities until detachment sets in due to intensive
carbon radiation. Stable partial detachment can beestablished in W7-AS through careful choice of the island
configuration, while in LHD it is not yet successful tostabilize the radiation layer outside the confinement
region. 3D simulations suggest that loss of the SOL
neutral screening efficiency after detachment transition
prevents the radiation layer from being stopped in the
SOL. More detailed analysis on this issue is under way.
References[1] R. König et al., PPCF 44, 2365 (2002)[2] P. Grigull et al., PPCF 43, A175 (2001)[3] H. Renner et al., Nucl. Fusion 40, 1083 (2000)[4] N. Ohyabu et al., Nucl. Fusion 34, 387 (1994)[5] Y. Feng et al., J. Nucl. Mat. 266-269, 812 (1999)

5. Conclusions
Low-order magnetic islands are the basic
elements forming helical SOLs of the divertor
configurations in both W7-AS and LHD. Although thelarge shear in LHD leads to overlapping of multi-island
chains, the basic island structures of the low-order modes
are not destroyed completely to allow really a diffusive
approximation of field-line trajectories. EMC3-EIRENE
simulations show that the SOL transport in both devices
is governed by the low-order islands, which is supportedby Thomson Te-measurements in LHD. Counter plasma
flows reside in different parts of the islands chains.
Viscous transport due to spatial approach of the counter[6] D. Reiter, Fusion Sci. Technol. 47, 172-86 (2005)[7] Y. Feng et al., Nucl. Fusion 46, 807 (2006)[8] B. V. Chirikov B. V. , Phys. Rep. 52, 265 (1960)[9] M. N. Rosenbluth et al., Nucl. Fusion 6, 297 (1996)[10] M. Kobayashi et al., J. Nucl. Mater. 363-365, 294 (2007)[11] Y. Feng et al., “Fluid features of the stochastic layertransport in LHD”, to be published in Nucl. Fusion, (2007)[12] Y. Feng et al., 32nd EPS, vol 29C (ECA), P1.012 (2005)[13] M. Kobayashi et al., this conference[14] Y. Feng et al., Nucl. Fusion 45, 89 (2005)