J. Plasma Fusion Res. SERIES, Yol.4 (2001) 4347

Internal Transport Barriers in W7-AS
STROTH Ulrichr*, ITOH Kimitaka2, ITOH Sanae-I.3, HARTFUB Hans, LAeUA Heinrich,the ECRH and the W7-AS TeamMPI filr Plasmaphysik, EUMTOM Association, D-85748 Garching, Germanyr

Institut fiir Experimentelle und AngewandtePhysik, CA\J Kiet, Germany
2National InstituteFusion Science, Toki, Gifu 509-5292, Japanfor3Kyushu University, Kasuga 816-8580, Japan(Received: 5 December 2000 / Accepted: 16 August 2001)

Abstract
The three-dimensional magnetic configuration of a stellarator offers a specific mechanism for atransition to improved particle and energy confinement. The pathway opens due to the layer of a strongly
varying radial electric field which is present in the transitional region from neoclassical electron to ionroot confinement. This type of improvement acts on turbulent transport.

Keywords:
W7-AS, intemals transport barrier, neoclassical transport

1. lntroduction

The three-dimensional magnetic field confi guration

Transport of energy and particles in magneticallyconfined high-temperature plasmas is in general strongly
enhanced above the neoclassical transport, i.e. the collisional flux-level estimates. The enhancement is at-of stellarators bears an additional loss channel forparticles and energy. It opens due to the collisionlesstributed to turbulence and this is independent of thespecific magnetic configuration. Systems with toroidal
symmetry, like tokamaks, show the same level ofcreate a radial electric current to modify the radial
electric field. This electric field generation opens twostellarator-specific routes to transport reduction: The
neoclassical electron root (ER) and in addition theformation of a neoclassically driven internal transportbarrier in the transition laver from electron-root to ionroot (IR) confinement.

loss of particles trapped in local magnetic mirrors. The
related particle fluxes are non-ambipolar and hence theytransport as devices without this symmetry, like helicalsystems [,2]. For the construction of a fusion powerreactor, a transport reduction with respect to the socalled L-mode confinement level is needed. The mostefficient reductions achieved are by transport barriers,
where in a radially limited area the diffusion coefficientsare reduced to the collisional level. The most prominent

Generally, in both cases a plasma with strongly
heated electrons is needed to make electron losses
superior to ion losses. In the plasma center, the plasma
potential turns from negative or small positive totransport barriers known are the H-mode [3] and the socalled internal transport barriers (ITB) t4l. It is generally

accepted that the turbulence reduction is due to asheared poloidal plasma flow generated by a radiallystrongly positive values. This feature is called theelectron root and has been observed in CHS [7,8] and inW7-AS [9,10] right in the plasma core. The electron

varying radial electric field (See for a review, e.g.,root is characterized by a strong reduction of thet5,61).

*Corresponding author's e-mail: stroth@ physik.uni-kiel.de+J@2001 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Stroth U. et al., lnternal Transport Barriers in W7-AS

temperature is fixed at 500 eV. The central peak iscaused by the loss of hellically trapped particles while
the two other bumps are due to the toroidal resonance.
Due to the higher velocity, in the electron transport only
the hellically trapped particles can be seen as T"
increases. Ambipolarity is satisfied where the two lines
intersect. At T" = 500 eV. only oire solution is foundcorresponding to the ion-root. At the intermediate Z"

neoclassical transport within the region where a strong
positive electric field exists. The neoclassical diffusivity
drops to values of the order of 0.1 m2ls. An additional
potential for transport reduction occurs at the transition
layer from the electron root to the ion root regime. In
this region the potential changes from strongly positiveto small or negative values. It therefore consists of alayer with strongly sheared plasma flow, which is ablevalue, three solution are possible. A small change in Z"
can lead to strong changes in E.. At the highest 2",

to reduce turbulent transport.

This article discusses the observations in relation
with a transport barrier in the transition layer between
the two neoclassical regimes [11] and focusses on thehysteresis in the transition with respect to a neoclassicalwhich corresponds to a situtation, where experimentally
an electron-root was found, only one solution isobtained at strongly positve E,. In the figure it can beseen that, once the electron-root is realized, Z" has totransition.
The neoclassical process leading to the transition isdiscussed in Fig. l. For three values of the electron

drop to very small values until a back transition to theion-root occurs. Hence, a neoclassical transition willtemperature, it shows neoclassical electron and ion
fluxes as function of the radial electric field. The ion

have a very strong hysteresis in[.

In the following a regime will be investigated
where a shear layer co-exists with the ER regime, wherethe neoclassical transport must be very low. Therefore, aturbulence suppression in the radially limited shear layer
will lead to a transport barrier with a strong increase of
the temperature gradient. The structure of transportbarriers has been discussed in 12-141. Since thedevelopment of a transport barrier depends in a nonlocal way on plasma parameters, a hysteresis both inelectron temperature Z. and heating power P should

ion root
Te = 500 eV

appear [15].

multiple roots

2. Experimental Results

Te=2kev

Figure 2 depicts contours of the ECE electron
temperature from a W7-AS discharge undergoingseveral pronounced forth and back transitions into
improved core confinement. The core temperature
increases by 0.7 keV to about 4.8 keV. The line averagedensity was n" = 3.5 x lOre m-3, the magnetic field

electron root

strength B = 2.5 T, the rotational transform r = 0.34 and

Te=4kev

the heating power P = 1.27 MW . The presented phase of

the discharge has parameters sufficient to access theneoclassical electron-root regime; details of thedischarge can be found in [0,11]. Fig. 2 depicts theincrement of the electron temperature at various radii.
Negative radii indicate the high-field side of the plasma.
It can be seen, that the modification of the electron
temperature due to the transitions is concentrated to theplasma core with an effective radius of lrl < 6 cm. The
asymmetry between high and low-field side is due toimperfect correction of the Shafranov shift. Hence one
has to symmetrizes the data. The increase of the electron
temperature is almost the same in the inner region, ThisE, (10" V/m)Fig. 1 Neoclassical electron (dashed) and ion (full line)transport as function of the radial electric field for'[ 500 eV and three value of[. The calculation=is done with the DKES code for W7-AS at a radiusof 13 cm. Circles indicate where the ambipolarity
condition is sattisfied.
44

Stroth U. et al., lntemal Transport Barriers in W7-AS

indicates that the improvement is due to a localized
transport barrier.

In Fig. 3, the change of the temperature gradient isexplored. The data were obtained by taking thedifferences of adjacent channels and dividing them by
the radial separation. Due to the Shafranov shift, one has

to symmetrize to obtain the radial information. Since
radiative losses and ion-electron coupling are negligible

in the core, the time traces are closely related to thethermal diffusivity. The increment of dT"ldr amounts up

to 0.4 keV/cm, which is approximately twice thegradient in the low confinement regime. Absolute values

for the electron heat diffusivity deduced from adjacent
ECE channels at r = 4 cm during the improved phase
are in the range of O.2 m2/s and the reduction is of theorder of 50 Vo.lt is found that the increment of theFig. 2 ECE measurements of the electron temperature indischarge 42975 with multiple transitions low andimproved confinement. The average tempearture
was substracted from each ECE channel, hencetemperature gradient is localized near the surface aroundr = 4 cm. The full width of the layer in which dT"ldr

the data represent the increment during thetransitions.

increases is about 3 cm. This implies that the reduction

in transport, which drives the incremental jump of thecentral electron temperature, is restricted to a narrowlayer around r = 4 cm. For the inner channels, rather adecrease of the gradient than an increase is observed.
Theoretical neoclassical estimates using the DKES
code [16,17] yield that the discharge should transit into

the electron-root regime already at an electronu.5t

temperature of 2 keV. Hence the depicted phase withTeQ) = 4.5 eV should be deeply in the ER state andtransitions seen at 4 keV are not consistent with a neoclassical prediction for the access of the ER state. The
radial region of ER confinement is predicted to be inside
6 cm. This would lead to a shear layer at about 6 cm andwould be consistent with the interpretation, thatconfinement improvement is due to a transport barrier in
the neoclassically generated shear layer. Furthermore,
the observation of a diffusivity well below 1 m2ls showsthat turbulent transport is strongly suppressed. As a third' r. -,)Fig.3 Change of Electron temperature gradient estimated from the data of discharge 42975
shown in Fig.2.

point in favour of a transport barrier, the hysteresis
behavior of the transition is discussed below.
A consistent picture emerges as follows: The phasevertical drift of non-thermal electrons generated by theof the discharge shown in Figs. 2 and 3 is in the ER
state throughout. Therefore, already prior to theintense ECRH.

transitions the shear layer can have already a reducing
impact on turbulence. This explains the low value of Xe

3. Evidence for Bifurcations
The bifurcation behavior of the transport barrier
was investigated by power-ramp experiments. The= 0.5 m2ls in the low confinement phase. The jump inelectron temperature can then be attributed to thedevelopment of a transport barrier, where the sheared
flow fully stabilizes the turbulence. The responsible

plasma parameters were B = 2.5 T,

radial electric field is mainly provided by theneoclassical particle flux but also influences by theFig. a). Fig. 4 shows the resulting time traces of thei.= | x lOre m-3 andt = 113. The power was ramped down from 0.7 MW to0.3 MW and ramped back up again (see upper trace inelectron temperature at three inner radii. The discharge
45

Stroth U. et al., lnterc:z,l Transport Barriers in W7-AS

MWo\<o>r5o,OOo-:a;st-t-ol l0.3

o.4 0.5 0.6 0.7 0.8 0.9(otime (s)1time (s)Fig. 5 The temperature gradient of the dithering phaseshown in Fig. 4 calculated from the time traces for
r= 0.5 and 3 cm. For one cycle a fit is also shown

Fig. 4 Heating power (top curve) and three channels(radii in centimeters are indicated) of the ECE
electron temperature diagnostics in the powerramp discharge 46388.

(solid line). From the fit, the insert is calculated,which shows the hysteresis of power flux vs.
temperature gradient during the cycle. Thedistance in the time steps of the insert is 0.02 ms.

in the time frame of Fig. 4 starts in the improved
regime. In these discharges, an effect of transport
reduction is only observed at r < 3 cm. This might beo!odue to the reduced available power of 0.7 MW.

C\At 0.62 s the back transition into the lowooN

confinement occurs at a heating power of 0.34 MW. The
temperatures at the three radii are 3.4,2.8 and 2.4 keV,
respectively. Due to the back transition, the temperatureor()

difference between r = 2 cm and r = 3 cm drops bymore than 60 Vo, and that between r = 0.5 cm and r = 2cm by more than 50 Vo. This reduction in the gradientreflects the strong increase of total transport at the back:=r"'gtransition. After increasing the power again, thetransition into improved confinement is observed at aheating power of 0.5 MW and temperatures of 3.8, 3.2
and 3.0 keV. Hence the data show a hysteresis in bothtemperature and heating power. After the transition into

01234

the improved state, the temperature difference between rT" (keV)= 2 cm and r = 3 cm increases by a factor of two and is

the same as between r = 0.5 cm and r = 2 cm. This
indicates the reduction of the energy transportcoefficient by about a factor of two. These prominent
jumps of the transport coefficient (which is dominatedby anomalous transport) at both transitions clearly
illustrates the existence of the transport barrier for theFig.6 Hysteresis expected according to the DKES codefor the transitions from electron to ion-root
regimes calcualted with the parameters of thedischarge of Fig. 4.

electron energy. Neoclassical calculations of the200 eV. This indicates that the sudden confinement
improvement is due to a suppression of turbulent
transport in a region which might be preconditioned byhysteresis are shown in Fig. 6. According to this figure,the back transition to the IR regime is expected at T" <46Stroth U. et al., lntemal Transport Barriers in W7-AS

neoclassical transport.

drifts of non-thermal electrons produced by ECRH)

In the transition to the improved state (/ = 0.8-0.84sec), i.e. near the threshold condition, dithering cycles
are observed. In Fig. 5, one of these cycles is analyzed
in view of the hysteresis. To this end, the temperature
data at r = 0.5 and 3 cm from Fig. 4 where used towhich stabilizes turbulence and reduces the turbulent
transport contribution in a narrow layer.

Acknowledgments
Two of the authors (KI and SII) acknowledges
hospitality of Alexander von Humboldt Stiftung andcalculate temperature gradient and average temperature.
Both time traces were fitted to calculate the dependence

Max-Planck-Institut fur Plasmaohvsik.

of power flux (heating power corrected due to thetemporal change of the energy content) on temperatureReferences[]

gradient as plotted in the insert of Fig. 5. Data and fit of
the temperature gradient are also depicted. The arrows

F. Wagner and U. Stroth, Plasma Phys. Control.
Fusion 35, l32l (1993).
U.
I2l Stroth, Plasma Phys. Control. Fusion 40, 9

indicate the course of time for the transition to low
confinement (1) and back to improved confinement (2).
The dots in the insert mark time points every 20 ps. The
swing of the hysteresis in power flux is about 140 kW.

(1998).

[3] F. Wagner et al., Phys. Rev. Lett.49,1408 (1982).
[4] E.J. Strait er al., Phys. Rev. Lett. 75, 4421(1995).
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This behavior shows again that it is not a smoothtransition to improved confinement but rather thedevelopment of a barrier which can suddenly appears
and vanish. The hysteresis occurs at very different
values from those expected in a neoclassical transition

Fusion 38, I (1996).

t6l K.H. Burrell et al.,Phys. Plasmas 4, 1499 (1997).
t7l H. Idei et al., Phys. Rev. Lett.71,22 (1993).
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as shown in Fig. 6.

fl998).

t9l M. Kick et al.,Ptasma Phys. Control. Fusion 41.,
4. Conculsions

As49 (1999).

In conclusion, several observations indicate that theconfinement improvement observed in strongly ECR
heated plasmas is due to the development of an internaltransport barrier rather than due to a reduction of neoclassical transport in the electron root regime. The low
value of the diffusivity points to a suppression of

tl0l H. Maassberg et al.,Phys. Plasmas 7,295 (2000).
[11] U. Stroth e/ a/., Phys. Rev. Lett. 86, 5910 (2001).
[12]P.H. Diamond et al.,Phys. Plasmas 2,3685 (1995).
U3l P.H. Diamond et al., Phys. Rev. Lett. 78, 1472

turbulent transport, the transport reduction appears in anarrow radial region and the forth and bacfk transitions
as well as the dithering phase prior to the transition
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Structural Formation in Plasmas (IOP, England,(1997\.

tl4l K. Itoh, S.-I. Itoh and A. Fukuyama, Transport andLondon, England, 1999), chapter 12.
ll5l S.-I. Itoh and K. Itoh, Phys. Rev. Lett. 60, 2276
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temperatures inconsistent with the neoclassicalprediction for the ER transition. It can be conjectured
that it is the flow shear layer inbetween the neoclassicalelectron- and ion-root regimes (possibly increased by116lW.I. van Rij and S.P. Hirshman, Phys. Fluids, B 1,s63 (1989).

tlTl H. MaaBberg et al.,Plasma Phys. Control. Fusion
3s, B3l9 (1993).

47