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Oak Ridge National Laboratory is managed by UT-Battelle, LLC, for the U.S. Department of Energy.
Published by Fusion Energy Division, Oak Ridge National Laboratory
Building 5600 P.O. Box 2008 Oak Ridge, TN 37831-6169, USA
Editor: James A. Rome Issue 134 December 2011
E-Mail: jamesrome@gmail.com Phone (865) 482-5643
On the Web at http://www.ornl.gov/sci/fed/stelnews
ESTELL, a quasiaxisymetric
stellarator
The Evolutive Stellarator of Lorraine (ESTELL), shown in
Fig. 1, is a project proposed by the University of Lorraine
(Nancy, France) in the framework of the “Investissement
d’Avenir” program of the French Research Ministry. The
main goal of ESTELL is to provide the first experimental
demonstration of quasiaxisymmetry (QA) as a valuable
concept for efficiently confining magnetized plasmas. The
aim is to investigate the frontier between the tokamak and
stellarator concepts through dedicated experiments in QA
geometry. As is well known to the stellarator community,
such a configuration could offer solutions to some of the
problems of tokamaks (e.g., ITER): inherent steady state;
absence of disruptions; reduced requirements for plasma
control systems; no current drive system required, resulting
in low recirculating power; and the potential for highdensity
operation.
ESTELL aims at becoming a worldwide open facility with
high flexibility and accessibility, intermediate in size
between small laboratory devices and large international
facilities. It will require approximately 13 M€ for construction.
In addition to plasma confinement studies, the
device will be useful for strengthening the bridge between
academic research and fusion studies in several critical
areas: plasma turbulence, heating, plasma-surface interactions,
and diagnostics. ESTELL will be suited to test innovative
concepts at lower risk and cost than on larger
facilities. It also aims at addressing other fundamental
issues, notably in astrophysics, through the investigation
of three-dimensional (3D) magnetic reconnection.
Fig. 1. Cutaway view of ESTELL.
In this issue . . .
ESTELL, a quasiaxisymmetric stellarator
The University of Lorraine is proposing to build a
medium-size, modular, quasiaxisymmetric stellarator
to test new concepts, perform supportive research for
larger devices, and train new scientists and engineers.
The coil configuration was designed by IPP Greifswald........................................................................
1
Observation of intrinsic toroidal rotation in
Large Helical Device
A spontaneous rotation in the co-direction is observed
in plasmas with an ion internal transport barrier (ITB),
where the ion temperature gradient is relatively large
(dTi/dr~ 5 keV/m and R/LTi ~ 10) in the Large Helical
Device (LHD). In these conditions, the magnitude of
the spontaneous toroidal flow, V
spon, becomes large
enough to cancel the toroidal flows driven by tangential
injected neutral beams (NBs) and the net toroidal
rotation velocity is almost zero at the outer half of the
plasma minor radius, even in plasmas with counterdominant
NB injection. The effect of velocity pinch is
excluded even if it exists because of the zero rotation
velocity. The spontaneous toroidal flow appears in the
direction of co-rotation after the formation of the ITB,
not during or before the ITB formation. The relationship
between the change in V
spon and dTi/dr clearly
shows that the spontaneous rotation is driven by the
ion temperature gradient as the off-diagonal terms of
momentum and heat transport. .............................. 4
Stellarator News -2- December 2011
Summary of main features and parameters
ESTELL is a two-field period modular stellarator with an
aspect ratio ~5, formed by 20 optimized modular copper
coils of 5 different types (Fig. 2). The magnetic configuration
and the coil design come from the Stellarator Theory
Division at Max Planck Institute for Plasma Physics,
Greifswald. Aiming for operating at a plasma  value of
0.5%, a low rotational transform of iota ~0.2 was chosen,
making it possible to achieve quasiaxisymmetry to a high
degree of accuracy with relatively simple coils. As a result
of the large spacing between coils (up to 80 cm, never less
than 14 cm, but keeping reasonable magnetic ripple
~ 1%), it will be possible to install up to 100 ports of various
sizes, whereas about only 20 will be needed for basic
operation of the device. Consequently, many ports will be
available for installing additional diagnostics or auxiliary
systems (e.g. additional heating systems). 3D magnetic
flexibility and plasma shaping will be achieved by using 5
separate power supplies, one for each type of modular coil.
The main parameters of ESTELL in its starting configuration
are given in Table 1.
Such a flexible, worldwide open, medium-size facility
would be a suitable locale to perform fundamental investigations
needed to support the research programs at larger
facilities such as Wendelstein 7-X (W7-X). The experimental
and theoretical programs will also closely follow
Fig. 2. Top view and side view of ESTELL 20 modular coils as designed by IPP Greifswald.
Configuration Quasiaxisymmetric
Number of field periods 2
Number of coils 20 of 5 different kinds
Major radius <R> 1.4 m
Minor radius <a> 0.28 m
Vacuum chamber volume 3 m3
Magnetic field strength ≤0.5 T (continuous)
Heating Power 400 kW ECH (20 s pulse)
Plasma β 0.5%, or up to 1% given enough heating power
Rotational transform 0.23 (β = 0)
0.35 (β = 0.37%)
Plasma density ne 5  1018 m-3
Peak electron temperature 1 keV
Ion temperature 100 eV
Table 1. main parameters of ESTELL.
Stellarator News -3- December 2011
the HSX device program, in order to compare specific
properties of quasihelical and quasiaxisymmetric geometries.
Connection to training and education programmes
Nancy University is known to be a special node in the
French plasma science community and also in the European
fusion education networks through its participation in
initiatives to organize master, doctoral, and post-doctoral
levels in plasma science (http://www.em-masterfusion.
org, www.em-fusion-dc.org). ESTELL will substantially
help to improve the university’s education for
both plasma physicists and engineers. As a flexible facility
designed for experiments and demonstrations, ESTELL
will be the focus of dedicated training courses for experienced
machine operators, experienced engineers, and
fusion scientists who will potentially operate future facilities
such as W7-X, ITER, and DEMO.
Status of the project
Most of the ESTELL equipment requires customized
design. In order to overcome specific technical issues and
to reduce the costs, conservative and successful technologies
have been chosen for most critical components (e.g.,
water-cooled copper coils). This makes it possible to focus
on innovative relevant components, couplings, and
designs. Feasibility studies have been carried out in 2011
with the participation of the ALORIS private engineering
group and a consortium of several industrial partners, most
already involved in the Fusion Program. These studies
have concluded that all the essential elements, without any
exception, can be manufactured and delivered by industrial
partners at very low risks, by using conservative technological
options already successfully tested elsewhere.
The complete proposal was submitted to the French
Research Ministry in September 2011, and the final decision
will be known in early 2012. The Nancy urban
agglomeration and Lorraine regional council have already
decided to underwrite the construction of the building that
will host ESTELL in Nancy. If ESTELL is approved, its
construction is scheduled to be completed in mid 2016,
and first plasmas are expected in the second half of 2016.
ESTELL has been designed in order to permit future
upgrades, which could be undertaken given adequate
financial resources. In particular, the vacuum vessel will
be large enough (the distance between the wall and last
closed flux surface will be about 10 cm) to evolve from a
limiter configuration to a more promising divertor configuration.
Given ESTELL’s flexibility, a relatively inexpensive
divertor limited to some specific value of iota is
possible. The numerous ports which will be available,
some of them very large, will make it possible to install a
large set of diagnostics for measurements ranging from
turbulence and transport characterization to fundamental
investigations of plasma-wall interactions. They will also
make it possible to extend heating capabilities, thus further
extending the range of plasma parameters, by including
lower hybrid and RF systems.
Acknowledgments
The ESTELL project has already benefited from the help
of many people throughout the world, who have participated
in its design or by providing strong support letters.
We thank all of them warmly.
Frédéric Brochard and the ESTELL team
Nancy, France
E-mail: Frederic.Brochard@ijl.nancy-universite.fr
Website: http://estell.blog.uhp-nancy.fr/
Stellarator News -4- December 2011
Observation of intrinsic toroidal
rotation in Large Helical
Device
1. Background
Spontaneous rotation has been observed in many tokamaks.
It has been observed in ohmic discharges in PLT
[1], PDX [2], and Alcator C-mod [3], where there is no
external momentum input. Spontaneous rotation becomes
more significant in plasmas with additional heating with
no momentum input, such as ICRF heating in JIPP-TIIU
[4], JET [5], and Alcator C-mod [6] and ECH in CHS [7]
and D-IIID [8]. The rotation can be in either the same (co)
or opposite (counter) direction as the plasma current; it is
usually co in H-mode and counter in the internal transport
barrier (ITB) mode and can be either co or counter in Lmode,
depending on the plasma conditions. The momentum
transport analysis to investigate the mechanism of
spontaneous rotation has been done, and a non-diffusive
term of the momentum transport was found in JT-60U [9]
and JFT-2M [10,11]. Therefore it is important to investigate
intrinsic rotation in a plasma with an ITB, and an ion
temperature gradient large enough to drive intrinsic toroidal
rotation in the Large Helical Device (LHD).
2. Effects of BNB injection on toroidal rotation
Since spontaneous rotation driven by the temperature gradient
may be in either the co- or the counter-direction to
the plasma current (equivalent toroidal current in helical
plasmas), this spontaneous rotation appears as the disparity
of co- and counter-driven toroidal rotation profiles in
discharges with neutral beam (NB) injection in the co and
counter direction with similar injection power [12]. This
disparity is mainly due to spontaneous rotation in the codirection
(parallel to the equivalent plasma current).
Because of the existence of spontaneous rotation, a large
toroidal rotation velocity peaked at the plasma center in
the co-direction is observed as indicated by the blue
arrows in Fig. 1, when the NB is injected in the co-direction
(parallel to the spontaneous rotation). In contrast, the
toroidal rotation is almost zero (a slight counter rotation at
the center as indicated by the red arrows in Fig. 1, when
the NB is injected in the counter-direction (anti-parallel to
the spontaneous rotation).
Fig.1. Toroidal rotation velocity iwhen external torque is (a) parallel and (b) anti-parallel to the direction of spontaneous
rotation. The lengths of arrows are proportional to the rotation velocity. Red arrows indicate rotation in the counter-direction
(anti-parallel to equivalent plasma current), and blue arrows indicate rotation in the co-direction (parallel to equivalent
plasma current).
Stellarator News -5- December 2011
Figure 2 shows the radial profiles of toroidal rotation
velocity, ion temperature, and torque deposition in plasmas
with one NB injector (NBI) (co- or counter- injection)
and with three NBIs (2 co-, 1 counter-injection and 1 co-,
2 counter-injection) discharges in LHD. The sign of the
toroidal rotation velocity is positive for co-rotation and
negative for counter-rotation. In plasmas with one NBI,
the toroidal rotation profile in the plasmas with co-injection
is similar to that in plasmas with counter-injection
except for the sign differences. Toroidal rotation velocity
is measured from the Doppler shift of fully ionized carbon
impurities using charge-exchange spectroscopy viewing
the plasma tangentially.
The main ion in this experiment is hydrogen. Since the of
toroidal rotation is measured using carbon impurities, the
velocity difference between the main ion and the impurity
is evaluated with a neoclassical formula in the heliotron
configuration. The main ion rotates more in the co-direction
than do the carbon impurities, as shown by the dashed
lines in Fig. 2. Therefore the spontaneous rotation
observed in the carbon impurity cannot be explained by
the neoclassical effect. The spontaneous rotation evaluated
for the main ions should be even larger than that evaluated
using carbon impurities, because the spontaneous rotation
observed in LHD is in the co-direction.
In this plasma, the radial profiles of toroidal rotation
velocity are mainly determined by the external torque
resulting from NB injection, and by radial diffusion of
toroidal momentum and parallel viscosity, which increase
sharply towards the plasma edge, similar to the toroidal
rotation profiles reported in CHS. In heliotron plasmas no
momentum pinch has been observed. As seen in
Fig. 2(e)(f), the net toroidal torques are somewhat similar
(especially for 1 counter-NBI and 2 counter- plus 1 co-
NBIs) in discharges with one counter-NBI and with three
counter-dominant NBIs.
Here the deposited torque profiles are calculated using the
FIT code based on a database calculated using a threedimensional
Monte Carlo simulation code including orbit
loss and charge-exchange loss of fast ions. In plasmas with
three NBIs, however, the radial profile of the toroidal rotation
velocity in plasmas with a counter-NBI dominant discharge
is quite different from that in plasmas with a co-
NBI dominant discharge. The plasma rotates in the codirection
in the outer part of the plasma minor radius when
counter-NB injection is dominant. The disparity of co- and
counter-driven toroidal rotation profiles is significant in
plasmas with three NBIs and a large ion temperature gradient
because of the formation of the ITB. Three NBIs are
required to achieve ITB plasmas in LHD. The sharp
increase of toroidal rotation in the counter-direction near
the plasma periphery is due to spontaneous rotation driven
by the positive radial electric field, which is strongly localized
near the plasma edge in this discharge. The direction
of the spontaneous rotation due to the radial electric field
is opposite to that observed in tokamak plasmas, where
spontaneous rotation in the co- (counter-) direction is
observed in the region with positive (negative) electric
fields.
3. Relation between ion temperature gradient
and intrinsic rotation
Figure 3 shows contour plots of ion temperature gradients
and toroidal rotation velocity gradients in plasmas with
counter-NBI dominant and co-NBI dominant discharges.
As seen in Fig. 3(a), the ITB region appears at reff/a99 =
0.7 and t =2.15 s, as indicated by an abrupt increase of the
ion temperature gradient. After the formation of the ITB,
the ion temperature gradient exceeds 5 keV/m and the ITB
region, where the ion temperature gradient is large,
expands toward the plasma center. A positive velocity gradient
(dV/dr < 0) appears near the plasma center in the
plasmas with a counter-NBI dominant discharge, while a
negative velocity gradient (dV/dr > 0) is observed near
the plasma center. These gradients are due to the external
NBI torque. The negative gradients observed at reff/a99 =
0.7 in both the co- and counter-NBI discharges are due to
the non-diffusive term of momentum flux as seen in
Fig. 3(b) and (c).
Fig. 2. Radial profile of (top)) toroidal rotation velocity, v
measured from carbon impurity, (middle) ion temperature,
Ti, and (bottom) torque deposition, T for the plasmas with
either co-injecting (blue) or counter-injecting (red), and
(right) three NBIs, either two co-injecting and one counterinjecting
(blue) or one co-injecting and two counter-injecting
(red).
Stellarator News -6- December 2011
A clear hysteresis is observed for the stronger ITB, where
the ion temperature gradient reaches 9 keV/m as seen in
Fig. 4. Note that this is a discharge with the co-NBI dominant
and that the velocity shear near the plasma center
increases in the direction of co-NBI. Although the ion
temperature gradient starts to decrease in the later phase of
the ITB period, the velocity gradient maintains a large
value at reff/a99 = 0.35, 0.85. This observation indicates
that the spontaneous rotation is a transition phenomena
and there are two modes in the spontaneous rotation, one
small, and the other large. The control parameter for this
transition seems to be a temperature gradient. It is interesting
that the non-diffusive term as well as the diffusive
term of the momentum transport (1
N and 2
N as well as
D) can bifurcate, while only the diffusive term i can be
bifurcated in the heat transport.
Fig. 3. Contour plot of (a) ion temperature gradient and (b)
and (c) toroidal rotation velocity gradient in plasmas with
(b) dominant counter-NB injection and (c) dominant co-NB
injection [12].
Fig. 4. The hysteresis curve in the relation between the ion
temperature gradient and toroidal rotation velocity gradient
in plasmas dominated by co-injected NBs [12].
Stellarator News -7- December 2011
4. Mechanism
The mechanism of spontaneous rotation has been investigated
theoretically. The symmetry breaking of turbulence
with the existence of radial electric field shear can produce
an internal toroidal torque and results in a spontaneous
velocity gradient [13]. Plasma turbulence is driven by the
temperature gradient, and the radial electric field shear
should be related to the curvature of the ion temperature
profiles because when the pressure term is
dominant in the radial force balance equation of bulk ions.
Figure 5 shows a conceptual image of the symmetry
breaking of turbulence. When the tilting direction of the
vortex of turbulence is random, turbulence plays a role as
a viscosity that causes momentum transfer in the direction
of reducing the velocity gradient. However, when the tilting
direction of the vortex of turbulence is aligned, it can
cause the momentum transfer to increase the velocity gradient.
This is a possible mechanism to cause momentum
transfer against the velocity gradient, which results in
intrinsic toroidal rotation in the plasma.
References
[1] S. Suchewer et al., Nucl. Fusion 21, 1301 (1981).
[2] K. Brau et al., Nucl. Fusion 23, 1643 (1983).
[3] J. E. Rice et al., Nucl. Fusion 37, 421 (1997).
[4] K. Ida et al., Nucl. Fusion 31, 943 (1991).
[5] L.-G. Eriksson et al., Plasma Phys. Control. Fusion 34,
863 (1992).
[6] J. Rice et al., Nucl. Fusion 38, 75 (1998).
[7] K. Ida. et al., Phys. Rev. Lett. 86, 3040 (2001).
[8] J. S. deGrassie et al., Phys. Plasmas 11, 4323 (2004).
[9] K. Nagashima et al., Nucl. Fusion 34, 449 (1994).
[10] K. Ida et al., Phys. Rev. Lett. 74, 1990 (1995).
[11] K. Ida et al., J. Phy. Soc. Jpn. 67, 4089 (1998).
[12] K. Ida et al., Nucl. Fusion 50, 064007 (2010).
[13] O. D. Gurcan et al., Phys. Plasmas 14, 042306 (2007).
Katsumi Ida
National Institute for Fusion Science
Toki, Japan
E-mail: ida@nifs.ac.jp
Er  Ti  r
Fig. 5. Mechanism of intrinsic rotation and angular momentum transfer when the tilting direction of the vortex is random or
aligned.