Overview of Experiments with the Dynamic Ergodic Divertor on TEXTOR

Abstract

The Dynamic Ergodic Divertor (DED) has recently been taken into operation on TEXTOR. The device is rather flexible and allows the investigation of very different questions. In the present context we concentrate on the divertor aspect and on results of the m/n=12/4 base mode. The DED-field generates the proper ergodic zone and an area of open magnetic field lines, the laminar zone and the tangle structure. The properties of the laminar zone resemble the divertor region of a poloidal divertor. However, the distribution of the density and temperature is highly 3D and strongly related to the structure of the laminar and ergodic zones. The structures of the heat and particle fluxes to the wall agree well with the predicted patterns. A prominent feature of the ergodization is the creation of an edge electric field which results in a rotation of the plasma. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Full text

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Contrib. Plasma Phys. 46, No. 7-9, 515–526 (2006) / DOI 10.1002/ctpp.200610038
Overview of Experiments with the Dynamic Ergodic Divertor on
TEXTOR
K. H. Finken∗1, S. Abdullaev1, W. Biel1, M.F.M. de Bock2, S. Brezinsek1, C. Busch1, I.
Classen2, D. Harting1, M. von Hellermann2, S. Jachmich3, M. Jakubowski1, R. Jaspers2, H.R.
Koslowski1, A. Kr¨ amer-Flecken1, Y. Kikuchi1, M. Lehnen1, Y. Liang1, M. Kobayashi5, A.
Nicolai1, A.Pospieszczyk1, D.Reiter1, T.VanRompuy4,U.Samm1,O.Schmitz1,G.Sergienko1,
B. Unterberg1, E. Westerhof2, R.C. Wolf1, and O. Zimmermann1
1Institut f¨ ur Plasmaphysik, Forschungszentrum J¨ ulich GmbH, EURATOM Association, Trilateral Euregio
Cluster, D-52425 J¨ ulich, Germany
2FOM-Institutefor PlasmaPhysics Rijnhuizen, Association EURATOM-FOM,Trilateral Euregio Cluster, P.O.
Box: 1207, NL-3430 BE Nieuwegein, The Netherlands, www.rijnh.nl
3Laboratory for Plasma Physics, Association EURATOM - Belgian State, KMS - ERM, Trilateral Euregio
Cluster, B-1000 Brussels, Belgium
4Department of Applied Physics, Ghent University, Rozier 44, B-9000 Ghent, Belgium
5National Institute for Fusion Science, 322-6 Oroshi-cho, Toki-shi 509-52 Toki, Japan
Received 19 October 2005, accepted 9 February 2006
Published online 22 August 2006
Key words Ergodization, laminar zone, ergodic divertor, edge physics.
PACS 52.30.-q, 52.35.Vd, 52.55.Fa, 52.55.Tn
The Dynamic Ergodic Divertor (DED) has recently been taken into operation on TEXTOR.The device is rather
flexible and allows the investigation of very different questions. In the present context we concentrate on the
divertor aspect and on results of the m/n=12/4 base mode. The DED-field generates the proper ergodic zone
and an area of open magnetic field lines, the laminar zone and the tangle structure. The properties of the
laminar zone resemble the divertor region of a poloidal divertor. However, the distribution of the density and
temperature is highly 3D and strongly related to the structure of the laminar and ergodic zones. The structures
of the heat and particle fluxes to the wall agree well with the predicted patterns. A prominent feature of the
ergodization is the creation of an edge electric field which results in a rotation of the plasma.
c ? 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1Introduction
During the last two decades, considerable progress has been made in improving the plasma confinement. The
sufficiently low error margin from the different devices makes it now possible to extrapolate the confinement
data to a reactor scenario such it can be expected that the plasma of the proposed ITER experiment will most
likely ignite. The essential ingredient for a good confinement is the existence of magnetic flux surfaces which
form - typically eccentric - onion shell like structures inside the fusion devices. Magnetic field lines stay always
on “their” magnetic surface and these surfaces also form isobars. A key element for obtaining the good plasma
confinement quality is the poloidal divertor which allows for a relatively easy access of the high confinement
mode (H-mode) of a tokamak. The H-mode operation is considered the standard scenario for ITER. In the H-
mode, a barrier is formed at the plasma edge which - together with an observed profile stiffness - leads to the
overall improvement of the confinement.
For ITER, however, the power to the walls is so high that it may determine the lifetime of the device. This
is one of the reasons why ergodicity and ergodic divertors attract recently high attention to the fusion commu-
nity. Ergodization of magnetic field lines is used in this context in contrast to “good magnetic surfaces” where
∗Corresponding author: e-mail: k.h.finken@fz-juelich.de, Phone: +00492461615645, Fax: +00492461615452
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516K.H. Finken et al.: Dynamic Ergodic Divertor
a magnetic field line remains on one surface; ergodic magnetic field lines span up a whole volume. In partic-
ular, ergodicity means that any magnetic field line comes infinitely close to any point in an ergodized volume.
Ergodization results from perturbations which are resonant to specific values of the safety factor q. When using
an external perturbation, one can select whether one ergodizes preferentially the inner surfaces or surfaces closer
to the edge. In the first case, the “woven” magnetic field lines form an internal ergodic layer which is typically
characterized by an enhanced radial transport of particles and energy. In the second case one generates in addi-
tion to the ergodic field lines those which leave the plasma and intersect the walls. These field lines will carry
enhanced fluxes of particles and energy to the wall and will lead to areas of enhanced plasma - wall interaction.
In this way, an open chaotic system is formed.
The open magnetic field lines, i.e. those which intersect the wall twice, form the so called laminar zone. This
zone is equivalent to the scrape-off layer (SOL) of a poloidal divertor; however, in contrast to the conventional
SOL, the connection lengths of the magnetic field lines is not uniform and it consists of continuous sets of mag-
netic flux bundles with connection lengths of 1, 2, 3 ... poloidal turns. The investigation of structure of the
laminar zone, of the ergodic zone and the consequences for the transport are of particular interest.
The topics of research on the DED in J¨ ulich are [1,2]:
- the investigation of the properties of a helical divertor,
- the analysis of the transport in the flux tubes of the plasma edge,
- plasma shielding,
- the distribution of the average power flux to the walls,
- study of the edge electric field and modifications of the plasma rotation,
- the reduction and mitigation of ELMs [3,4],
- effects of the DED on the plasma confinement,
- modification of the transport inside the plasma,
- the excitation of MHD - modes by the DED - field,
- a reduction of excited tearing modes by the DED.
The DED has been designed such that it can operate in different modes such as static or dynamic, in a fine
perturbation mode (m/n = 12/4) and in a coarse mode (m/n = 3/1). Different scenarios may be optimum for
different DED - conditions and therefore this specific point can be investigated only in one specific mode of
operation. In the following, a short introduction into the background for the ergodization is provided, followed
by a description of the proposed DED experiment, then the magnetic field line structure is discussed and some
experimental results, in particular those with the DED divertor aspects will be presented; finally the dynamic
option is highlighted.
2The DED - Arrangement
The coil arrangement of the DED [5,6] is shown on the left hand side of Fig. 1. In addition, on the right hand
side the spectra of Brfor the two coil configurations are shown for r = 42 cm. The DED configuration consists
of quadruples of helical conductors, aligned parallel to the magnetic field lines (for βpol=1) at the nearby q = 3
surface. If, as in the top left part of Fig. 1, consecutive coils have a phase difference of 90◦(e.g. AC - current),
the system is called m = 12, n = 4 base mode; if four neighboringcoils are switched in parallel and neighboring
quartets have the phase differenceof 90◦, the system is called m = 3, n = 1 base mode and is shown at the lower
left part of the figure.
The DED has been constructed by coils inside the vessel located at the high field side. It is an optimum
solution for the available space, the technical constraints (such as current density, skin effect, heat capacity,
cooling aspects, etc.) and the physics requirements, namely the resonance at the q = 3 surface. The coils cover
about 30 % of the inboard vessel surface on the high field side. They are energized by a 4 phase current (up to
15 kA) at selected frequencies (DC, 90 Hz, 1 kHz and a band of 1 kHz to 10 kHz). These frequencies correspond
to a rotation of the perturbation field around the torus similar to the propagating field of an AC motor; the phase
velocities projected on the poloidal coordinate of v = ωr/m = 65m/s at 90 Hz, and 7225 m/s at 10 kHz
respectively; for the m = 3, n = 1 base mode, the velocity is four times higher.
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Contrib. Plasma Phys. 46, No. 7-9 (2006)517
poloidal mode number
m/n = 12/4
m/n = 3/1
q = 3 surface
q = 3 surface
Perturbation spectrum
6 7 8 9 10 11 12 13 14 15 16
123
4
5
6
7
8
B
[a.u.]
nm
B
[a.u.]
nm
Fig. 1
perturbation coils in TEXTOR (left side)
and the related poloidal spectra (right
hand side). A color version of the fig-
ure is given in the electronic version of
the Journal. (Online colour: www.cpp-
journal.org).
Schematic arrangement of the
The characteristic feature of a perturbation system such as the DED is its spectrum. For obtaining the spec-
trum, the magnetic field lines have to be transformed first to intrinsic coordinates; in this coordinate system
the spatial Fourier components with respect to m and n have to be evaluated. The spectrum determines a) the
location and strength of the resonances and b) the radial penetration of the perturbation field. The resonance
location is at the radii with the safety factor q = m/n; the radial penetration of the perturbation scales roughly
as B(r)/B(rDED) ∝ (r/rDED)m/β1. The factor β1(0.5 ≤ β1≤ 0.6) is determined by the pitch of field lines
at the high field side. It follows from this formula that the action of the m = 12, n = 4 base mode is restricted
to the plasma boundary while the m = 3, n = 1 base mode penetrates deeply into the plasma.
The coils are bundled such that the outlets are at 4 toroidal locations, 4 on the top of TEXTOR and 4 at the
bottom. Thisgroupingofthecoilsis technicallyfavorable,butitrequirestheinstallationofapairofcompensation
coils which are indicated in green color. During the DC operation of the DED, the maximum ergodization is
reached when 2 neighboring coils are switched in parallel and supplied with the maximum current. This case
corresponds in the AC case to the moment when coil #1 has a phase of 45◦and the coil number2 the phase 135◦.
For the base mode m/n = 6/2 and 3/1 each 4 or 8 coils have to be bundled. The coils are covered by ceramic
tiles and by 2D shaped graphite tiles forming a smooth toroidal surface, the divertor target plate.
3Description of magnetic field lines
Magnetic field lines in a toroidal system are conveniently presented in a Hamiltonian form. It gives the most
convenient way to describe the regular and chaotic field lines in the presence of non - axi-symmetric magnetic
perturbations.
In magnetically confined plasmas, like tokamaks and stellarators, magnetic field lines lie on nested toroidal
surfaces, magneticsurfaces, woundarounda closed magneticfield line, magneticaxis. The magneticsurfaces are
labelled by the toroidal flux, ψ = ψ(x,y,z) = const, equal to a magnetic flux through the surface perpendicular
to the magnetic axis where ψ = 0. When representing the magnetic field in the Clebsch form (see, e.g., [7–9])
B = ∇ψ × ∇ϑ + ∇ϕ × ∇H,
(1)
the equations for magnetic field lines take the Hamiltonian form
dψ
dϕ= −∂H
∂ϑ,
dϑ
dϕ=∂H
∂ψ,
(2)
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518K.H. Finken et al.: Dynamic Ergodic Divertor
with (ϑ,ψ) as canonical variables, ϕ as independent time - like variable, and the function H = H(ϑ,ψ,ϕ), a
poloidal flux, plays role of Hamiltonian. This form is the basis of advanced methods of field line mapping by
S.S. Abdullaev for the problem of the DED [5,10,11]. The mapping is much faster than conventionalintegration
schemes and allows therefore easier the systematic analysis of the structures imposed by the DED and also the
statistical analysis. Important application of the mapping are the visualization of the ergodic and laminar zones
and in the statistical approach the analysis of the field line diffusion coefficient due to ergodization.
4 The Ergodic Structure Generated by the DED
The ergodic structure resulting from this perturbation is often shown in the so called Poincar´ e plot. In this plot
a characteristic plane has to be defined which for a tokamak is a poloidal cut of the torus with the coordinates
r for the minor radius and Θ for the poloidal angle. In this plane starting points for magnetic field line tracing
are selected and marked by a dot. The field lines are traced many times (typically several 1000 times) around
the torus and every time the location of the intersection of the field line and reference plane is marked by a dot
(puncture plot). If the perturbation field is not applied, the puncture sequence will remain on a flux surface in the
Poincare´ e plot, thus forming a closed curve.
If the starting point is on a (preferentially low) rational q-number surface, the curve will degenerate to indi-
vidual points - e.g., at the q = 3 surface to three points per starting condition. With applied perturbation field,
the pattern is modified in a characteristic way. The big advantage of the Poincar´ e representation is that the 3-D
chaos problem can be cast into a 2-D picture which is easily graphically represented. Two Poincar´ e plots for the
TEXTOR DED are shown in Figs. 2 . The figures are cut at the outer equator (Θ = 0) and unfolded; the abscissa
is the poloidal angle and the ordinate is the radius. This representation has been selected to enhance the radial
resolution with respect to the poloidal one. In the left subfig. 2 the perturbation current is relatively low, 50 % of
the maximum allowed value. The rectangle on the center top represents the location of the DED coils.
0 50100 150200 250300350
39
40
41
42
43
44
45
46
47
poloidal angle [deg]
minor radius [cm]
Ra = 1.73 [m], Ip = 450 [kA], Bϕ = 1.9 [T], IDED = 7.5 [kA], βpol = 0.1
DED
050100150200250300350
39
40
41
42
43
44
45
46
47
poloidal angle [deg]
minor radius [cm]
Ra = 1.73 [m], Ip = 450 [kA], Bϕ = 1.9 [T], IDED = 15 [kA], βpol = 0.1
DED
Fig. 2 Left side: Poincar´ e plot for a low perturbation field (Ipert/Imax = 0.5). As expected, magnetic islands develop at
low rational q-values. The ordinate represents the radial direction (plasma side to the bottom) and the abscissa is the poloidal
angle. Right side: similar plot for the perturbation current condition Ipert/Imax = 1. The whole outer plasma boundary is
ergodized
The Poincar´ e plot shows all the structures expected in the sub - ergodic phase: At q = 2.5,2.25 and 2, the
clear islands are formed with mode numbers m/n = 10/4, 9/4 and 8/4 (m stands for the poloidal mode number
and n for the toroidal ones; the resonance condition requires q=m/n). Towards the plasma core (bottom part of
the figure) the flux surfaces are nearly unchanged resulting in well ordered puncture curves. Between the main
islands, intact surfaces are clearly visible. Between the q = 2 and q = 2.5 surfaces, smaller island chains are
found; these and sub-islands within the main islands result from higher order perturbations. The structures are
well described by the KAM (for Kolmogorov,Arnold and Moser) theory which is treated in text books [12–15].
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Contrib. Plasma Phys. 46, No. 7-9 (2006) 519
With increasing perturbation amplitude, the island width increases and the islands start to overlap as shown
on the left side of subfig. 2. For IDED = 7.5kA the region for q > 2.5 surfaces becomes ergodic, i.e., field
lines from any starting point reach any other point in that area. With increasing perturbation strength, the barrier
disappears in the whole boundary and allows an enhanced field line diffusion as one can see in the right sub -
figure 2.
For the evaluation of the field line diffusion, different methods are used. The most basic one is to relate the
mean square displacement ∆r of a magnetic field lines from the unperturbed surface to the diffusion coefficient
DFL:
DFL=(∆r)2
r · dϕ
(3)
where rdϕ is the progression step along the magnetic field lines which is equivalent to the progression step
of the field line mapping which we apply. As soon as the field lines leave the plasma volume, they are no longer
taken into account.
For a fully ergodized system, often the quasi linear approximation is applied which is written as:
DQ= 2πqR0· (bmn
Bt)2
(4)
The diffusion of the magnetic field lines is shown in Fig. 3 for conditions close to those of Fig. 2. Plotted
are the field line diffusion coefficients according to formula 3 (solid curves 1 and 2) and 4 (dashed curves 3 and
4) for a DED current of 7 kA (curves 1 and 3) and for the full DED current of 15 kA (curves 2 and 4). All data
are calculated for Ip= 380 kA, βpol=0.5 and R0= 1.72 m, i.e. a plasma shift of 3 cm towards the DED. The
solid curves refer to the left scale while the dashed ones refer to the right scale which differs by a factor of 20.
One observes that the diffusion coefficient obtained by the quasi-linear approach is about an order of magnitude
larger than DFL. Obviously, the quasi - linear approximation can lead to substantial discrepancies to the true
diffusion coefficient; we attribute the failure of the quasi-linear approximation to the incomplete ergodization, to
the presence of magnetic islands and to the low number of resonances.
0
5
1
1.5
2
2.5
3
x10-6
414243 4445
0
1
2
3
4
5
6
x10-5
DFL m2/m
DQ
ρ [cm]
1
2
3
4
Fig. 3 Plotted are the field line diffusion co-
efficients according to formula 3 (solid curves)
and 4 (dashed curves) for a DED current of 7
kA (curves 1 and 3) and for the full DED cur-
rent of 15 kA. The solid curves refer to the left
scale while the dashed ones refer to the right
scale.
5The Laminar Zone
For practical considerations, the plasma edge is best characterized by laminar plots [16] and Poincar´ e plots; both
plots are essential for the later analysis of the data in the rather complicated 3D structured plasma edge. As
already mentioned, the laminar plot is characterized by the connection lengths of the magnetic field lines with
the walls. We typically construct a laminar plot by choosing a poloidal cut of the plasma edge e.g. at the low
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520K.H. Finken et al.: Dynamic Ergodic Divertor
field side as shown in Fig. 4. In this example the poloidal axis spans from −30 < Θ < 30 and the minor
radius from 44 cm to 48 cm. From each point of this area we start magnetic field line tracing in both directions
until the magnetic field line intersects the wall. The total connection length is then decoded into the figure e.g.
by coloring the points. The areas with the longest connection length are plotted dark (red) and the ones with
a shorter connection length in lighter colors. The longest connection length we count to the laminar zone is 5
poloidal turns. The field lines with the longer connection lengths originate from the ergodic zone, the island
region or even the confinement region. These areas have to be investigated in more detail with Poincar´ e plots.
Because of the symmetry of the DED configuration, we have 4 independent areas of the laminar plots which
are image-symmetric. These are those plots where field lines have the same length to the two intersections in
front of the DED; the plasma flows connected with these flux tubes form there a stagnation point. Two of these
stagnation points are at the low field side, namelyfor those magneticflux bundles with an odd numberof poloidal
turns between the intersection with the walls and two others for those of even connection lengths. In figure 4,
the magnetic field lines in the area “S” have a connection length of 3 poloidal turns and represents the stagnation
point of those flux tubes.
-30 -20 -10 0 10 20 30
?* (deg)
Laminar plot (LFS) Laminar plot (LFS)
48 48 48
46 4646
4444 44
r [cm]
Number of
poloidal turns poloidal turns
fingers fingers
-30 -20 -10 0 10 20 30
?* (deg)
r [cm] r [cm]
Number of
" " S
Fig. 4 The laminar plot gives the connection lengths
of the magnetic field lines in color coding; the right bar
refers tothe colorsof thelengths. Thelaminar zone cor-
responds to the scrape-off layer of a poloidal divertor,
however, the connection lengths patters is more compli-
cated. A color version of the figure is given in the elec-
tronic version of theJournal. (Onlinecolour: www.cpp-
journal.org).
Fig. 5 Deformation of a magnetic flux tube obtained by field
line mapping; the starting point is the stagnation point “0” and
the end point #-16 when the flux tube intersects the wall.
The simplest structure of the laminar zone is the one formed by the single turn field lines which correspond to
the conventional scrape-off layer (the number of toroidal turns is q times the poloidal number). In contrast to the
poloidal divertor case, these areas are no longer toroidally symmetric but show strong indentations. On laminar
plots of the high field side, one can also recognize field lines with even shorter connection length, the private flux
zone.
The light (blue) area represents field lines which intersect the divertor target plate after two poloidal turns.
Because the field lines move twice around the torus, they must appear twice in the figure. For this reason, the left
and right “oval” structures have the same area and are interconnected by the field lines.
The stagnation point area of three poloidal turns is - as already mentioned - the area “S” of figure 5. The field
lines of this area must reappear twice and they form the trapezoid structures next to the oval structure. Figure
5 shows the development of the sickle - shaped magnetic flux tube along its path in one toroidal direction. The
contour line of the area is mapped every 90◦and the numbers indicate the mapping step. The starting point is at
subfigure “0” (left bottom). The shape of the is very little modified as long as one stays away from the DED coils
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Contrib. Plasma Phys. 46, No. 7-9 (2006)521
(-1 .. -3). By the DED field, the flux tube is strongly deformed and elongated reflecting the trapezoidal figure (-4
.. -6). Outside of the DED area, the flux tube experiences only the shearing of the equilibrium field (-7 .. -13).
When entering again the zone in front of the DED, the flux tube is further deformed and deflected towards the
divertor target plate where the mapping is stopped.
The areas of flux tubes with with longer connection lengths become increasingly small and merge with the
ergodic structure. However, an important ingredient is the set of flux tubes which interconnect the ergodic area
with the walls. The flux tubes are rather thin and are called “fingers” or “tangles”. Since these flux tubes come
from a deeper zone of the plasma, the ergodic zone, it is expected they are effective in carrying heat and particles
towards the walls. Part of the particles and power will diffuse thereby to neighboring field lines in the laminar
zone such that the deposition pattern will be smeared out. Details of this redistribution will depend on the edge
density and temperature. For understanding of the transport, several modelling studies [17,18], of the area of
both the ergodic zone and laminar zone have been performed.
The electrons in the plasma boundary are cooled by ionization and radiation. With ergodization, their tem-
perature is lowered in addition by the enhanced heat conductivity along the field lines and as a consequence, the
ionization and excitation zones are broadened and shifted inward. Moreover, the impurity release due to energy
dependent processes (e.g. sputtering) can be reduced significantly. Thus the combined effects of the increased
electron density and decreased electron temperature at the plasma boundaryin conjunction with the enhanced ra-
dial transport are responsible for the beneficial effects observed on devices with ergodic divertors [19–21]; from
those the expected improved radiation efficiency of the impurities and the better impurity screening is an issue
for TEXTOR experiments.
6 Experimental Results
Fig. 6 Overview of the plasma edge structure of the DED
- dominated plasma in the light of CIII emission. Superim-
posed are the location of the DED coils and the Poincar´ e plot
of the magnetic field lines. The bottom subfigure is rotated by
90◦and it shows the details of the “fingers”. A color version
of the figure is given in the electronic version of the Journal.
(Online colour: www.cpp-journal.org).
An overview over the edge structure of the DED plasma is shown in Fig. 6. Plotted is the CIII line emission
of carbon recycling at the divertor target plate. In addition the location of the DED coils is indicated by the dots
representing the two directions of the electrical current. Overlaid to the picture is a Poincar´ e plot of the magnetic
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522K.H. Finken et al.: Dynamic Ergodic Divertor
field lines in the edge. One sees that the light of the recycling particles follows nicely the structure imposed by
the DED - field. The maximuminteractionis - as expected- close to the locationwhere the fingers touchthe wall.
One also sees that the radius of the ergodization zone amounts to 10% of the minor radius. The lower subfigure
shows the interaction zone in higher detail. The fingers are plotted either as black or as white dots depending on
the direction of field line tracing. The lower figure is tilted by 90◦with respect to the upper one.
ATLAS Code: connection length [p.t.]
ECE Imaging:
normalised electron temperature
Fig. 7 ECE imaging provides directly a 2-D image of the electron temperature in the laminar zone as shown in the right
subfigure. The left subfigure gives again the corresponding laminar plot. A color version of the figure is given in the electronic
version of the Journal. (Online colour: www.cpp-journal.org).
The ECE imaging diagnostic technique provides a 2D picture of the electron temperature. Shown in Fig. 7 is
a laminar plot and the temperature distribution for the area of the yellow rectangle. One sees that the area of the
fingers is hotter than that area which is strongly connected with the plasma wall. The temperature field agrees
well with the expectations, even though the measurements are performed at the low field side, far away from the
DED; the properties of the plasma in the magnetic flux tubes are strongly determined by the parallel transport
along magnetic flux tubes; this leads to a strong poloidal structuring.
Helium beam: electron pressure [Pa]
q = 3.1
a
0.45
radius
poloidal angle
0
150
100
50
ATLAS Code: connection length [p.t.]
Fig. 8 By a slow rotation of the DED - field, the 3-D structure of the plasma boundary can be shown even for a measurement
which records data along a radial line as shown here for the atomic helium beam diagnostic. The left subfigure gives a laminar
plot while the right one is the actual measurement for the yellow square. A color version of the figure is given in the electronic
version of the Journal. (Online colour: www.cpp-journal.org).
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Contrib. Plasma Phys. 46, No. 7-9 (2006) 523
The slow rotation of the DED with few Hz only allows the visualization of 3D structures during local mea-
surements. Because one can program only positive DED currents in this case, the rotation angle is limited to 1/4
of the full phase. Fig. 8 shows on the left side a laminar plot at the low field side and the right sub-figure gives
the radially resolved electron pressure derived from a helium beam signal. The laminar plot has been evaluated
for the position of the diagnostics. The yellow square in the left figure gives the range over which the DED - field
moves during the rotation. The electron pressure variation in right subfigure agrees well with the expectation of
the field line tracing.
The heat flux pattern at the divertor target plate is dominated by the deflection of the magnetic field lines in
front of the DED coils [22]. On therefore obtains a helical pattern as shown in Fig. 9; again a good agreement is
found between the predicted laminar and footprint plots and the measured ones. The DED resembles a poloidal
divertor system with 4 X - points; therefore, one expects 8 strike points in front of the DED coils. At low DED
current, the pairs of the strike zone merge together such that one sees only four strike lines. With increasing
current the strike zones split more and more similar to the splitting of the strike zones in a poloidal divertor. The
similarity between poloidal and helical divertor are very high which even yields for the existence of a private flux
zone.
5
4
3
2
1
0
090
toroidal angle [deg]
ATLAS: target footprint
poloidal direction
Langmuir Probes
7 7
165210
160
20
140
120
100
80
60
40
IR Camera: target temperature [°C]
toroidal angle [deg]
Fig. 9 The top of the subfigure shows the power deposition pattern on the divertor target plates during DED operation
while the left subfigure shows the result of a 3D plasma transport modelling for the same condition. The arrows in the right
subfigure indicate the direction of the incoming flow. A color version of the figure is given in the electronic version of the
Journal. (Online colour: www.cpp-journal.org).
The DED tile alignment shows some imperfections. These imperfections can be utilized to show that the
heat flux of neighboring strike zones arrives from opposite direction. The power flux heats either sharply the
protruding edges of the tiles or - if arriving from the opposite direction - the whole tiles. The arrows show the
power flow direction.
One finds a good correlation between the particle and power fluxes and the structure of the fingers. However,
in agreement with our earlier modelling, the particle flux - due to diffusion - extends beyond the location of
the fingers, which connect the ergodic zone with the target plate; particles diffuse beyond this layer and fill the
laminar zone. Also in agreement with the expectations is the asymmetry of the pair of divertor strike lines. In
contrast to the poloidal divertor, the toroidal symmetry is lost and the details of the fingers reaching from the
ergodic zone to the divertor are highly complicated. This figure shows again the importance of the 3D aspects of
the flow pattern along the open field lines and the benefit of the visualization by the laminar plot.
Figure 9 shows also the location of Langmuir probes [23]. These probes are utilized to measure the local
particle flux, electron temperature and plasma potential in front of the divertor target plate which are displayed
in Fig. 10. For the measurements, seven probes are used which are indicated by different colors; in addition, the
DED field is swept slowly such that one obtains a nice overlap of the data. In addition to the experimental data,
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524K.H. Finken et al.: Dynamic Ergodic Divertor
0
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Fig. 10
electron density and the plasma potential measured by
7 Langmuir probes as a function of the toroidal angle.
In addition, the connection length of the magnetic field
lines is displayed. A color version of the figure is given
in the electronic version of the Journal. (Online colour:
www.cpp-journal.org).
The subfigures shows the particle flux, the
the connection lengths of the magnetic field lines (in units of poloidal turns, right scale) are plotted. The data
cover a toroidal angle of 90◦which corresponds to one pair of divertor strike lines and show the good correlation
of enhanced particle flux, electron temperature and plasma potential with the location of the “fingers” which are
characterized by the large connection length.
7 The Dynamic Aspect
So far we have only discussed divertor properties of the helical divertor in the m/n = 12/4 base mode. We have
neglected the other mode of operation, the m/n = 3/1 base mode; even though some divertorproperties are clearer
in this configuration, one faces the problem that internal tearing modes are easily excited which make some
interpretations more difficult. Another important aspect not touched up to now is the dynamic feature of the
DED. Even though this is a characteristic element of the Dynamic Ergodic Divertor we can only make a few
remarks here. The motivation for applying different frequency ranges is:
1) the application of a low frequency - 50 Hz (vph= 12m/s) proposed for technical convenience - is aimed
at spreading the heat load evenly either over the protection tiles of the helical divertor located at the high field
side or over the pump limiter located at the low field side. Shifting the plasma position and/or changing the
plasma aperture allows the control of the relative distribution of the total heat and particle flux between these two
main plasma facing components. This puts the proposed DED program in a unique position to answer a number
of critical questions which address the physics of mixed ergodic island layers and how they can be used as an
adaptive interface between hot, well confined plasmas and plasma facing components.
2) In contrast to the 50 Hz case, the medium frequency of 1 kHz (vph = 240 m/s) opens experimental access
to the interesting question of whether a rotation of the perturbation pattern which is faster than the transit time
of recycling particles - penetrating the boundary layer - will affect particle transport and in consequence also the
recycling process and the screening efficiency.
3)Last butnotleast, byapplyingthe upperfrequencybandof1kHzto 10kHz- thevelocityofthe perturbation
is then of the same order as the natural diamagnetic drift velocity of the plasma - one can investigate whether the
rotating field will induce an angular momentum in the plasma and whether the resulting torque [24] will affect
confinement and stability properties.
The experimental results show differences as compared to the initial ideas of the plasma acceleration. It turns
out that the torque transfer is not the dominant feature for the plasma acceleration: The DED - field accelerates
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Contrib. Plasma Phys. 46, No. 7-9 (2006) 525
always the plasma in co - direction of the plasma current, independent whether DC or AC field are applied on the
DED coils and independent whether the plasma has a large initial velocity or not. The acquired toroidal plasma
velocity (difference of velocity relative to the initial velocity) is shown in Fig. 11 for different DED conditions.
The velocity gain can be described by a third power parabola as a function of the DED current. The present
interpretation of the plasma acceleration is the formation of an edge electric field due to the open field lines
where electrons have a higher mobility than ions. The direction of imposed rotation and the observed magnitude
of rotation agree with this picture.
Fig. 11 Gain of incremental toroidal plasma
rotation as a function of the applied DED cur-
rent. A color version of the figure is given in
the electronic version of the Journal.. (Online
colour: www.cpp-journal.org).
8 Outlook
The technical solution for the DED on TEXTOR has been chosen to provide a wide range of experimental
possibilities with a limited investment, the aim being the explorationof the potential and the limits of the DED as
a means to influence and control plasma - wall interaction. In this context, the benefit of the studies is seen in the
improvement of the understanding of edge transport, island formation, effects of ergodicity etc. which may lead
to theincorporationofsomefeaturesoftheTEXTORDEDintootherexhaustconceptsandmayalsostimulatethe
search for novel concepts and technical solutions which would have potential for development towards ultimate
application on a burning fusion plasma.
TherotatingDEDfieldhas apositiveeffectontheMARFEs. Instatic operation,thedensitylimitoftheplasma
is often preceded by either a MARFE near the inner wall or at the X - point of the divertor. By the rotation of
the DED - field, one obviously can influence the recycling path of the particles positively such that the MARFE
onset is delayed [4].
Beyond the divertor aspects treated so far, the DED provides a rich physics field for the understanding of
tearing modes. In particular in the m/n = 3/1 base mode, the perturbation of the DED penetrates deeply into
the plasma and is resonant to n = 1 modes which have a low level for inducing tearing modes. In particular
the m/n = 2/1 tearing mode is exited at less than 30% of the possible DED current. One topic of research is
the analysis of the threshold of the perturbation field on the mode excitation for the different plasma and heating
scenarios. These investigationson error fields are in particularimportantfor largerdeviceswhere verylow values
of a tolerable error field are predicted.
The induced tearing mode is highly reproducible and the radial, poloidal and toroidal location of the X -
points and O - points are well known because the tearing mode is locked by the DED - field. this is in particular
interesting for the rotating DED - field. A standard scenario is the DED operating at a frequency of 1 kHz.
A major topic of research at this condition is the reduction and suppression of the tearing mode by ECRH /
ECCD. The experiments show a tearing mode suppression if the adjusted ECR is coupled before the DED - field
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526K.H. Finken et al.: Dynamic Ergodic Divertor
is switched on and a reduction when the DED is applied before ECR; the reduction and suppression depend
sensitively on the interaction radius and on the phasing between the ECR - pulses and the DED - field.
A rather recent area of research bases on the observation on DIII-D [3] that ELMs can be reduced or even
suppressed by edge ergodization. It is obvious that this method would have enormous consequences for ITER
and next step experiments, if it is successful and can be applied to larger devices. For this reason, the TEXTOR
team has started to create a limiter H - mode and to mitigate the ELMs by ergodization. The experiments are in a
very preliminary state but we obtained encouragingresults on ELM reduction in the 12/4 base mode of the DED
while in the 3/1 base mode the induced modes were limiting the plasma stability.
In the near future, the DED will be prepared for the operation in the 6/2 base mode. It is expected that in
this scenario the DED field penetrates deeper into the plasma than in the 12/4 base mode without reaching the
threshold for tearing mode excitation. This regime might optimize the divertor scenario and the ELM mitigation
effects and avoid the sometimes disturbing effect of induced modes.
Acknowledgements
meinschaft.
The work was partly supported by the Sonderforschungsbereich 591 of the Deutsche Forschungsge-
References
[1] K.H. Finken, S.S. Abdullaev, M.F.M. de Bock, et al., Phys. Rev. Lett. 94, 0150031 (2005).
[2] K.H. Finken, S.S. Abdullaev, W. Biel, et al. Plasma Phys. Control. Fusion 46 B143, B155 (2004).
[3] T.E. Evans, R.A. Moyer, P.R. Thomas, et al., Phys. Rev. Lett. 92, 235003 (2004).
[4] Y. Liang, H.R. Koslowski, F.A. Kelly, et al. Phys Rev Lett. 94, 105003, 2005.
[5] S.S. Abdullaev, K.H. Finken, and K.H. Spatschek, Physics of Plasmas 6, 153 (1999).
[6] K.H. Finken, S.S. Abdullaev, A. Kaleck, and G.H. Wolf, Nucl. Fusion 39,637 (1999).
[7] A.H. Boozer, Physics of Fluids 26, 1288 (1983).
[8] A.H. Boozer, Plasma confinement in Encyclopedia of Physical Science and Technilogy, Academic Press, Vol. 13, New
York, 1992.
[9] R. Balescu, Transport processes in Plasmas, North Holland, Amsterdam, 1988.
[10] S.S. Abdullaev. J. Phys. A: Math. & Gen. 32, 2745, (1999).
[11] S.S. Abdullaev. J. Phys. A: Math. & Gen. 35, 2811 (1999).
[12] J.A. Lichtenberg and M.A. Liebermann, Regular and Stochastic Motion, Applied Mathematical Sciences 38, Springer
Verlag, New York, 1983.
[13] M.C. Gutzwiller, Chaos in Classics and Quantum Mechanics, Interdisciplinary Applied Mathematics, Springer Verlag,
New York, 1990.
[14] R.J. Goldston and P.H. Rutherford, Introduction to Plasma Physics, in IOP Publishing Ltd, 1995.
[15] W. Horton and Y.H. Ichikawa, Chaos and Structures in Nonlinear Plasmas, World Scientific, Singapore, 1996.
[16] M.W. Jakubowski, S.S. Abdullaev, and K.H. Finken, Nuclear Fusion 44, 1 (2004).
[17] K.H. Finken, T. Eich, and A. Kaleck. Nucl. Fusion, 38, 515 (1998).
[18] M. Kobayashi, D.Reiser, G. Sewell, K.H. Finken, and S.S. Abdullaev. J. Nucl. Mater., 313-316, 1056 (2003).
[19] A. Samain, T. Blenski, Ph. Ghendrih, et al., Contrib. to Plasma Physics 30, 157 (1990).
[20] Ph. Ghendrih, H. Capes, J. Nguyen, and A. Samain. Contrib. to Plasma Physics, 32, 179 (1992).
[21] C. de Michelis, A. Grosman, X. Garbet, et al., Nucl. Fusion 35, 1133 (1995).
[22] M.W. Jakubowski, S.S. Abdullaev, K.H. Finken, M. Lehnen, and TEXTOR team. J. Nucl. Mater. 337-339, 176 (2005).
[23] M. Lehnen, , K.H. Finken, Ma. Jakubowski, et al., Journal of Nuclear Materials 337-339, 171 (2005).
[24] K.H. Finken, Nucl. Fusion 39, 707 (1999).
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