The Dynamic Ergodic Divertor (DED)
Background
For a fusion reactor based on magnetic confinement, the "heat insulation" of the
central plasma has to be good enough to build a reactor of a "reasonable" size. In practice
this is realized by setting up a configuration of nested closed magnetic surfaces. The plasma
particles remain relatively long on "their" magnetic surface until a collision brings them
to the next surface. This scheme provides "good confinement".
The requirement for good confinement is only needed for the plasma core; at the plasma edge,
it is even counterproductive because it provides an extremely high heat flux density for those
magnetic field lines which intersect the wall. These field lines form the ScapeOff Layer
(SOL) and the interaction zone with the wall is called the divertor (for cases where a mdification
of the magnetic field configuration separates the wall from the nested closed magnetic surfaces).
The interplay between the particle flow along the magnetic field lines and the diffusion across
field lines determines the radial decay characteristics of the power load on the divertor plate.
Experimentally it is observed, that the radial power decay length amounts to about 1 cm for all
experiments; it is not expected that this value increases in a fusion reactor.
The power deposition area is determined by the product of radial decay length, circumference
of the reactor and a flux expansion factor which amounts to about 5. A small power deposition area
means a high concentration of the power deposited to the wall. In 3 GW reactor, this power amounts
to 600 MW and is deposited on a strip of a few centimeters width only. This high power
concentration imposes severe requirements on the choice of material. Therefore the value of the
decay length is a very important quantity and it is desirable to increase it.
 Fig. 1: Concepts of the conventional
divertor and the ergodc divertors 
For this reason, the investigation of a new concept has started in our institute, with the
installation of the Dynamic Ergodic Divertor (DED) on TEXTOR. The basic idea is to break the
closed magnetic flux surfaces and the plasma boundary, braid the magnetic flux tubes and increase
the perpendicular transport. This should then provide an increased power decay length. However,
previous experiments have shown, that ergodization of the magnetic field not only increases the
radial transport but produces additional patterns of enhanced power deposition. This feature
will be taken into account by the dynamic component which can rotate and thus smear the heat load
over large areas.
The rotation of the external field is a new feature which  worldwide unique  allows TEXTOR
to investigate the effect of induced plasma rotation. From this rotation also several other
beneficial effects with respect to confinement, stability and the operational space of a tokamak
are expected: The rotation might lead to the destruction of turbulent cells and the avoidance
of wall locked modes.
The DED setup
The magnetic flux surfaces can be broken up with a minimum of perturbation by making use of
resonances. The resonance condition is fulfilled, if external perturbation coils are arranged
parallel to the magnetic field lines at a preselected radius of the plasma. For this a coil
system consisting of 16 conductors was installed at the inboard side of TEXTOR (high field side).
The individual coils run helically around the torus with feedthoughs at both ends. This setup
allows full flexibility for coil connections.
The coils can be fed with dirct of alternating current (DC or AC) with an amplitude of up to
15 kA each. The DC mode of operation is similar to previously built ergodization experiments
(e.g. at Tore Supra, TEXT of JFT2M) while the AC modes are novel providing a rotating field:
The phase difference of neighbouring coils amounts to 90 degrees yielding a moving field pattern
similar to an induction motor. The frequencies can be selected ranging from 50 Hz (low frequency)
up to several high frequencies in the band between 1 and 10 kHz.
 Fig. 2: Sketch of the DED coils and a photograph of the actual arrangement 
Ergodization
For the representation of the topology of magnetic fiels lines, they are traced over long
distances around the torus: each time when a field line intersects a preselected poloidal cut of
the torus, the point is marked resulting in a pattern characterizing the magnetic field topology.
This procedure is commonly applied in Nonlinear dynamics and Chaostheory and is called a
Poincaréplot (after the French mathematician H. Poincaré). For the DED this yields:
 "Regular areas" with closed curves which are equivalent to the flux surfaces, which
to a good approximation are circular in TEXTOR
 "Ergodic areas" show a more diffuse picture; magnetic field lines are no longer
restricted to a surface but fill a certain area.
 "Magnetic island structures" from the transition region between regular and full
ergodic pattern. Island chains are formed by a relatively low perturbation level. With
increasing perturbation strengt the island width grows; if several island chains overlap,
the region becomes ergodic. A measure of the degree of ergodicity is the Chirikov parameter
which is the ratio of the island width to the island separation.
For the normal mode of operation, the DED is laid out such, that the perturbation field is only strong at
the boundry and decays rapidly
to the plasma core. This guarantees that our requirement is fulfilled, namely to enhance the transport in
the edge but not to deteriorate the
confinement in the core. The rapid radial decay of the DEDfield is realized technically by the choice
of a highly multipolar coil setup (base mode: m/n=12/4). For more special investigations of core islands,
a coarser mode structure with a deeper penetration can be implemented, e.g. 6/2 and 3/1 modes.
 Fig. 3: Ergodization for different perturbation levels 
The top left picture shows an ergodization pattern calculated for TEXTOR: The inner "intact" region of
magnetic field lines is surrounded by the ergodic zone. The DED coils are located on the left part of the
figure and are protected by divertor target plates. For a better representation, we "cut" the picture at the
equational plane at the low field side and unhold it as shown in Fig. 3ac. In this way, the radial direction
can be streched relatively to the poloidal one. The DED coils are positioned around Θ=π at a radius
of 53.25 cm. The figures a), b) and c) represent three typical cases where a) stands for a condition with strong
edge ergodization, b) for a modest ergodization and c) for a low ergodization level which is island dominated.
These cases can easily be selected either by a variation of the perturbation level (current amplitude in the DED
coils), or by a variation of the ratio between plasma current and magnetic field strength; in the latter case,
the resonances (resonant qsurfaces) are moved towards or away from the boundary such that they are more or less
affected.
In particular Fig. 3a) shows "white" areas between the ergodized zone and the wall. This lacking of
Poincaré points results from the stopping of the field line tracing after hitting the wall. This
interception is introduced because plasma particles flowing along the magnetic field lines would be neutralized
there and deposit their power to the walls. The field lines in the white areas have a short connection length
between two intersections with the wall. This area is called the laminar zone. In this region, the
interaction with the wall is particularly intense and it is to some extent degree to the Scape.Off layer in a
conventional divertor tokamak.
The conception "Ergodization"
The term "ergodization" stems from theoretical physics or mathematics. It means e.g., that for the
trajectory of an object "time averaging and spatial averaging can be exchanged". this definition was
used by Boltzmann to explain the increase of the entropy in phase space. the definition can also be formulated
in another way:"the trajectory of an object starting from any point in an ergodic area comes infinitely
close to any other point of this volume". The definition is valid only for systems without losses, which
can be written in a Hamiltonean formalism.
Fields of specific interest
So far the theoretical analysis has mainly concentrated on the following topics:
Ergodic area:
Under this heading the topology of the magnetic fields is investigated, such as the strength of the
ergodization, the "diffusion" of the magnetic field lines, particle orbits in the ergodic zone etc. for the
field line tracing two methods are applied: Integration of the trajectory and mapping of the trajectory.
The latter is a modern technique for Hamiltonean systems and is more than an order of magnitude faster than
the integration.
Divertor (laminar zone, area of near field)
For the modelling of the plasma transport in the ergodic and laminar areas, a new 3D plasmacode has been
adepted and developed which is based on Monte Carlo methods to solve the Braginskii equation. A picture of the
heating pattern on the DED target plate in front of the DED coils is shown in the figure below. The heating
pattern closely follows the structure of the coils. Details of the structure result from the trajectory of the
field lines in the laminar zone. The left picture shows the characteristic heat deposition pattern for low,
the middle one for medium and the right one for a high ergodization level.
 Fig. 4: Power deposition pattern for low, medium and high degree of ergodization 
Dynamic aspect
the analysis of the dynamic operation of the DED is the most complicated one. At low frequency operation
of the DED, a quasistatic response of the plasma is expected. The main aim of this mode of operation is the
distribution of the heat over a large area. At high DED frequencies, a torque will be transferred from the
external currents to the plasma. At the same time, included currents should shield the plasma interior from a
further penetration of the DED field. The resulting differential plasma rotation should have a strong influence
on the confinement properties of the plasma. This mode of operation is worldwide unique and it is expected to
obtain a novel possibility to positively influence the plasma properties.
