Proceedings of ITC/ISHW2007

Effect of Ellipticity on Thermal Transport in ECH Plasmas on LHD
H.Yamada, M.Yokoyama, S.Murakamia, K.Y.Watanabe, H.Funaba,Y.Narushima, S.Sakakibara, T.Morisaki, Y.Nagayama,
S.Kubo, T.Shimozuma, K.Tanaka, T.Tokuzawa, I.Yamada and LHD Experimental Group
National Institute for Fusion Science, 322-6 Oroshi-cho, Toki 509-5292, Japana Dept. of Nucl. Engr., Kyoto Univ., Yoshida-honmachi, Sakyo, Kyoto 606-8501, Japan
Effect of ellipticity on thermal transport has been investigated for ECH plasmas in LHD. Ellipticity κ is scanned
from 0.8 to 1.4 by controlling quadrupole magnetic field. Experimental data of energy confinement time align withthe scaling for all configurations, however, there exist systematic offsets. Performance τEexp/τEISS04 is summarized as
0.94±0.02 for κ=0.8, 1.41±0.07 for κ=1.0, and 0.91±0.03 for κ=1.4. Local transport analysis based on power
balance indicates that plasma transport is predominated by anomalous transport. However, the observed anomaly
shows correlation with the change of an effective helical ripple εeff. Physical background of this correlation, thedependence on the poloidal viscous damping rate Cp is discussed. The present experimental comparison suggests anegative evidence for relevance of Cp.
Keywords: Thermal transport, Configuration effect, Neoclassical transport, Anomalous transport,
Net-current free plasmas, Ellipticity

1. Inroduction
Exploration of the effect of magnetic configuration onconfinement is prerequisite for optimization of a helicalsystem. Extensive efforts in experiments as well as theories
have been done. Geometrical optimization for theneoclassical transport has been demonstrated in NBI
plasmas on LHD and the anomalous transport has been
suppressed as well in the neoclassical optimized
configuration [1]. In these configuration studies, theposition of the magnetic axis is the key control parameter[2].
International collaboration for the stellarator/heliotron
confinement database has progressed [3-6] and acomprehensive comparative study has suggested thatnet-current free plasmas have robust and similar
dependence on magnetic field, density and heating power[3-5]. Gyro-Bohm nature explains experimental trend in avariety of devices quite well, like in the ISS04 scaling [5];τ EISS 04 = 0.134a 2.28 R 0.64 P −0.61ne0.54 B 0.84 ι20.41/3.
−0.79
−0.19
0.00 1.06 −0.07∝ τ Bohm ρ *β ν b * ι2 / 3 εTogether with confirmation of this commonality, existenceofsystematic
offsets
betweendifferent
configurations/devices has been pointed out. These
device/configuration dependent offsets have been
quantified by comparisons of subsets which reflectcharacteristic
configurations,however,physicalbackground of this quantity has not been clarified yet. The
measure of the offsets correlates with the effective helicalripple εeff which is characterized by the neoclassicalhelical ripple transport in the collisionless 1/ν regime [5].
author’s e-mail: hyamada@LHD.nifs.ac.jp

It should be noted that the transport in experiments itself
is significantly larger than the neoclassical transport.
Since the anomalous transport is predominate, a physicalpicture of neoclassical transport is not directly applicable
to explain experimental observation. Therefore theseobservations postulates a working hypothesis thatneoclassical optimization can suppress anomaloustransport.
Large flexibility of the coil system of LHD enables us
configuration scan other than the position of the magnetic
axis, i.e., plasma elongation. Although the plasma
elongation scan for NBI heated plasmas have been alreadyreported [1], ECH plasmas which are located in thecollisionless regime have not been studied yet.

2. Experimental Set-up
Plasma elongation has been controlled by thequadrupole field and scanned in the range between κ=0.8
and 1.4 (see Fig.1). Here elongation is defined by thetoroidal averaged value since the elliptic surface rotatesalong the toroidal angle. The position of the magnetic axis
Rax is fixed at 3.6m. The magnetic field is fixed at 1.5 T,
which provides centrally well focused deposition of ECH
with 84GHz. The plasma volume, in other words, theplasma minor radius is kept the same by the control of theeffective aspect ratio of helical coil. A helical coil consistsof 3 blocks with independent power supplies, which canchange the effective current center of the helical coil.
Although the Shafranov shift and resultant change inrotational transport is sensitive to ellipticity [7], finite-β
effect is not significant in the present study since the β isProceedings of ITC/ISHW2007
limited to 0.3% in ECH plasmas.
1.0

κ=1.4

κ=1.0

κ=0.8

Therefore which parameter; εeff or Cp is more essential
in transport cannot be distinguished. However, plasma
elongation can separate these two effects. As seen in Fig.2,
a vertically elongated configuration (κ=1.4) has larger εeff
than the standard configuration (κ=1.0) while it has smaller
Cp.

Z (m)

0.5

03. Experimental Results

3.5

4.0

3.5R (m)

Fig.1

4.0

R (m)

3.5

4.0

R (m)

Magnetic flux surfaces for elongation scan.
Cross-section at vertical elongated position
where the helical coils are located on theequatorial plane.

In this study, the poloidal viscous damping rate is
explored as a potential key parameter to bridge theneoclassical optimization and suppression of anomaloustransport. Generally speaking, zonal flows are generated
efficiently in the configuration with low poloidal viscosity
and then suppression of anomalous transport is anticipatedin such a configuration. The poloidal viscous damping rate
Cp [8] is plotted with εeff for Rax in Fig.2. Since Cp isaffected by a toroidal curvature as εeff, Cp and εeff has aclear correlation. Indeed, in the standard ellipticity κ=1.0,
both quantities have the same trend for Rax and become theminimum in the vicinity of Rax~3.6m where highperformance can be obtained in the experiment.

100

εeff (κ=1.0)

0.0-0.6 -0.4 -0.2

00.2

0.4

0.6

reff (m)Fig.3 Electron density profiles in discharges withdifferent elongation.

κ=0.8 #59717
κ=1.0 #59010

2.0Cp (κ=1.0)

Cp(2/3)εeff(2/3)

0.5

0.1

10-1
κ=1.4
κ=0.8
3.6

κ=0.8 #59717
κ=1.0 #59010

1.0

2.5

κ=1.4
κ=0.8

10-2
3.4

1.5

3.8

Te (keV)-1.0

Two dimensionally similar discharges with different
elongation have been compared to clarify the elongation
effect on heat transport. The line averaged density iscontrolled at 1×1019m-3 and electron temperature is also
controlled to be the same in two case with κ=0.8 and 1.0(see Fig.3). Heating power is also controlled to realize thesame electron temperature (see Fig.4)

ne (1019m-3)

-0.5

1.5
1.0
0.5
0-0.6 -0.4 -0.2

0.01

Rax (m)Fig.2 Dependence of effective helical ripple εeff andpoloidal viscous damping rate Cp on the positionof the magnetic axis. Elongation scans are plottedby triangles and circles at Rax=3.6m.

00.2

0.4

0.6

reff (m)Fig.4 Electron temperature profiles in discharges withdifferent elongation.

Here it should be noted that the investigated plasmas
lie in 1/ν regime and that they do not enter so deeply incollisionless regime that electric field effect on neoclassicalProceedings of ITC/ISHW2007
Exp. κ=0.80
Exp. κ=1.0
N.C. κ=0.80
N.C. κ=1.0102

χ (m /s)1etransport is not significant. Since the case with κ=1 shows
the better confinement, the heating power is 0.93 MW forκ=0.8 and 0.35 MW for κ=1. The plasma parameters
except for the elongation are similar to each other,
therefore, representative non dimensional physicalparameters such as normalized gyro-radius ρ*,collisionality ν*, and beta are also similar to each other.
Figure 5 shows the ratio of the electron heatdiffusivity of these two cases. Since the plasma parametersof these two cases are the same, the deviation of this ratio
from 1 can be attributed to the remained difference, i.e.,elongation. Corresponding to the global confinement
nature, local heat diffusivity in the experiment shown in asolid curve indicates enhancement of heat transport in thecase with κ=0.8 by a factor of 2 to 3. A dotted line is theprediction from neoclassical theory. These two curves areclose to each other, which suggest the neoclassicaltransport may make the difference in heat transport.
However, this is not the case. Figure 6 shows the heatdiffusivity profile. The fat solid curve is the experimental
value in the case with κ=0.8 and the dotted fat curve is thecorresponding neoclassical prediction. The experimental
value is significantly larger than the neoclassical value,
which indicates heat transport is anomalous even for thecase with κ=0.8. Therefore, this is another example that
configuration effect on anomalous transport is correlated oraccidentally happens to coincide with nature ofneoclassical transport [5].

0.100.20.4

ρ

0.6

0.8

1Fig.6 Experimental and neoclassical heat diffusivity.

Experimental data align with the scaling for all
configurations. Each performance τEexp/τEISS04 issummarized as 0.94±0.02 for κ=0.8, 1.41±0.07 for κ=1.0,
and 0.91±0.03 for κ=1.4. If the Cp is more relevant
parameter, the confinement should become the maximumat κ=1.4. However, the experiments indicate that theconfinement is the best at κ=1.0 and declined by the bothprolate (κ=1.4) and oblate (κ=0.8) modifications. The
present experimental comparison suggests a negative
evidence for relevance of Cp.

0.20eχ (κ=0.8) / χ (κ=1.0)

100.15

τEexp (s)1eNeoclassical theory
Experiment

0.100.2

0.4

ρ

0.6

0.8

κ=0.8
κ=1.0
κ=1.4

0.10

0.05

100Fig.5 Ratio of heat diffusivity of two discharges withdifferent elongation

Figure 7 shows the comparison of experimental
energy confinement time with the prediction from theISS04 scaling for plasmas with different ellipticity as
shown in Fig.1. Energy confinement times have themaximum performance at κ=1 and degrades in both prolate(κ>1) and oblate (κ<1) directions. These trends agree withthe observation in NBI heated plasmas [2].

Fig.7

0.05

0.10

τEISS04 (s)0.15Comparison of experimental energy confinement
time with prediction from the ISS04 scaling

4. Conclusions
Effect of ellipticity on thermal transport has been
investigated for ECH plasmas in LHD. Ellipticity κ isscanned from 0.8 to 1.4 by controlling quadrupole
magnetic field. Experimental data of energy confinement

Proceedings of ITC/ISHW2007
time align with the scaling for all configurations, however,there exist systematic offsets. Performance τEexp/τEISS04 issummarized as 0.94±0.02 for κ=0.8, 1.41±0.07 for κ=1.0,
and 0.91±0.03 for κ=1.4. Local transport analysis based on
power balance indicates that plasma transport ispredominated by anomalous transport. However, theobserved anomaly shows correlation with the change of aneffective helical ripple εeff. Since εeff should not be directly
linked with anomalous transport model, clarification ofconfiguration dependent parameter to bridge anomaloustransport and εeff is required for establishment ofoptimization scenario of magnetic configuration. In thisstudy, the poloidal viscous damping rate is explored as apotential key parameter. Generally speaking, zonal flows
are generated efficiently in the configuration with low
poloidal viscosity and then suppression of anomaloustransport is anticipated in such a configuration. Since thepoloidal viscous damping rate Cp is affected by a toroidal
curvature as εeff describes, Cp and εeff generally have acorrelation. Indeed, the inward shift of the magnetic axis
realizes suppression of both Cp and εeff simultaneously.
However, plasma elongation can separate these two effects.
Here elongation is defined by the toroidal averaged value.
A vertically elongated configuration (κ=1.4) has larger εeff
than the standard configuration (κ=1.0) while it has smaller
Cp. The experimental results indicate that the confinement
is the best at κ=1.0 and declined by the both prolate(κ=1.4) and oblate (κ=0.8) modifications. The present
experimental comparison suggests a negative evidence forrelevance of Cp.

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[8] C.D.Beidler et al. Plasma Phys. Control. Fusion 36, 317(1994)