The effect of the magnetic topology on particle recycling in the ergodic divertor of TEXTOR

Abstract

The influence of the divertor geometry of the dynamic ergodic divertor (DED) in TEXTOR on particle recycling is discussed. The geometry can be varied by the choice of the base mode, the edge safety factor and the divertor coil current. The divertor volume is split into the upstream and the downstream area. Strong plasma flows in the downstream area, essential for high screening efficiency, are predicted. The source strength of deuterium and carbon in the downstream area is estimated by using the two-dimensional distribution of D a and CIII emission in front of the target. The results are compared to EMC3 and ERO-code calculations.

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The effect of the magnetic topology on particle recycling in
the ergodic divertor of TEXTOR
M. Lehnena,*, S.S. Abdullaeva, S. Brezinseka, K.H. Finkena, D. Hartinga,
M. von Hellermannb, M.W. Jakubowskia, R. Jaspersb, A. Kirschnera,
A. Pospieszczyka, D. Reitera, U. Samma, O. Schmitza, G. Sergienkoa,
B. Unterberga, R. Wolfa, The TEXTOR Team
aInstitut fu ¨r Plasmaphysik, Forschungszentrum Ju ¨lich, Association EURATOM-FZJ, Germany1
bFOM-Rijnhuizen, Association EURATOM-FOM, The Netherlands2
Abstract
The influence of the divertor geometry of the dynamic ergodic divertor (DED) in TEXTOR on particle recycling is
discussed. The geometry can be varied by the choice of the base mode, the edge safety factor and the divertor coil current.
The divertor volume is split into the upstream and the downstream area. Strong plasma flows in the downstream area,
essential for high screening efficiency, are predicted. The source strength of deuterium and carbon in the downstream area
is estimated by using the two-dimensional distribution of Daand CIII emission in front of the target. The results are
compared to EMC3 and ERO-code calculations.
? 2007 Elsevier B.V. All rights reserved.
PACS: 52.55; 52.25; 52.40
Keywords: Divertor; Edge plasma; Stochastic boundary; Textor
1. Introduction
In this paper, the influence of the DED divertor
geometry on the particle recycling behaviour is dis-
cussed. Especially the radial extent of the divertor
volume with respect to the mean free path of neu-
trals plays an important role for the control of the
recycling in a divertor. Such a control is essential
to achieve divertor regimes like high-recycling and
improve the impurity screening in the divertor.
These properties were first studied in limiter and
poloidal divertor machines. More recently these
studies were also intensified for helical, island and
ergodic divertor geometries [1–4]. The higher com-
plexity of these configurations makes the analysis
more challenging.
The ergodic divertor at TEXTOR generates a
resonant magnetic perturbation which focuses the
0022-3115/$ - see front matter ? 2007 Elsevier B.V. All rights reserved.
doi:10.1016/j.jnucmat.2007.01.125
*Corresponding author. Tel.: +49 2461 615102; fax: +49 2461
615452.
E-mail address: m.lehnen@fz-juelich.de (M. Lehnen).
1www.fz-juelich.de/ipp.
2www.rijnh.nl.
Journal of Nuclear Materials 363–365 (2007) 377–381
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particle flux on the divertor target plates at the high
field side. The magnetic topology is determined by
the position of the resonant surfaces (surfaces with
low rational safety factor) and the base mode of
the divertor coil current distribution [5]. Three base
modes have been investigated with poloidal/toroidal
mode numbers of m/n = 3/1, 6/2 and 12/4. Depend-
ing on the base mode, 2, 4 or 8 strike zones appear
on the divertor target and neutrals penetrate radi-
ally into a complex structure consisting of flux bun-
dles with different connection lengths to the target.
An example for m/n = 6/2 is given in Fig. 1(a).
The target loading pattern is determined by the con-
nection length of the field lines hitting the target.
Peak particle and heat fluxes are found where 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 from the LCFS. They are filled by diffusion
and can take a substantial part of the particle and
heat to the target [6,7].
For the discussion of the particle recycling in the
divertor, the plasma flow plays an important role as
was shown for example for the ergodic divertor in
Tore Supra [8]. Also in poloidal divertors it is the
strong flow to the target that facilitates impurity
screening. For high screening efficiency, the extent
of the so-called ‘downstream area’ is of importance.
This area comprises all field lines, with their shortest
distance to the target less than one poloidal turn,
e.g. those field lines which do not pass the LFS
before they intersect the target (Fig. 1(b)). This def-
inition is in analogy to the downstream area in a
poloidal divertor. Within this area, high flow veloc-
ities towards the target are expected [6]. Fig. 2
shows an example for m/n = 6/2 calculated by the
three-dimensional fluid code EMC3 [7,9]. Indicated
is the boundary of the downstream area. The Mach
number is close to 1 in most of this area, whereas in
the upstream area stagnation is seen.
2. Source distribution
The aim of this work is to quantify the source
distribution for deuterium and carbon. We analyse
the radial and poloidal distribution of the Daand
CIII (465 nm) emission with respect to the magnetic
target
target
Lc[p.t.]
Fig. 1. m/n = 6/2 configuration with edge safety factor qa= 3.6. (a) Connection length giving the total length of the field lines in poloidal
turns (p.t.) from target to target. Field line tracing is stopped for Lc> 5. The black line indicates the boundary of the downstream area. (b)
Shortest distance along the field lines from the poloidal plane shown to the target plates. The downstream area (blue) consists of field lines
with shortest distance well beneath 0.3 p.t.
radius [m]
0.46
0.44
0.42
0.40
0.48
0.38
1.0
-1.0
-0.5
0.0
0.5
Mach number
poloidal angle [deg]
220140180
Fig. 2. m/n = 6/2 configuration: flow pattern in front of the DED
target calculated by EMC3-Eirene. The boundary of the down-
stream area is indicated by the black line.
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topology. The ratio between downstream sources
and total source, Qdown/Qtot, has been chosen as a
representative parameter describing the recycling
pattern. Qdownis defined as the line emission inte-
grated over the downstream area, Qtotis the total
emission in front of the target.
Fig. 3(a) shows the Daemission, Fig. 3(b) the
CIII emission in front of the target. The black line
indicates the boundary of the downstream area.
The discharge was heated by neutral beam injection
with a total input power of 1.55 MW. The plasma
current is IP= 315 kA, the toroidal field Bt=
1.9 T, resulting in qa= 3.6. The DED current is
7.5 kA, which is the maximum amplitude for
m/n = 6/2. The magnetic topology is that shown in
Fig. 1. For both species, the main plasma–wall
interaction zone is located between 160? and 215?.
The CIII pattern is influenced by the plasma param-
eters which are strongly modulated depending on
the field line connection length. The two thin fingers
connecting the ‘x-point’ at 184? to the target are
clearly seen on the emission pattern. This depen-
dence on the plasma parameters is used to identify
the predicted magnetic topology at the plasma
boundary [10,11].
The extent and structure of the downstream area
can be modified by the DED current, the safety fac-
tor and the base mode configuration. Fig. 4 shows
the ratio Qdown/Qtotas a function of the safety fac-
tor for the three different base modes. The electron
densities vary between 2 and 4 · 1019m?3. The total
heating power is about Ptot= 1.5 MW (3/1 and 6/2)
and Ptot= 0.8(2.4) MW (12/4). The DED coil cur-
rent is varying from 11.5 kA in 12/4 configuration
(77% of the nominal value) to 7.5 kA in 6/2
(100%) and 2.0 kA in 3/1 (53%). Restrictions arise
from technical reasons in 12/4 and from the thresh-
old for tearing mode excitation in 3/1 configuration
[12]. This excitation threshold limits the accessible
qarange in 3/1 and also in the 6/2 configuration.
The m/n = 12/4 base mode operation creates a
rather small scale magnetic structure, where flux
tubes of different connection length are interwoven
in front of the target plates. Most of the neutrals
penetrate into regions with field lines which travel
more than one poloidal turn until they reach the
target. The maximum radial extent of the down-
stream region is up to 25 mm which is 6% of the
plasma minor radius. For both species, D+and
C3+, we find that Qdown/Qtotis at maximum 30%
with a peak around the main resonance at qa= 3.0.
The m/n = 3/1 base mode operation leads to a
more coarse structure where flux bundles of differ-
ent connection length are well separated and the
downstream area is larger compared to the 12/4
target
intensity [a.u.]
minor radius [m]
poloidal angle [deg] poloidal angle [deg]
target
#99484#99484
Fig. 3. m/n = 6/2 configuration: Da(a) and CIII (b) emission pattern in front of the DED target.
[%]
96415, 96421, 97793, 99299, 99484, 99486
0.8MW
2.4MW
12/4
6/2
3/1
Fig. 4. Fraction of downstream emission for Daand CIII as
function of the edge safety factor. Lines are guide to the eye.
M. Lehnen et al. / Journal of Nuclear Materials 363–365 (2007) 377–381
379

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base mode. The radial extent of the downstream
area for IDED= 2 kA is up to 45 mm, which is
10% of the minor radius. In this operation mode
up to 45% of the D+and even more than 60% of
the C3+sources lie inside the downstream area.
The radial extent of the downstream area in the
6/2 base mode is up to 70 mm. Qdown/Qtotreaches
values of up to 75% for C3+and about 50% for
D+. When the safety factor is decreasing, the radial
extent of the downstream area increases and peaks
around qa= 3.0. Accordingly Qdown/Qtot shows
the same dependence.
The source distribution does not only depend on
the radial extent of the downstream area and the
radial penetration of the neutrals, but also on the
detailed topology in radial and poloidal direction.
For example, a large safety factor above 6.0 in the
case of the 6/2 configuration leads to a topology
where most of the particles penetrate into the
upstream area. Although the radial extent of the
downstream area is still significant, it overlaps
strongly with the private flux region with very low
source strength.
3. Interpretation by a simple ERO model
In the above analysis, we used the light emission
to quantify the source distribution. For Daemission
this is justified, because it reflects the D+source.
Since the C2+distribution is unknown, the radial
source distribution for C3+cannot easily be deduced
from the CIII emission. In order to justify Qdown/
Qtot as a parameter describing the screening effi-
ciency of the ergodic divertor, a simple model was
set-up using the ERO code [13]. The model divides
the perturbed plasma edge in front of the target into
two areas (Fig. 5): (a) the downstream area with
Mach number M = 1 at the target and a slow decay
in radial direction adapted to the EMC3 model
results; (b) the upstream area with M = 0. Area
(a) has a strong modulation of the plasma parame-
ters in poloidal direction with a peak temperature of
Ti= Te= 50 eV and a peak density of ne= 5 ·
1019m?3at the position of the strike point. The e-
folding length of the plasma parameters is assumed
to be 20 mm towards the private flux zone (area
around h = 180?) and 70 mm towards the DED-
SOL. These values are adapted from target probe
measurements [10]. The plasma parameters increase
linearly towards the boundary of the area (b), where
the plasma parameters are kept constant along the
poloidal direction and increase in radial direction
to approximate the experimental values.
Fig. 6 shows the relative downstream emission as
a function of the width of the downstream area
ddownfor the base mode m/n = 6/2. Increasing the
DED coil current leads to a broadening of that area.
Accordingly Qdown/Qtotincreases. This dependence
is well reproduced by the simple model. The screen-
ing efficiency is described in the model by the factor
fscreen, which is the ratio between carbon atoms/ions
redeposited on the target and the overall carbon
source at the wall. This factor is increased from
ddown= 0–50 mm by about 30%. It has to be noted
that the simplified magnetic geometry (all field lines
radial position [mm]
poloidal position [mm]
0
200
100
Te[eV]
I(CIII)[a.u.]
0
250
0 200
0
50
100
0 200
target target
Fig. 5. ERO model: temperature distribution in the model
volume (left). The temperature in the strike point and at the
boundary to the upstream area is 50 eV. The density has the same
distribution. Shown is an example for ddown= 50 mm CIII
emission as calculated by ERO (right).
1.0 kA
3.75 kA
7.5 kA
Fig. 6. Fraction of downstream emission for Daand CIII as
function of the width of the downstream region for the m/n = 6/2
configuration. The screening factor fscreenand Qdown/Qtotcalcu-
lated by the simple ERO model is added. Lines are guide to the
eye.
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in the volume are connected to the target) leads to a
statistical offset of fscreen= 50% at ddown= 0.
4. Conclusions
The ergodic divertor at TEXTOR can provide a
sufficiently broad divertor volume to screen impuri-
ties from the confined plasma. However, no strong
effect on the C6+concentration measured by CXRS
for r/a < 0.65 is seen. The absolute value of the
impurity concentration in the plasma center varies
at maximum by 30%. In most cases an increase of
the carbon content in the core is seen, which might
be caused by increased impurity fluxes at e.g. hot
spots on the divertor tiles or particle transport
changes. A reduction of the core contamination is
seen in discharges with reversed neutral beam injec-
tion, which might be related to confinement changes
provoked by the DED. These effects are not yet
understood and have to be investigated further.
In contrast to limiter operation, the high-recy-
cling regime is easily accessed in poloidal divertor
machines, because of the localised ionisation in
front of the target plates. For the calculation of
the ionisation fraction in the DED downstream
area, the integration in poloidal and radial direction
is essential, because of the strongly varying width of
this area. The comparison between ionisation length
(in this case 20–40 mm) and averaged extent of the
downstream area (ddown= 50 mm) might overesti-
mate the screening efficiency. A maximum ionisa-
tion fraction inside the DED downstream area of
about 50% is found for the 6/2 configuration. This
is less than estimated for poloidal divertors [14] or
island divertors (>75%) [15]. Accordingly, a high-
recycling regime as it was found in the ergodic
divertor of Tore Supra [3] was not yet seen in this
configuration. This might be related to the divertor
geometry and a larger extent of the perturbed vol-
ume; the plasma parameters in the divertor are of
comparable magnitude for TEXTOR and Tore
Supra. However, the divertor screening of the
DED might be further increased with higher heating
power and densities.
The simple ERO model gives a rough estimate
for the screening efficiency of the DED. It does
not account for the three-dimensional structure of
the plasma parameters in the perturbed boundary
layer. For a more detailed analysis, the code
EMC3–EIRENE including carbon transport has
to be used. Moreover, modelling with the ERO code
using a background plasma produced by EMC3 will
give more insight into the carbon source distribu-
tion, which is needed to quantify the impurity
screening.
Acknowledgement
This work has been partially supported by the
Sonderforschungsbereich (SFB) 591 of the Deutsche
Forschungsgemeinschaft (DFG).
References
[1] R. Ko ¨nig et al., Plasma Phys. Control. Fus. 44 (2002) 2365.
[2] T. Morisaki et al., J. Nucl. Mater. 337–339 (2005) 154.
[3] J. Gunn et al., Plasma Phys. Control. Fus. 41 (1999) B243.
[4] Ph. Ghendrih et al., Nucl. Fus. 42 (2002) 1221.
[5] K.H. Finken et al., The structure of magnetic field in the
TEXTOR-DED, Schriften des Forschungszentrum Ju ¨lich,
Energy Technology 45, 2005. ISSN 1433-5522.
[6] Th. Eich, D. Reiser, K.H. Finken, J. Nucl. Mater. 290–293
(2001) 849.
[7] O. Schmitz et al., J. Nucl. Mater., these Proceedings,
doi:10.1016/j.jnucmat.2007.01.067.
[8] R. Giannella et al., Plasma Phys. Control. Fus. 43 (2001)
271.
[9] M. Kobayashi et al., Nucl. Fus. 44 (2004) S64.
[10] M. Lehnen et al., Plasma Phys. Control. Fus. 47 (2005)
B237.
[11] M.W. Jakubowski, O. Schmitz, et al., PRL 96, 035004.
[12] H.R. Koslowski et al., Nucl. Fus. 46 (2006) L1–L5.
[13] A. Kirschner, V. Philipps, U. Ko ¨gler, J. Winter, Nucl. Fus.
40 (2000) 989.
[14] C.S. Pitcher, P.C. Stangeby, Plasma Phys. Control. Fus. 39
(1997) 779.
[15] Y. Feng et al., J. Nucl. Mater. 313–316 (2003) 857.
M. Lehnen et al. / Journal of Nuclear Materials 363–365 (2007) 377–381
381