Modelling of Plasma Rotation under the Influence of the Dynamic Ergodic Divertor in the Tokamak TEXTOR
turbulence on rotation is included by adding an anomalous viscosity to the neoclassical perpendicular one.
Computations performed for TEXTOR reproduce the change in the central toroidal plasma velocity v φ with the DED
perturbation in reasonable agreement with the experimental findings. Thus, |v φ | grows by ≈ 5km/sec in shot # 94092 with co
neutral beam injection and an equivalent perturbation current of I hel ≈ 6kA and decreases by ≈ 20km/sec in the case of shot
#97613 with predominantly counter injection and a perturbation current of I hel ≈ 20kA.
Keywords: Plasma rotation, Dynamic Ergodic Divertor
The plasma rotation is considered as an important factor for the confinement properties of fusion plasmas-.
Therefore, the plasma spin up in the toroidal direction and the concomitant change in the electric field and the
poloidal flow velocity discovered on tokamak TEXTOR operated with the Dynamic Ergodic Divertor (DED) has
evoked considerable interest. Such a spin up has been observed both in the 3/1 and 12/4 configurations of DED coils
which provide resonant effect on magnetic field lines on the q=3 surface and result in field line stochastization. In this
contribution we study the physical mechanisms leading to the observed plasma rotation in stochastic layers. -.
The revisited neoclassical theory - which is based on Braginskii’s equations -, allows within the
framework of a rigorous analytical approach calculation of the two dimensional velocity field on the flux surfaces
and the perpendicular ambipolar electric field. This theory is valid in collision dominated plasmas with steep gradients
and was able to reproduce the toroidal spin up in ALCATOR C-MOD , , . It was extended to include
anomalous viscosity which is believed to be important in all collisionality regimes .
Since the ITG (Ion Temperature Gradient) threshold is exceeded in the TEXTOR L – mode, this instability, together
with the trapped electron mode, are considered as the main sources of turbulence. The friction with the recycled neutral
gas due to charge exchange is in limiter devices a strong source of momentum loss, as pointed out in .
The ambipolarity constraint requires in the case of unperturbed magnetic surfaces that the radial component of the
electric current perpendicular to the magnetic field  vanishes. If the field lines are ergodized, however, the radial
gradients of the plasma parameters and, according to Ohm’s law, the radial electric field generates electric currents
which are parallel to the field lines and have a nonzero average radial component . In this case the ambipolarity
constraint requires that the sum of this current component and the radial component of the classical electric current
perpendicular to the magnetic field  is zero.
RADIAL CURRENTS DUE TO FIELD LINE STOCHASTIZATION
The electric currents under the condition of magnetic field line stochastization originate from the radial excursion RESULTS AND DISCUSSION
We use as examples the plasma parameters of shots # 94092 (low power co-NBI) and #97613 (large power counter-
NBI) They are given by (# 94092) : rin = rs=46 cm, R=175 cm, Timax = 1.3 keV, Temax = 1.63 keV, nmax = 3 1013cm−3,
η=1.6, Bφ = 2.23 T, PMWco = 0.25 MW, PMWcounter = 0, plasma current Ip = 300 kA, and (# 97613) Timax = 2.2 keV, Temax
= 2.1 keV, nmax = 3.4 1013cm−3, η=1.6, Bφ = 2.25 T, PMWco = 0.35 MW, PMWcounter = 1.3 MW.
To show the effect of an ergodic layer between re1=40 cm and re2=45 cm (typical for the 12/4 configuration) field
line stochastization with the typical parameters DFL = 2 10−6m and ˜LK=40 m (Ihel ≈ 20kA) The gradient lengths of
density and temperature in this layer are Ln = LT = 0.05m. The temperature at the inner rim of ergodic layer is 100
eV. As indicated in  σerg ∼ Ihel is assumed.
In the following figures vt is defined as vt =|vφ |, i.e. counter injection effects a positive vt . The unperturbed maximum
toroidal velocities vTmax = 40 km
sec (# 94092, Fig. 1) and vTmax = 140 km
sec (# 97613, Fig. 2) can be reproduced within
an accuracy of 10 %. In the case of shot # 94092 the toroidal velocity increases by ≈ 5 km
sec if the the ergodic layer
(Ihel ≈6kA) is switched on (Fig. 3). To avoid the mode locking, the NBI of shot # 97613 is predominantly in the counter
direction. Therefore Tergo (Ihel ≈ 20kA ) effects a reduction of vt by Δvt ≈ 20 km
sec (Fig. 4). The velocity gradient stays
outside the ergodic layer almost the same. These results are in reasonable agreement with the experimental findings.
Figs. 5 and 6 show the temperature and density profiles of shot # 94092. In the case of shot #97613 similar profile
shapes had been assumed. Concerning the poloidal speed measurements of the impurity CIII rotation are available.
However a computation of impurity ion velocities is beyond the scope of this contribution. The obtained change Δv θ ≈
sec in the case of shot # 97613 seems to be in rough agreement with that of the impurity speed.
The inclusion of the ergodization terms into the modified neoclassical theory shows that the change of toroidal velocity
can be described properly. However, at present the theory is still not able to predict the poloidal velocity of the impurity
ions, mainly because the impurity and main hydrogen ions are in different collisionality regimes.
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