J. Plasma Fusion Res. SERIES, YoI.5 (2002'1 77-81

Physics Aspects of the Dynamic Ergodic Divertor (DED)
FINKEN KarI H.I, KOBAYASHI Masahirol'2, ABDULLAEV Sadrilla S.I and JAKUBoWSKI Marcin1,3
llnstitut

fiir Plasmaphysik, Forschungsryntrum Jiilich GmbH, EURATOM Association,
D-52425 Jiilich, Germany, Partner in the Trilateral Euregio Cluster

2Depa,menI;::;7,r:;T";:;::::,,:::,h;ilif,?""xi,:,";n;*:"r",a,lapan(Received: 1l December 2001 / Accepted:24 April 2002)

Abstract
The Dynamic Ergodic Divertor (DED) is presently being installed in the TEXTOR tokamak. Itconsists of 16 helical coils wound helically around the torus at the high fietd side (HFS). The
perturbation currents in these coils generate predominantly islands of m=10...14 and n=4leading both torather closed ergodic and to open laminar structures. In the "laminar mode", the DED forms a helicaldivertor'. 3D modelling (2D finite element/l D finite volume) of the plasma transport in the laminar zone
has started. By the "dynamic" operation of the DED, the heat is deposited to a wide area and forces aretransferred from the currents in the DED-coils to the plasma edge.

Keywords:
ergodization, 3D modelling, force transfer

1. lntroduction
The formation of an ergodic layer can be aninteresting means of destroying the good confinement
properties of closed flux surfaces at special locations.
Such a location of interest is the boundary of thesmeared out over the large area of the divertor target
plate; at frequencies up to 10 kHz, locked modes can beplasma: The power - with the exception of the radiatedcurrent generates a torque at the plasma edge.

unlocked, or a differential rotation in the plasma edge
can be imposed with hopefully favourable effects on theconfinement. It is estimated that the rotating DED

fraction - leaves the plasma conductively or
2. The Experimental Set-Up

convectively and passes through a relatively thinboundary layer. In order to spread the heat to a larger

The Dynamic Ergodic Divertor (DED) is shown inarea, the Dynarnic Ergodic Divertor (DED) tll has beenFig. 1. The main component of the DED is a set ofmagnetic perturbation coils whose purpose is todeveloped and is presently being installed in theTEXTOR tokamak. The DED will create an ergodic

improved screening of impurities, and for an enhanced

ergodize the magnetic field structure in the plasma edge
region; these coils are located inside the vacuum vesselat the high field side of the torus at a minor radius ofr"o1 = 53.25 cm. The set consists of 16 individual coils

particle removal by the pump limiter ALT-II. The(4 quadruples) plus two compensation coils. The

expression "d1'namic" refers to a rotating perturbationindividual perturbation coils follow the direction of theequilibrium magnetic field of the plasma edge helicallyonce around the torus. The maximum coil currents

boundary layer of the plasma and thus it is expected toallow for wider power deposition pattern, for anmagnetic field imposed by the DED coils. For therotation, different frequencies are foreseen: At few
Hertz, the heating pattern of the divertor strike zone is@2002 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Corresponding author's e-mail: k.h.finken@fz-juelich.de77

Finken K.H. e/ dl., Physics Aspects of the Dynamic Ergodic Divertor (DED))

5048

e46o:444240380l2n50
Fig. 1 Schematic view of the DED-coils.

48
E946

amounts to 15 kA.

The main perturbation modes (m = 10...14, n = 4)

44create chains of magnetic islands destroying theresonant magnetic surfaces e = mln. Due to a strong

42

radial decay of the modes they do not disturb the plasmacore. The DED has the unique feature that theperturbation field is not static as in most other devices
but that it has the option of rotation. To our knowledgeonly the tokamak CSTN [2] at Nagoya University hassimilar features and - at low perturbation current levels also the TEXT [3] tokamak. The DED can be operated
DC, around 50 Hz or at 7 frequencies in the band from I
kHz to 10 kHz.

40

0.0

o.2

0.6

0.4

0.8

1.0

Q/2nFig. 2 Variation of the ergodization pattern with increasing plasma current (at full perturbation current) (a)/" = 460 kA, (b) /" = 600 kA. Due to the shift of theresonant q-surfaces towards the DED-coils, theedge Chirikov parameter increases leading to an
opening of the laminar zone (field lines with shortconnection length).

3. The Ergodic Layer
The perturbation coils impose structures withdifferent properties in the plasma boundary: The interior

via the plasma current; in this way the ergodic zone canclosed flux surfaces, q(r) 32, remain nearly undisturbed

be shifted radially in the range 0.9 3 rla < 1 keeping theChirikov parameter above one. Individual adjustment ofand form for at least the well structured Kolmogorov,Arnold, Mozer (KAM)-surfaces [4]. Further towards thethe coil currents allows the superposition [11] ofdifferent base modes. In order to minimise theboundary, islands develop and start to grow; finally,different islands overlap and form an ergodic sea [5-7]interaction with the core plasma, high mln (e.g. mln =l2l4) are preferred; for the given coil arrangement,
Fourier mode numbers m 18 can be neglected. This
choice creates many small islands instead of a few
islands with large poloidal extent.
Figures 2(a) and (b) show Poincar6 plots -obtainedby field line mapping - for "low" and "high" plasma
currents (a: 46O kA, b: 600 kA) at the full perturbation
current. The starting points were taken at the ergodic
zone (dark regions). These field lines intersect the wallsuch that the magnetic surfaces are destroyed. The very

outermost magnetic field lines intersect the divertor
target plate. These field lines form the so called laminarzone [8]; here the transport changes character fromdiffusive to convective with plasma streaming to theplasma facing components as in the conventional
scrape-off layer.
Field line tracing and field line mapping [9,10] arebasic techniques for investigating the ergodic structure.
These techniques provide a picture of the areas with
intact magnetic surfaces, of island structures and ofergodized regions. The resonant radius can be adjusted

elements along the elongated areas (fingers); they do notenter the white area located between the fingers whichcorrespond to the field lines of short connection length.
78

Finken K.H. et al., Physics Aspects of the Dynamic Ergodic Divertor (DED))

With increasing plasma cuffent, the resonant surfaces

with field lines of short connection length region will bemost responsible for the final step of the transport ofenergy and particles to the wall. In this sense thelaminar zone is similar to the scrape-off layer of adivertor tokamak.
The topology of the flux tube is now three
dimensional. Figure 3 shows one of the examples for 2
poloidal turn region, where the area is mapped incounter-clockwise direction and is projected onto thesame poloidal plane after each 90 degrees mapping
along torus. Starting from the stagnation point at HFS(0), the flux tube is traced following the consecutive
number shown in the figure and after (10) it reaches thewall. The clockwise mapping creates the same but
symmetric pattern around the stagnation point, which
are not plotted in the figure. The flux tube experiences alarge deformation especially in front of the DED coils,(2.25 < q < 3.75) move towards the outside, closer to theDED coils. Highest ergodization levels with Chirikov
parameters up to 6 are expected for plasma currents
around 600 kA. The results of the field line mapping
seem at a first glance to be in conflict with thisexpectation: the radially widest ergodic zone is found atthe relatively krw plasma culrent of 460 kA while at 600
kA the properly ergodic zone is only a small band at aradius at about r = 44 cm. The outer zone of Fig. 2(b) is
nearly empty of Poincar6 intersection points and appffirs

white. The absence of the intersection points is aconsequence of the fact that the field line tracing isstopped after an intersection with a wall element. We
have stopped the tracing because the field lines
represent also particles which would be neutralised andcan leave their field line. The "white" area contains thefield lines with a short connection length, i.e. a few
poloidal turns. This area of short connection length isi.e., HFS, due to the strong perturbation there. The area

is stretched, bended and compressed, it can be attributed
to one of chaotic properties.

called the "laminar zone" |2,131and is discussed in thenext section. Because ofits short connection lengths, thelaminar zone is related to the scrape-off layer properties.
The attempt to increase the ergodic zone by increasing
the resonant perturbation at the edge evidently leads

As in a normal SOL model, the transport isassumed to be convective along the field lines anddiffusive perpendicularly. The numerical scheme is a
splitting method with a finite element method (FEM) fora cross-field transport, where we use the FEM solver
PDE2D [4], and with a finite difference method forparallel one. Based on the argument above, we take up
the one and two poloidal turn regions, and others are
considered as an ergodic region where the physics are

more to an increase of the laminar layer than to awidening of the ergodic zone.

4. Modelling of the Transport in the Laminar
Zone

reflected in the increased transport coefficients. Simple

Properties of the laminar zone are best represented
in a poloidal cut of the plasma edge at the low field side(LFS) where areas are ordered according to theconnection lengths of the magnetic field lines between
two intersections with the walls. The poloidal width of(10)the laminar plot corresponds to the m = 12 mode, thedominant mode of the DED. By this choice all fieldlines intersect for at least once the reference frame; inaddition this area is opposite of the perturbation area
and it contains the stagnation areas for those field lines
which have an odd number of poloidal tums connecting

ail

46.0

(4) (3) (2)ilrIilil[45.0the walls.

\l\t\]

44.0

For the case of a strong laminar zone, the areas
shortest connection length (one poloidal turn) is0

relatively large, followed by successively smaller areasof two and three poloidal tum areas. The structure of thelaminar zone are simple as compared to the one of theergodic zone, which has fractal properties. The channel
offield lines connecting the inner ergodic zone with thewall is narrow (called fingers), for some conditions evensmaller than the Larmor radius. In our picture, the area

Ittl
(1)
(0)

il/,[,I,50 100 150 200 250 300 350
e* (deg.)

Fig. 3 Development of flux tube areas of 2 poloidal
turns.The starting area (0) is close to the stagnation point. Each flux tube in the figure is apart by

90 degrees of toroidal angle from each other,those are projected onto the same poloidal plane.
79Finken K.H. et al., Phy srcs Aspects of the Dynamic Ergodic Divertor (DED))!

electromagnetic wave of the DED effectively propagatesin the area between coils and resonance layer as theWcompressional Alfvdn wave (fast wave) [16]. At theresonance layer of the plasma different approximations
is described either by a resistive annulus or by tearing
modes. The interaction of the extemal rotating field withthe current driven in the shielding layer results in thetransfer of angular momentum between DED-coil andplasma [15]. The maximum poloidal torque applied tothe plasma amounts to about 100 Nm; this maximum
occurs at a frequency which seems to depend mainly on
the width of the current layer. In detail it depends on the9-assumed plasma temperature, on the applied frequency

and on the assumed island or ergodization width. The
toroidal projection of the applied force has about thesame value as the one imposed by tangential NBL Dueto the combined action of the DED and NBI torques, aFig. 4 3D grid for 2 poloidal turn flux tube. The grid wascreated first at the stagnation point (0), which wasmapped in both clock and counter clockwise direction to obtain the grid over the whole length offlux tube. The figure shows only the counter

differential rotation may be induced. It may be
speculated whether the differential rotation suppresses
convective cells and thus improves the confinement.

clockwise mapping. The dots inside the triangles
represent the centre of gravity.

6. Summary
estimates indicate that the transport in the laminar zone

Considerable progress has been made in recent

is predominantly convective while in the other mainly

years in the understanding of the static ergodic divertor

diffusive. The flux tubes of the laminar zone aretriangulated first at the symmetric point (stagnationpoint) and those are mapped along the field lines toobtain the 3D grid over the whole length of flux tube.
Figure 4 shows the grid for 2 turn region. The grid is[12], both theoretically and experimentally. It has been
understood that the ergodic zone with very longmagnetic field lines - which show (sub-) diffusive
properties in a finite volume - and the laminar zone
with open field lines are important, and that both regions
have different and partially complementary properties.
For analysing the ergodic zone and the transport in that

optimised to fit the deformation by carefully studying
the direction of stretching, bending and compression of
the flux tube. The scheme was tested with a simple heat
conduction problem in cylindrical geometry, where weobtained a good agreement with analytic solution. A
straight SOL model is now under processing. After
carefully checking the results, the calculation will beextended to the real DED geometry.

region, powerful mapping methods have beendeveloped.

The understanding of a rotating perturbation
magnetic field on the other hand is very new ground andthis contribution is one of the first steps into the field. A
first basic question concerns the physics of thereconnection of the magnetic field in an ergodized layer

5. Dynamic Aspects
The dynamic option of the DED has been

and what assumption to make about the thickness of theinduced shielding current layer there. An earlier modelof the shielding current is extended and new results arepresented for the torque exerted by the external field on

introduced in order to distribute the heat flow to thedivertor target plate to a large area. During the static
DED operation, the heat flux is guided towards thedivertor target plate; the divertor strike points follow

the plasma.

helically the DED coils. By the rotation of theReferences[]

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80

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