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Published by Fusion Energy Division, Oak Ridge National Laboratory
Building 5700 P.O. Box 2008 Oak Ridge, TN 37831-6169, USA
Editor: James A. Rome Issue 124 February 2010
E-Mail: jar@ornl.gov Phone (865) 482-5643
On the Web at http://www.ornl.gov/sci/fed/stelnews
New small scale stellarator
experiments
Introduction
Many Stellarator configurations have been investigated
theoretically. They make use of different type of quasisymmetry
and different optimization concepts. The number
of experiments is strongly limited. Only LHD, Heliotron-
J, HSX (TJ-II, H-I, WEGA, TJ-K) are operational and
Wendelstein7-X (W7-X) will be operational in the near
future. The realization of other optimized stellarators
experiments like NCSX and QPS is not yet clear. At full
performance operation, W7-X it should be possible to test
its all optimization criteria at reactor relevant parameters.
Some optimization criteria like the reduction of the
Pfirsch-Schlüter currents and β stability have already been
tested in the medium size predecessor experiment W7-AS.
Neoclassical transport improvement for electrons was also
demonstrated on the small scale experiment HSX [1].
Transport investigations of ions, impurities and energetic
alpha particles require large machine size and high magnetic
fields. The same requirements hold for the ion driven
bootstrap current. Experiments on heliotrons can also be
used to test neoclassical theory even though they do not
make use of the full optimization potential of the non-axisymmetric
shaping of stellarators. In a stellarator reactor
burning plasma, transport will probably not be determined
by neoclassic confinement but by the MHD-driven transport
at the MHD stability limit. This is because in contrast
to today’s fusion plasma experiments, which are externally
heated with constant power, in a burning plasma the alpha
particle heating strongly increases with , which
overcompensates the characteristic confinement scaling
with heating power (~P−0.6). Therefore, if the temperature
is kept constant, which can be achieved by density control,
β will rise with the density until MHD-driven transport
and alpha particle heating balance each other, finally
determining reactor performance. The experimental experience
indicates furthermore that the β-limit in stellarators
is a soft limit without a disruption-like loss of confinement.
Therefore safe reactor operation can be expected at
that operation point.
High β values have been already achieved at W7-AS
(3.4%) [2] and LHD (5%) [3]. These experiments require
highest heating power, but can be performed at moderate
magnetic field strength <1 T. For W7-X high-β experiments
are also foreseen, but will require a heating power
of more than 10 MW. It is clear that under these conditions
MHD-stability cannot be tested for many optimization
concepts.
But the experimental results at W7-AS had shown that
MHD stability can already be tested at plasma parameters,
which are below that of a reactor. This is because resistive
effects will even degrade stability. In particular the electron
temperature was only about 300 eV. The limiting factor
reaching higher β at W7-AS was the NBI-heating
power and efficiency.
The achievable β scales with the heating power per volume.
But one cannot reduce the plasma size since fast ion
orbit losses become unacceptable. This is only an issue of
Pα ∼ β2
In this issue . . .
New small scale stellarator experiments
Small (~1 m major radius) stellarator experiments can
reach reactor levels of both density and beta. We
examine a down-scaled version of HSR4/18 to assess
its role as a high-beta test vehicle. Centralized electrostatic
Bernstein wave heating and innovative construction
techniques could make such a device interesting
and competitive. ..................................................... 1
Three dimensional numerical analysis of edge
plasma transport in the Large Helical Device
Optimization of three dimensional divertor configurations
for helical devices is being investigated in LHD.
The stochasticity induced in the edge region introduces
extremely long connection length field lines as
well as flux tube deformation. These geometrical features
are found to influence divertor plasma characteristics
significantly. The Consequences for divertor
design in future reactors are under discussion. ...... 7
Stellarator News -2- February 2010
the heating method, and not of MHD-physics. Therefore a
different heating method could enable such an experiment.
Small scale high-β experiment
In this section we investigate how much heating power is
needed to test the β limit of a down-scaled stellarator with
a HSR4/18-configuration (Helias Stellarator Reactor with
4 periods and 18 m major radius) shown in Fig.1. This
configuration was chosen because it was proposed for a
Helias type stellarator reactor [4] and because its coil
parameters were already available. In principle other configurations
could be scaled down to that size. The HSR4/
18 configuration is of course already optimized for a high
β limit by a reduction of the Pfirsch-Schlüter (PS) currents.
We have reduced its dimensions by a factor of 25
and the magnetic field strength by 10. The resultant device
is approximately half the size of W7-AS and is a little
smaller than HSX. Therefore, any confinement prediction
is more an interpolation of experimental data than an
extrapolation towards larger size like the prediction for
W7-X, which makes it more reliable. Because this experiment
is a down-scaled version of HSR4/18, henceforth the
working title HSR4/18-DS will be used. The comparative
device parameters are listed in Table 1.
Table 1. Dimensions and magnetic parameters of HSR, HSR4/18-DS, and W7-AS.
Fig. 1. Magnetic surfaces and modular coils of HSR4/18.
HSR4/18 Downscaled HSR4/18 W7-AS
Major radius [m] 18 0.72 2.1
Minor radius 2.1 0.084 0.155
Aspect ratio 10.7 10.7 13.5
Iota(0) 0.83 0.83 0.51
Iota(a) 1.0 1.0 0.555
0.74 0.74 1.6
Plasma volume [m3] 1670 0.106 .996
Magnetic Field [T] 4.4−5 0.44−0.5 0.9T (for high-β experiments)
〈 jpar ⁄ jperp〉
Stellarator News -3- February 2010
With these numbers we calculated the average β from the
confinement scaling making use of
,
where τe is the energy confinement time, P the heating
power, V the plasma volume and B the magnetic field
strength. For comparison we used three different confinement
scalings from [4].
The ISS95 with
The W7-scaling based only on the data from the W7-A
and W7-AS experiments
and the Lackner-Gothardi scaling
.
Stellarators do not have an density limit, based on stability.
The achievable density is mainly limited by power balance.
For the density we used the empirical formula [5]
[1020 m-3],
which was applied to the confinement scaling. It should be
noted that this estimation should not give an exact prediction
of the expected plasma parameters for HSR4/18-DS,
but should show the possibility of such an experiment. The
results are shown in Fig.2.
With a just a moderate heating power of 300 kW, the
results of W7-AS could be reproduced. With a power of
500 kW a record β of 5% could be achieved. In addition,
the density would access the reactor density regime. The
main challenge is to develop an efficient heating method,
that is able to deposit its power in a small plasma volume
at densities of 1–3 ×1020 m−3. An average temperature is
expected to be of the order 50–100 eV. But with a localized
central heating method, a highly peaked temperature
profile with a peaking factor up to 10 is expected.
High density electron Bernstein heating.
Electron cyclotron resonant heating (ECRH) has demonstrated
highly localized power deposition in high temperature
plasmas (Te > 500 eV) and at moderate densities
(>1×1019 m−3). However, for a magnetic field strength of
0.5 T, the fundamental resonant frequency is only 14 GHz.
Therefore the critical density (cutoff) for electromagnetic
wave propagation is only 0.25 ×1019 m−3. Even for the
second harmonic frequency of 28 GHz the cut-off is
1×1019 m−3, thus the high-β plasma with ne > 1×1020 m−3
would be highly over-dense for ECRH using electromagnetic
waves. For electrostatic waves, the Bernstein waves
(EBW), this propagation limit does not exist. Furthermore
they are strongly absorbed at the cyclotron resonance,
even at low temperature and a higher harmonic frequency.
This makes them to an attractive candidate for high-β
plasma heating.
The key element is an efficient excitation of the EBWs.
The usual method for this is OXB-mode conversion [6].
Efficient OXB plasma heating has been already demonstrated
in tokamaks [7] and stellarators [8], but only as an
additional heating method in the presence of ohmic heating
and neutral beam injection, respectively. Recently at
β 32
--
Wkin ⁄ V
2μ0B2 ------------------
⎝ ⎠
⎜ ⎟
⎛ ⎞ 32
--
τeP ⁄ V
2μ0B2 ----------------
⎝ ⎠
⎜ ⎟
⎛ ⎞
= =
τISS95 0.25a2.21R0.65P–0.59ne
= 0.51B0.83ι0.4
τW7 0.36a2.21R0.74P–0.54ne
= 0.50B0.73ι0.43
τLG 0.175(0.25)a2R1P–0.6ne
= 0.6B0.8ι0.4
nW7-DL = 1.46(P ⁄ V)0.48B0.54
Fig. 2. Expected average β and density as a function of the
heating power.
0.2 0.4 0.6 0.8 1
Power [MW]
0.02
0.04
0.06
0.08
0.1
Beta B = 0.45 T , green : w7 , red : LG , blue : ISS95
0.2 0.4 0.6 0.8 1
Power [MW]
0.5
1
1.5
2
2.5
3
Ne [1020m-3]
B =
0.45 T
density limit
Stellarator News -4- February 2010
the WEGA Stellarator an over-dense plasma was achieved
with 28-GHz OXB-heating exclusively [9]. WEGA is a
classical Stellarator of approximately the same size as
HSR4/18-DS. Therefore the demonstration of efficient
over-dense operation clearly proves the EBW heating concept
for HSR4/18-DS. In the WEGA experiment it was
shown, that even with a low ECRH power of 9 kW densities
above 1 ×1019 m−3 could be achieved. But more
important is the fact that the EBWs have been absorbed
resonantly in the plasma center, which is shown by the
strongly peaked radiation profile in Fig.3. The maximum
density was only limited by radiation losses. There should
be no limitation reaching a higher density if the heating
power would be increased from 9 KW to 500 KW for
example. The high electron cyclotron absorption of EBWs
enables higher harmonic heating, when the cut-off density
of the higher frequency is exceeded [10]. Therefore heating
with higher harmonic EBWs should be also possible.
For example, 70-GHz gyrotrons can be used for EBW
heating at the 4th or 5th harmonic resonance.
Technical realization
The relatively small size of the experiment enables to use
new and low-cost manufacture methods. The three-dimensional
(3D) vacuum vessel could be manufactured by casting,
where the lost form is made by rapid prototyping.
This vacuum vessel could already incorporate the support
structure of the coil winding and the port tubes similar to
the report in [11]. The surface should be appropriately
treated for sufficiently good vacuum conditions. The fourfold
symmetry can be used to divide the torus into four
pieces, which then can be rotated in total for simultaneous
winding of the ten coils directly on the vessel. Keep in
mind that the module size is only about one meter as
shown in Fig. 4.
This method would guarantee a sufficiently high positional
accuracy of the coils without time-consuming and
expensive measurement and adjustment procedures. In
addition the parallel coil winding would speed-up the
assembly process. Of course, attention must be paid to the
precise assembly of the four modules, which would be
done by careful welding. Finally standard CF-flanges will
be welded on the port tubes. Inside the vacuum vessel
there is sufficient space available for a quasioptical ECRH
antenna system as shown in Fig. 5, which is by the way, a
copy of the antenna system used in the successful WEGA
28 GHz EBW heating experiments. In addition, for higher
harmonic heating (3rd at 42GHz, 4th at 56 GHz, at 5th 70
GHz) the optimal launch angle for the OXB mode conversion
can also be achieved by a remote steering type
antenna. The ports also give sufficient access for diagnostics
and vacuum pumping. The current needed to achieve
0.5 T is 47 kA/(winding number). The current density is
5.9 kA/cm2. In total, an electrical power of 3.25 MW is
needed. Of course such an experiment could also be built
in the traditional way with individually winded coils and a
“classical” vacuum vessel.
Discussion
Several questions should be discussed. The first and of
course the most important is:
Does such an experiment contribute to the fusion program?
One could argue that experiments of this size can also be
justified by the academic interest exclusively. But in our
opinion MHD-stability is an important issue for an economic
fusion reactor as mentioned in the first section. This
experiment can reach the two reactor parameters of density
and β. The temperature will be low and thus neoclassical
effects will be not as dominant as in a W7-X size
machine or in a reactor. But neoclassical effects are less
important for MHD-stability except for the bootstrap current,
which contributes much to the iota profile and can
lower the β limit by neoclassical tearing mode activity,
just as in tokamaks. For stellarator concepts with minimized
bootstrap current and thus with a stiff iota profile,
this does not matter. If a configuration with finite bootstrap
current such as NCSX is chosen, the effect of toroidal
plasma current could be tested with an additional
current driven by an ohmic transformer. One should consider
that this kind of experiment would be a continuation
of the high-β experiments at W7-AS, which have already
brought new insight on β stability in stellarators. In addition
the centrally-peaked temperature profile would generate
a more realistic reactor pressure profile than a NBIFig.
3. Radiation profile of over-dense EBW-heated plasma
with central total single-pass absorption in comparison with
the profile of a low-density plasma with multi-pass O2 heating.
The profiles are reconstructed from the signals of a 12-
channel bolometer camera.
0 2 4 6 8 10 12 14 16
0 5
10
15
20
25
30
35
40
45
50
55
60
Prad (mW/cm3)
reff (cm)
#30344/ He /iota 0.3/ECRH 7 kW
28 GHz OXB-heating
28 GHz O2/X2 multipass heating
Stellarator News -5- February 2010
heated plasma with a broad temperature profile. At this
point we come to the second question:
Are the physical predictions given by the scaling laws reliable?
The answer is, that it does not matter much, since in case
of a less good confinement, only the heating power must
be increased to reach high β. But the plasma parameters of
HSR4/18-DS are closer to those of W7-AS than it is the
case for W7-X, therefore their scaling should not differ
Fig. 4. Vacuum vessel and ports of HSR4/18 DS.(original picture from HSR4/18)
section
ca. 1 m
Fig. 4. Scheme of ECRH launching in the poloidal and toroidal crossection.
0.72 0.8
0.041
Waveguide
parabolic mirrors
coils
remote
launcher
plasma
Stellarator News -6- February 2010
much. On the other hand, due to the small volume to surface
ratio, the impurity concentration could be higher than
in W7-AS. We should also note that in contrast to previous
high β experiments, HSR4/18-DS will be heated by central
ECRH and thus a peaked temperature profile is
expected. This would generate an edge radiation dominated
plasma similar to the HDH-regime of W7-AS [12].
In addition there is experimental evidence that ECRH
helps to reduce impurity accumulation. There are of
course additional methods to reduce the impurity radiation
if needed. For example, lithium coating was recently successfully
used for high-density experiments at TJ-II. The
vacuum vessel size would also allow use of graphite tiles
as a divertor. But the divertor physics in small devices
have not yet been investigated. Technically, positioning of
the tiles would be straight forward, because the vacuum
vessel is a part of the coil system.
Finally we have to discuss the cost and the staff needed to
build and to run such an experiment. There are already
several experiments of this size operating. Examples are
HSX, WEGA, TJ-K, H-I and CTH. But none of them are
equipped with a powerful enough ECRH system to reach
high β. Only in the Heliotron-DR experiments [13], which
were performed 20 years ago, the 28-GHz 200-kW ECRH
was sufficiently powerful to demonstrate over-dense
plasma operation at moderate β of 0.5%. Unfortunately the
ECRH launching system was not optimized for mode conversion.
From the experience of the other small machines like HSX
the cost for a pure HSR4/18-DS β machine would be of
the order one million €. The costs of the auxiliary systems
such as power supply, diagnostics and the ECRH would be
at least twice that price. But these installations and components
are already in existence at many institutes. HSR4/
18-DS could also operate as a satellite of a large size stellarator
like NCSX, W7-X, LHD for complementary high β
studies.
References
[1] J. M. Canik et. al., Phys. Rev. Lett. 98, 085002 (2007).
[2] A. Weller et al., Plasma Phys.Control. Fusion 45 A285-
A308.
[3] O. Motojima et al., Nucl. Fusion 47 (2007) S668-S676.
[4] H. Wobig., Nucl. Fusion 43 (2003) 889-898.
[5] L. Giannone et al., Plasma Phys. Contr. Fusion 45(9),
(2003)1713-1731.
[6] J. Preinhaelter. and V. J. Kopecký, Plasma Phys. 10
(1973) 1.
[7] A. Mueck et al. Phys. Rev. Lett. 98, 175004 (2007).
[8] H. P. Laqua, Phys. Rev. Lett. 78, 3467 (1997).
[9] H. P. Laqua et al., Proceedings of the 36th EPS Conference
on Plasma Phys. Sofia, June 29–July 3, 2009 ECA
33E, O-4.047 (2009).
[10] H. P. Laqua, Nuclear Fusion 43 (2003) 1324-1328.
[11] Vicente M. Queral, Stellarator News 118.
[12] K. McCormick et. al., Phys. Rev. Lett. 89, 015001
(2002).
[13] S. Morimoto, N. Yanagi, M. Sato, et al.,Nucl.Fusion 29
(1989) 1697.
H. P. Laqua, J. Kisslinger
Max Planck Institut für Plasmaphysik
Griefswald, Germany
E-mail: laqua@ipp.mpg.de
Stellarator News -7- February 2010
Three dimensional numerical
analysis of edge plasma transport
in the Large Helical
Device
Divertor optimization in magnetically confined fusion
reactors is one of the most critical issues in terms of target
power load mitigation, impurity control, and fuel/He ash
pumping. Breaking the axisymmetry of the magnetic field
configuration as introduced in helical devices as well as in
non-axisymmetric tokamaks has imposed the necessity of
three dimensional (3D) analyses of the transport properties
of the divertor plasma. Optimization of divertor configurations
for these 3D machines is, however, not yet fully
understood. Numerical codes have been developed to
investigate the transport properties, as a tool for interpretation
of experiments, as well as for prediction of performance
in future devices, e.g., EMC3 [1], E3D [2], FINDIF
[3], etc. These codes are nowadays widely used in various
devices.
In the Large Helical Device (LHD) [4], EMC3 (which
stands for Edge Monte-Carlo 3D) has been implemented
for analyzing the plasma transport in the edge stochastic
region. LHD has a heliotron type configuration with poloidal
winding number of l = 2 and toroidal mode number 10
as shown in Fig.1. The major radius and averaged minor
radius are 3.9 and ~ 0.6 m, respectively. The edge stochasticity
intrinsically appears in this configuration because of
breakdown of helical symmetry due to toroidal effects that
induce overlapping of magnetic islands. The details of the
field line structure of stochastic region is incorporated in
the field line-aligned 3D grid of the computations, which
then also provides clear separation between parallel and
perpendicular transport to field lines.
Fig. 2(a) shows poloidal cuts of magnetic field connection
length (LC, the distance along field line during travel from
one intersection by divertor plate to another) distribution
at each 9 degrees of toroidal angle, as reconstructed from
the 3D grids. While the flux tubes travel in toroidal direction,
they experience compression in the vicinity of helical
coils (effect of helical ripple) as well as radial kicks
according to the mode spectrum of the coils. The strong
magnetic shear at the periphery then squeezes these flux
tubes (of different LCs), resulting in a stochastic structure.
Stretching from the both edges of elliptic shape of the
cross sections are divertor legs, which connect the divertor
plates situated in-between the helical coils. The stochasticity
introduces an extremely long connection length as indicated
by the color in the figure, up to an order of several
tens kilometers, which is one of the distinct features from
the standard X-point divertor tokamak scrape-off layers
(LC ≤ 100 m). Because of the large ratio of parallel to perpendicular
transport, the plasma parameter distribution is
strongly influenced by the magnetic field line structure.
Plotted in Fig.2 (b) is electron temperature (Te) distribution
in the same planes as Fig.2(a). Since the long flux
tubes tend to penetrate deep into the plasma, they deliver
hot plasma and thus bring higher Te as observed in the figure.
The calculated Te profiles are compared with the measurements
made by the Thomson scattering system, and
they show reasonable agreement each other [5,6], confirming
the presence of the stochasticity as well as the validity
of the fluid description of plasma transport adopted in the
code (at least, for this particular case).
The analyses have revealed the importance of perpendicular
transport in determining the divertor plasma properties,
which contributes through the accumulative effect along
the long field lines, as well as the enforced strong perpendicular
coupling due to the flux tube deformation as mentioned
above (compression, shearing). For momentum
transport, this leads to a leakage of total pressure from the
flux tubes [5,6]. The effects are observed experimentally
as weaker compression of divertor plasma, that might
degrade pumping efficiency without a closed divertor
structure, but on the other hand, that can be advantageous
to reach higher edge (core) density before detachment
onset. For energy transport, the perpendicular transport
provides a supplementary path in addition to the parallel
ones, which thereby eases development of parallel temperature
gradient. The consequences for the divertor plasma
are a somewhat higher temperature as well as a good
impurity screening due to the suppressed temperature gradient
force (thermal force) [7]. These transport characteristics
are common to both LHD and W7-AS [8]. For
divertor optimization, the pros and cons of these features
are being discussed, and further investigation is ongoing to
explore the possibilities of a 3D divertor.
Fig.1. Interior view of LHD. The two superconducting helical
coils (poloidal winding number l = 2) and the divertor
plates are indicated.
Divertor plates
Helical coils
Stellarator News -8- February 2010
References
[1] Y. Feng et al., Contrib. Plasma. Phys. 44 (2004) 57.
[2] A. Runov et al., Phys. Plasmas 8 (2001) 916.
[3] R. Zagorski et al., Nucl. Fusion 48, (2008) 024013.
[4] N. Ohyabu et al., 34 (1994) 387.
[5] M. Kobayashi et al., J. Nucl. Mater. 363–365 (2007)
294.
[6] Y. Feng et al., Nucl. Fusion 48 (2008) 024012.
[7] M. Kobayashi et al., J. Nucl. Mater. 390–391 (2009)
325.
[8] Y. Feng et al., Nucl. Fusion 49 (2009) 095002.
M. Kobayashi
National Institute for Fusion Science
Toki 509-5292, Japan
E-mail: kobayashi.masahiro@LHD.nifs.ac.jp
Fig. 2. (a) Connection length (LC) distribution in the edge
region of LHD in poloidal cross sections at each 9 degrees
of toroidal angle with iso-surface of LC =105 m (red). The
magnetic field structure is reconstructed from the field line
aligned 3D grid of EMC3. (b) Electron temperature (Te) distribution
at the same planes as in (a), together with iso-surface
of 200 eV (red), obtained by EMC3
LC (m)
105
104
103
102
101
200
150
100
50
Te (eV)
Stellarator News -9- February 2010