Proceedings of ITC/ISHW2007

The DED at TEXTOR: transport and topological properties of ahelical divertor
M. Lehnen1) , S. Abdullaev1) , S. Brezinsek1) , M. Clever1) , J.W. Coenen1) , K.H. Finken1) ,M. von Hellermann2) , M.W. Jakubowski3) , D. Reiter1) , U. Samm1) , D. Schega1) , O. Schmitz1) ,H. Stoschus1) , B. Unterberg1) and the TEXTOR team1)

Institut für Plasmaphysik, Forschungszentrum Jülich GmbH, EURATOM Association,
Trilateral Euregio Cluster, D-52425 Jülich, Germany
2)
FOM-Institute for Plasma Physics Rijnhuizen, Association EURATOM-FOM,Trilateral Euregio Cluster, The Netherlands, www.rijnh.nl3)
Max-Planck-Institut für Plasmaphysik, IPP-EURATOM Association, Teilinstitut Greifswald, Wendelsteinstr. 1, 17491
Greifswald, Germany
The topological and transport properties in the edge plasma of the dynamic ergodic divertor is studied toclarify the functionality of this type of helical divertor. The heat and particle fluxes at the DED target plates weremeasured with Langmuir probes. Peak fluxes are found where field lines end, which penetrate deep into theplasma. The comparison of the measured target profiles to the magnetic topology shows, that heat and particles
are mainly transported to the target plates via flux tubes of short connection length. About 65% of the fluxes arefound in areas, where field lines with a connection length of 1-2 poloidal turns connect to the target. Analysis of
the source distribution shows, that about 40% of the ion sources lie inside the downstream area of the divertor.
The high fraction of convective heat flux prevents from establishing high recycling in the divertor for the pulse
type discussed here.
Keywords: TEXTOR, stochastic plasmas, divertor
4/2

Introduction
The aim of this paper is to quantify the particle andpower exhaust capabilities of the dynamic ergodic divertor (DED) at TEXTOR. The DED is a helical type of divertor with an open structure, comparable to the ergodic
divertor in ToreSupra [1] . Such a divertor has topological similarities to helical or island divertors in heliotrons[2] or stellarators [3]. The ergodic divertor, existing of 16
helical coils at the HFS of TEXTOR, generates a resonant
magnetic perturbation which focuses the particle and heat
flux onto divertor target plates. In contrast to a poloidal divertor with a clear boundary between scrape-off layer andconfined plasma, the above mentioned divertor types havea region with magnetic islands in the edge layer. By island
overlap, this area turns (partly) into an ergodic layer.
Topology
The magnetic topology of the DED is determined by
the position of the resonant surfaces (surfaces with low rational safety factor) and the base mode of the divertor coilcurrent distribution [4]. Three base modes can be chosenwith poloidal/toroidal mode numbers of m/n = 3/1, 6/2
and 12/4. The spectrum of the m/n = 6/2 perturbation
field is given in figure 1. Depending on the base mode,
2, 4 or 8 helical strike zones appear on the divertor target. An example of the target footprint for m/n = 6/2 isauthor’s e-mail: m.lehnen@fz-juelich.de5/2

6/2 7/2
1.0vtor [10km/s]

fscreen

0.5

0.0

Fig. 1 Spectrum of the perturbation field Bm2 [T] for m/n = 6/2.
The white dashed line indicates the position of the resonances. The gray rectangles give the screening factor fora typical edge rotation.

given in figure 2. The colors indicate the penetration depthof the field lines. Peak particle and heat fluxes are foundwhere field lines of long connection length hit the target.
This is caused by the deep penetration of these field lines
up to the last closed flux surface (LCFS). Flux tubes of
one poloidal turn length are positioned further away fromthe LCFS [5, 6, 7]. They are filled by diffusion and cantake a substantial part of the particle and heat to the target.
The target structure is sensitive to the plasma equilibrium,Proceedings of ITC/ISHW2007
penetration depth [m]
220.
0.1

targetLc [p.t.]

0.08
200.
0.06

1800.04
160.

0.02
0

#99504

1400

100

200.

300

Fig. 2 Map of the penetration depth of field lines starting on theDED target. The white circles indicate the position of thetarget Langmuir probes.

e.g. edge safety factor, plasma beta and plasma position.
Moreover, plasma rotation can lead to screening currents,
reducing the perturbation at the resonances [8, 9]. An example for a screening factor is indicated in figure 1; thetoroidal rotation increases from about 1 km/s at the LCFS
up to 10 km/s in the plasma center. The screening is relatively weak at the very edge, because of low plasma rotation and low temperature. Towards the plasma center, thescreening increases. Thus the magnetic topology calculated usually for the vacuum case is valid for the outermost
resonance layers. However, further inside, the size of theislands shrinks with higher plasma rotation and the widthof the ergodic area is affected. In the following we concentrate on a pulse with m/n = 6/2, qa = 3.6, β ≈ 0.45 andthe horizontal position off-center by 2 − 5 cm towards theHFS to ensure particle recycling only at the divertor target
plates.
A poloidal cut through the magnetic structure at φ =180◦ is given in figure 3 for full perturbation field. This
plot shows the connection length of the field lines fromtarget to target as a function of poloidal angle and radius.
A strong intermixture between field line bundles of longand short connection length exists. The particles and heatare guided to the target along complex structures of about
15 cm width in poloidal direction, when touching the target. It is remarkable, that the wetted area is mainly defined by the topology rather than by transport properties(c.f. [10]). The field line bundles with short connection
length of less than 5 poloidal turns constitute the so calledlaminar area of about 7 cm width in this example. The link
between last closed flux surface (LCFS) and this laminarregion is the ergodic area of about 4 cm width.
Target Loads
Figure 4 shows the particle and heat flux at the target measured by Langmuir probes which are indicated infigure 2. A full profile is achieved by sweeping the strike
point by ±22.5◦ in toroidal direction. This is possible withFig. 3 Connection length of the field lines passing the poloidal
plane in front of the target at φ = 180◦ . The strikelines are indicated in yellow. The black line indicates theboundary of the downstream area.

a coil current of 3.75 kA, which is half of the nominal
coil current. The discharge had a total heating power of
1.1 MW and a radiated power of 0.5 MW, thus the power
entering the edge layer Pedge is about 0.6 MW. The wetted area is, for the case shown here, A = 2.4m2 . The
radial decay of heat and particle flux is mapped on thepoloidal coordinate on the target with an expansion ofabout 2. From the probe measurements, we get an average parallel heat flux of about 20MWm−2 in the strike
point, which is consistent with a perpendicular heat fluxof Pedge /A ≈ 0.3MWm−2 , taking into account an average
pitch angle of about 0.8◦ at the target. Because of the veryshallow angle, slight misalignment of the target tiles leads
to a non-regular distribution of the heat along the strike
points in toroidal direction as seen by the infra-red camera [11]. However, the probes stick out by 2 mm (domeprobe with r = 2 mm) and are therefore less sensitive toflux shadowing.
Additionally to the fluxes, the connection length Lc
and also the penetration depth ∆r of the field lines is indicated in figure 4. The calculation was done by field line
mapping. To fit the target profiles best, a slight deviationfrom the experimental settings had to be chosen: a 5 kA
higher plasma current (less than 2% higher than the measured current) and a 6◦ shift in toroidal direction. With
this, the best fit of the strike point separation and toroidal
position is achieved. Such adaptations are justified, taking into account the measurement errors on the dischargeparameter and the uncertainties in the safety factor profile assumed for the field line mapping. Additionally, theprobe has a radial extent of 2 mm, giving an uncertainty intoroidal direction of about 10 cm.
The area with Lc < 1 poloidal turn (p.t.) is equivalent to the private flux region. In this area almost no flux isreaching the divertor. About 65% of the particle and heat
flux is transported to the target plates via flux tubes with 1or 2 poloidal turns (Lc = 40 − 80 m). The magnitude of theProceedings of ITC/ISHW2007
ure 5. Flux in the private flux region (Lc < 8m) is indicated in blue, flux in the laminar field line bundles with
Lc = 40 − 80m are given in red and green are the datapoints for Lc > 2p.t.. From these profiles, e-folding lengths
can be estimated. For this analysis the toroidal range withφ < 250◦ was chosen, because of the large fraction of shortflux tubes. The e-folding lengths in the PFR is small, because of the short connection length: λΓ = 3.5 ± 0.4 mm
and λq = 2.4 ± 0.2 mm for particle and heat flux. In thelaminar flux bundles, these values are significant higher:λΓ = (28±4) mm and λq = (16±2) mm. The ratio between
the e-folding lengths of PFR and flux tubes corresponds tothe ratio of the connection lengths. Furthermore, the efolding length of the electron density and temperature canbe estimated to be λT = 38 ± 18 mm and λn = 45 ± 23 mm.
Exploiting the relation between λn /λT and χ/D [14],!
!
γe
λn 5 χ λn= 1++,(1)
1 − fconv
λT 2 D λT
Fig. 4 Particle flux on the target along the toroidal direction.
The red curve gives the field line penetration depth in[10−2 m] (right axis) and the blue curve the connection
length from target to target in poloidal turns (right axis).

heat and particle flux depends on the penetration depth of
the field lines with peak fluxes at field lines with deep radial penetration (c.f. [12, 13]). Those field lines are closest
to the LCFS. The thickness of the perturbed edge layer andthus the maximum ∆r is about 11 cm. The field lines withshort connection length penetrate about 4 cm towards theLCFS. Only after many poloidal turns the field lines reachthe innermost ergodised island chain and are thus close to
the LCFS. However, the peak flux at the target for thesefield lines is not larger than that of the laminar field lines.
The information of the field line penetration in addition to the toroidal profiles of the fluxes can be used
to reconstruct radial profiles of parallel heat and particle
flux. The increase of the fluxes with ∆r is shown in fig-Fig. 5 Particle and heat flux as function of the radial field line
penetration.

we can estimate the fraction of convective heat flux fconv tobe about 0.6 (assuming χ/D = 3).
Particle Recycling
The DED is an open divertor and the recycling neutrals can penetrate deep into the edge plasma by by-passing
the high temperature and high density areas. However,in comparison to the helical divertor in an heliotron device like LHD [2], the divertor legs are broad and theirradial extent is much smaller. Important for a high recycling divertor and for impurity screening is the closure of
the divertor by localised recycling in the divertor chamber.
The transition from divertor chamber to ergodic area in theDED can not be attributed to a distinct radial position. Thiscan be seen from figure 3, giving the connection length offield lines in front of the DED target at a toroidal angleof 180◦ . One finds a complex mixture of different typesof field lines. Field lines with long connection length cancome close to the target plates, but connect to these only
after they passed again several times the divertor coils (redareas). Thus, neutrals can penetrate into these flux bundles
at an upstream position. The downstream area of the divertor comprises all field lines connecting within less than
one poloidal turn to the target. This definition is equivalent to that of a poloidal divertor. This downstream area isindicated by the black line in figure 3.
The radial extent of the downstream area in the 6/2
base mode is at maximum 7 cm and varies, depending on
the DED current and the edge safety factor. Local divertor
recycling is established, when all the particle sources arelocated in the downstream region. A parameter reflecting
the divertor recycling fraction is the ration between downstream sources Qdown and total source Qtot , which equals
the incoming flux, if no wall retention is assumed. In theexperiment, Qdown is measured as the Halpha line emission
integrated over the downstream area and Qtot is the total
emission in front of the target. The distribution of the Hα

Proceedings of ITC/ISHW2007
emission is shown in figure 6, together with a contour plotof the shortest connection length to the target. Field lines,
which have to pass the divertor target again before they end
on the target plates, belong to the upstream area. Sourcesin these field lines contribute to convective flux to the divertor.
The ratio between downstream D+ sources and total D+ source strength, Qdown /Qtot , reaches values of up
to 50% [15]. The fraction of the sources in the downstream area of the flux tubes with 1 − 2 p.t. is about
25%. Assuming that Qtot = Γtot , we get for these flux
1,2
= 0.4. Thus about 60% of the heat flux
tubes Q1,2
down /Γ
is transported convectively to the target in these flux tubes.
Keeping in mind, that these are rough estimates, we find agood agreement with the above estimate from the e-folding
lengths.
The accessibility of a high recycling regime can be assessed by including the convective heat flux into the twopoint model:
qk = −κ0 T 5/2∂T
1+ ( mv2k + 5eT )Γk .
∂x2.
target.

.

.

Fig. 6 Magnetic structure in front of the DED target: shortest
connection length to the divertor target. The contour
lines indicate the intensity of the Hα radiation.
fconv = 02

qt = 30MW/m
2
qt = 5MW/m

fconv = 0.3(2)
fconv = 0.6

Neglecting the kinetic term and assuming that∂Γ0Γk = fconv,∂x
Lc

Lc [p.t.](3)

the heat flux equation ∂qk /∂x = qk,t /Lc can be solved. Figure 7 shows the temperature drop towards the target asfunction of the particle flux to the target. For the conditions of the pulse type discussed here ( fconv = 0.6 andq peak = 30MWm−2 ), no temperature gradient can build up.
Would a high recycling DED for this configuration be possible? Because of the density limit, the particle flux can
not exceed 1024 m−2 s−1 significantly. Thus the access tohigh recycling needs a reduction of convective heat flux aswell as a reduction of the power entering the edge layer.
The latter could be achieved for example by higher radiation through impurity seeding. The absence of a high recycling regime has also be found in the helical divertor and in
the island divertor. In the former case, because of the same
reasons found for the DED, too high convective fluxes [16],and in the latter case, because of the significant role of thecross field transport inside the island [17].
Conclusions
The heat and particle fluxes at the DED target plates
were measured with Langmuir probes. Peak fluxes arefound where field lines end, which penetrate deep into theplasma. The comparison of the measured target profiles tothe magnetic topology shows, that heat and particles aremainly transported to the target plates via flux tubes ofshort connection length. About 65% of the fluxes are foundin areas, where field lines with a connection length of 1-2
poloidal turns connect to the target. Analysis of the source
distribution shows, that about 40% of the ion sources lie
inside the downstream area of the divertor. The high frac-GFig. 7 Temperature ratio between target und upstream position
as function of the target particle flux. The green line indicates the peak particle flux for pulse #99504.

tion of convective heat flux prevents from establishing highrecycling in the divertor for the pulse type discussed here.
[1] Ph. Ghendrih et al, Nucl. Fusion 42 (2002) 1221.
[2] T. Morisaki et al., J. Nucl. Mater. 337-339 (2005) 154[3] R. König et al., Plasma Phys. Control. Fusion 44 (2002) 2365
[4] K.H. Finken et al., The structure of magnetic field in theTEXTOR-DED, Schriften des Forschungszentrum Jülich,Energy Technology 45, ISSN 1433-5522 (2005)[5] Th. Eich, D. Reiser and K.H. Finken, J. Nucl. Mater. 290293 (2001) 849[6] M. Lehnen et al. , Plasma Phys. Control. Fusion 47 (2005)
B237[7] O. Schmitz et al., J. Nucl. Mater. 363-365 (2007) 680[8] A. Cole and R. Fitzpatrick, Phys. Plasmas 13 (2006) 032503[9] Parail V. et al, Proc. 21st Int. Conf. Fusion Energy 2006
(Chengdu) (Vienna: IAEA) CD-ROM TP/P8-5[10] S. Masuzaki et al., Nucl. Fusion 42 (2002) 750[11] M.W. Jakubowski et al., J. Nucl. Mater. 337-339 (2004) 176[12] M.W. Jakubowski et al., Plasma Phys. Control. Fusion 49(2007) S109
[13] F. Nguyen et al., Nucl. Fusion 37 (1997) 743[14] M. Lehnen et al., Nucl. Fusion 43 (2003) 168178[15] M. Lehnen et al., J. Nucl. Mater. 363-365 (2007) 377[16] M. Kobayashi et al., J. Nucl. Mater. 363-365 (2007) 294[17] Y. Feng et al., Nucl. Fusion 46 (2006) 807