J. Plasma Fusion Res. SERIES, Vol.1 (1998) 80-83

The Role of Magnetic Shearin the Confinement of W7-AS Plasmas
BRAKEL Rudolf*. ANTON Mathias, ERCKMANN Volker, REDLER Stefan, GEIGER Joachim,
HARTzuB Hans-J, HIRSCH Mathias, JAENICKE Rolf, KUHNER Georg,MAASSBERG Henning, STROTH Ulrich, WAGNER Friedrich,
WELLER Arthur, the W7-AS Team and the ECRH-Groupl
Max- Planck- Institut filr Plasmaphysik, E U RATO M Association,
I Institut

D-85748 Garching, GermanY
fiir Plasmaforschung, Universitiit Stuttgart, Germany(Received: 30 September 1997/Accepted: 22 October 1997)

Abstract
Magnetic shear has systematically been varied by inductive current drive in moderate B, ECR
heated W7-AS discharges. Confinement is found to depend strongly on magnetic shear in the presenceof high order rational values of the rotational transform. For optimum confinement, high order resonances have to be avoided in the boundary region, or shear must be sufficiently large. The observed
improvement of degraded confinement with increasing shear is associated with a reduction of transport

to the neoclassical level.

Keywords:W7-AS, stellarator, magnetic shear, confinement, transport

magnetic islands of considerable size may form atrational rvalues being in resonance with the major external field perturbations ("natural" 5/rn-components
from the 5-fold toroidal symmetry, and I/3' and t/2-

1. Magnetic Shear in W7-AS Confinement
Shear in the magnetic field is generally expected toreduce anomalous transport by radial decorrelation ofturbulent structures. In tokamaks, a synergy of im-components from field enors)[2]. With increasing fl
the sensitivity of confinement to these resonances diminishes, giving evidence of a beneficial effect of pressure
induced shear [3]. Although the major resonances playa role, the detailed dependence of W7-AS confinementon the boundary value r" of the rotational transformcannot be explained by the extemal field perturbations[2]. Therefore perturbations at the higher order t: n/ mresonances may be important. Their impact will dependon the magnetic shear.
In the present study, shear has been applied byinductive current drive to ECR heated discharges atproved stability at low or reversed (in the tokamak
sense, i.e. dq/dr< 0) magnetic shear and EXB flow
shear is supposed to give rise to the recently observed
internal transport barriers[L]. In particular in stellarators, the quality of flux surfaces and their suscepti-

bility to magnetic perturbations sensitively depends onthe magnetic shear.

In Wendelstein 7-AS (W7-AS) the rotationaltransform r of the vacuum field has very low shear
which, at finite B, is modified by pressure driven (bootstrap- and, in W7-AS reduced but still significant,Pfirsch-schltiter (PS)-current) and, optionally, by externally driven plasma currents. Due to the small shear,@1998 by The Japan Society of Plasma
Science and Nuclear Fusion Research' Corresponding author's e-mail: brakel@ ipp'mpg.de80

Brakel R. et a/., The Role of Magnetic Shear in the Confinement of W7-AS plasmas

moderate fl (fr< 1%). The experiments are interpreted on the basis of e.profiles calculated by the(lp / kA, ara

10

NEMEC equilibrium code [4], with inductive andbootstrap current profiles from the DKES code [5].
Plasma currents up to 1o: t 30 kA have been applied.

)ts(25,0.15)

They contribute /t^:(poRlo)/(2nd B) to the boundary transform, i.e. 0.O07/kA for the typical parameters(15,0.09a)z"e.f--Ya:0.15 m, R-2 m and Bo:2.5 T of this study (positive currents increase the rotational transform). TheNEMEC calculations show that for fixed limiter aperture the effective plasma radius changes with plasma't'tr I=current as L,a/a:0.O041e/kA. Ohmic heating is negligible ( < 10 kW) as compared to ECRH (450 kW at140 GHz). The pulse length of 1.1 s is above the cur-(0,rent diffusion time scale.
Figure 1 shows the dependence of energy confinement on both r" and .Io. The plasma energy has been
derived from the diamagnetic loop signal, with a correction accounting for residual magnetic flux from large
plasma currents, which is determined from the kinetic
electron energy content at tu:9.51 (from profile integration). The electrons dominate the total energy: ion
temperatures are below 450 eV compared to electron
temperatures tp to 2 keV. Limiter aperture and lineintegrated densities are identical for all discharges, r'.e.
the plasma radius increases from 0.15 m at 1o:0 too)

(5, o.og4)

0.4 0.45 0.5 0.55 0.6t^
Fig.1 Dependence of plasma energy on the boundary rotational transform for various plasma currents. For
three discharges at /o = 5 kA density control was lost

and the measured energy (crossed squares) has
been scaled by n1l2 (squares)

0.6

0.165 m at Io:25 kA and the central densities decrease from 4 to 3.5 x 101e m-3 (optimum confinementin W7-AS scales *d/.s [6]). With small net current

0.55,P 0.5(1e < 5 kA) a strong dependence of confinement on therotational transform is observed which is smoothed byincreasing the current (to *15 kA) and disappears at
the highest current (+25 kA). Here, the level of opti
mum confinement in the current free case is reached.

0.45
0.4

2. Confinement at Moderate Shear
For the discharges of Fig. 1., degraded confinement00.05 0.1 0.15
rlm

0.2

Fig. 2 Calculated rprofiles for discharges with net plasma

is associated with a very flat electron temperature

current as indicated (full lines: optimum confine-profile at larger radii (r > 0.05 m), whereas for good
confinement, a strong {-gradient extends to the edge.
The density profiles are similar for all discharges.
Figure 2 shows the calculated profiles of the rotationaltransform for low current discharges (10:0 and 5 kA)

ment; dashed lines: degraded confinement). Rationals nlm, m<30, are given for reference (horizontallines; the shaded area covers the range of rationals

with m< 15).

at selected tu-values close to l/2, where the sensitivityof confinement to ra is strongest. The rational values
t:n/m up to m:30 are given for reference. The close
vicinity of t:l/2 is free from such resonances (see alsoRef. [7]). The calculated bootstrap current reaches up
to 7 kA in case of optimum confinement, but only up
to 2 kA for degraded confinement. For low confinement with small bootstrap current (dashed lines inFig. 2), shear is basically determined by the inductivecurrent, i.e. remains low if no net current is imposed.
For good confinement (full lines in Fig. 2), both low ormoderate shear may result from the combination of inductive and bootstrap current density profiles.
The analysis gives evidence that confinement inW7-AS essentially depends on magnetic shear and resonant rvalues in the outer plasma region: for optimum
81Brakel R. et al., The Role of Magnetic Shear in the Confrnement of W7-AS Plasmas

port with temperature and a simultaneous strong reduction of anomalous transport. The results are consistentwith those of Ref. [8] (low density in Fig. 3, T"<4keV) where 1" decreased by a factor of up to 2. At thehigher collisionality of the present study neoclassicalconfinement r(r) has to be in the "resonance-free" region (e.9. t":0.48 at 1o:5 kA), or shear has to be
sufficiently large in the presence of high ordet n/ mresonances of the rotational transform (e.9. q:0.495
at 1o:0). In contrast, degraded confinement is associ-ated with low shear in the presence of such resonances(e.g. 4:0.48 at /o:0). With respect to the maximum
nr-number which determines the width of the "resonance-free" region, the experimental tu-values for theonset of confinement degradation below (t" = O.49)

I /kA-30 -20 -10 0 10 20 30

and above (t" = 0.53) t^:I/2 are not consistent. However, since at present we do not know which specificperturbations at the high order rational surfaces enhance transport, there is no a priori reason for such asymmetry. Furthermore, the rather strong natural 5/9+ = 0.51?
\4operturbation will be important as well for t" > 0.53. It
gives rise to magnetic boundary islands which cannot beaccounted for by the NEMEC code.

fo= 0.424', -E- - --n-n=n / 1Ol sm-3:

3. Proceeding to High Shear
If, for t":0.51, the net current is increased from 5
to 7.5 kA, optimum confinement strongly degrades,
probably because t(r) is raised with low shear into the--a-4- -o,-4--o--2-0.2 -0.1 0

upper "resonance" region (Fig.3; here, the variation ofplasma radius with current is compensated by proper
adjustment of the limiter aperture). Confinement recovers, when shear is increased by higher currents. For

0.1

0.2

AtaFig.3 Dependence of the electron kinetic energy contenton plasma current for t" = 0.51 and 4=0.42.

q:O.42, confinement improves continuously with currents of both sign. In the low density case included inFig. 3 from a previous study, the stagnation with highnegative currents is attributed to the approach of verysmall central rvalues [8].
It is obvious, that the effect of magnetic shear on
local transport can at best be assessed from the degraded situation at q:0.42, which is free from effects
related to the "resonance-free" zones. Figure 4 shows
the radial profiles of electron temperature and heat
conductivity (from power balance analysis) for discharges with plasma currents of 0, + 10, and +25 kA.
With increasing shear a continuous steepening of theI1
1 -,i X" +10kA

10i\--"/TI\if^'/"f[.'OkA - ii\, . y'{.--}-'-f,l:#-+\\,i!
I t n'\=.{'1'[-gradient is observed at the boundary independent on
the sign of shear. In this region (0.08 to 0.14 m) theheat conductivity decreases by a factor of up to 5. As.-.}\..r....,.*,r.,';. t ... .1*\-,.{'tcompared to neoclassical transport, the experimental 6
is anomalous over the whole plasma cross section for/o:0, neoclassical in the very center for +10 kA, andneoclassical up to r/a30.7 for +25 kA. Only at thevery plasma edge transport remains strongly anomalous. Thus, with increasing shear, the region dominatedby neoclassical transport continuously expands towards
the boundarv due to the increase of neoclassical trans--10+25kA/-.1.O

feff.1.2['n]Fig.4 Measured l.-profiles and 1"-profiles from power
balance for discharges at t,=0.42 for various
plasma currents.
82

Brakel R. et al., The Role of Magnetic Shear in the Confinement of W7-AS plasmas-30

4. Summary-40

Confinement in W7-AS at moderate p is found to
be strongly related to high order rational values of therotational transform and to the magnetic shear. For
optimum confinement, these resonances have to beavoided in the boundary region or shear must be sufficiently large if they are present. Therefore, with moderate plasma current (up to the order of the bootstrap
current) the boundary rotational transform has to be

E -som7 -oo€ -zoot -ao

adjusted to the narrow "resonance-free" region close to
the major resonances l/2 and 1/3. With t" in the "res--90-1 00

onance" region, confinement degrades strongly sinceshear remains low. So far it is not clear which specificperturbations at the high order rational surfaces enhance transport and are stabilized or decorrelated by
the magnetic shear. Increasing the shear with higher
plasma current for a degraded situation continuously
improves confinement back towards the optimum.
Transport analysis indicates a strong reduction of transport to the neoclassical level. The effect is independentof the sign of shear.

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
frequency shift (MHz)Fig. 5 Reflectometry spectra from discharges with plasma

currents of 5 and 25 kA at 4=0.42. The spectrum
fromrrall reflection without plasma is given for ref-transport is significantly smaller, and the observed improvement by reduction of anomalous transport withincreasing shear is more pronounced.

Reflectometry spectra indicate significant systematic changes of plasma turbulence with increasing magnetic shear (Fig. 5). A broadening and a large red-shift
in the spectra is observed. In addition, the coherent
peak of the unshifted mm-wave carrier, which cannot
be observed for reflection in the low-shear plasma, reappears. These features gradually strengthen with themagnitude of shear and are independent of its sign. The
quantitative interpretation of reflectometry spectra isdifficult, since the propagation and k-spectra of theturbulence and the specific antenna-plasma geometry
influence the spectrum of the reflected and backscattered mm-wave. However, the observed broadening
and frequency shift would be consistent with a decreaseof the turbulence scale length and an increasing plasma
rotation in the electron diamagnetic drift direction,References[1] K. Burrel et al., Phys. Plasmas 4,1499 (1997).
[2] R. Jaenicke e/ a/., Nuclear Fusion 33, 687 (1993).
[3] H. Renner et al., Contr. Fusion and Plasma Heat-ing (Proc. 19th Europ. Conl, Innsbruck) ECA
16C part r,50r (1992).

[4] S.P. Hirshman et al., Compttt. Phys. Comm. 43,
143 (1e86).

[5] W.I. van Rij and S.P. Hirshman, Phys. Fluids B 1,563 (1e89).

[6] U. Stroth et al., Nucl. Fusion 36, 1063 (1995).

[7] H. Wobig er a/., Plasma Phys. and Control. Nucl.

Fusion Res. (Proc. Llth Int. Conf. Kyoto, 1986)
Vol. 2 (IAEA: Vienna) p.369 (L987).
[8] V. Erckmann et al., Plasma Phys. and Control.
Nucl. Fusion Res. (Proc. 16th Int. Conf.Montrlal,/ ee6) F1-CN-64 / CP-r (Lee7).

respectively. Unfortunately, direct spectroscopic
measurements of the plasma rotation which could
support this hypothesis are not available for these discharges.

83