All opinions expressed herein are those of the authors and should not be reproduced, quoted in publications, or
used as a reference without the author’s consent.
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 5700 P.O. Box 2008 Oak Ridge, TN 37831-6169, USA
Editor: James A. Rome Issue 121 August 2009
E-Mail: jar@ornl.gov Phone (865) 482-5643
On the Web at http://www.ornl.gov/sci/fed/stelnews
Magnetic field shaping
with high-temperature
superconducting monoliths
1. Introduction
Stellarators offer substantial physics advantages for fusion
reactors, both in the near term as experimental facilities,
and in the long term as commercial fusion reactors
[1,2,3,4]. Stellarators are attractive for reactors because
they do not have disruptions, are truly steady state, and
have high beta limits. On the other hand, engineering of
stellarators is challenging, in particular, the design of the
magnetic field coils and the diverter [5,6].
In this article and a forthcoming paper [7], a novel method
is investigated to simplify the magnetic field coils. The use
of monolithic high-temperature superconductor (HTS) for
field shaping in stellarators and tokamaks is presented.
The basic concept investigated in this paper is to use a relatively
simple coil set that generates a background magnetic
field, and to use HTS monoliths to shield/shape the
magnetic field to the desired configuration.
The properties of presently available monolithic HTS are
described in Section 2, as is the physical model used to
describe the superconducting monoliths. Yttrium barium
copper oxide (YBCO) has excellent properties, operating
at elevated temperatures (> 10 K). High-field, cryostable,
highly complex magnetic field topologies can be generated
using this material. The diamagnetic properties of the
bulk HTS material can be used to provide simple mechanisms
for field shaping.
Section 3 describes the design issues relevant to tokamak
magnets using single crystal or highly textured YBCO
monoliths. Engineering constraints, such as stresses in the
superconducting monoliths, support, quench protection,
superconducting stability of the monoliths, and required
external support structure are described.
Section 4 briefly touches on the application of this
approach to stellarators.
2. HTS monoliths
A. Properties and availability
There is a small program worldwide to develop monoliths
of HTS material. During the initial phases of hightemperature
superconductivity, the only materials that
were available were bulk materials. This was the case for
Bismuth-2 Strontium-2 Calcium Copper-2 oxide (B-2212)
and YBCO. Wires were initially made from B-2212, but
this effort was dropped because of the material’s relatively
poor superconducting properties at 77 K.
Presently, both B-2212 and YBCO are available. BSCCO-
2212 is more developed, because of its application as a
current lead, and more recently, as a component of fault
In this issue . . .
Magnetic field shaping with high-temperature
superconducting monoliths
As suggested by M. Zarnstorff, a group with members
at MIT and at PPPL is investigating the use of monolithic
superconductors for magnetic field modification.
In principle, simple fields can be adjusted to generate
complex fields, as in stellarators. To date, the concept
has been evaluated for TF ripple reduction. ........... 1
Nonlinear simulation of a collapse event in LHD
We performed a nonlinear MHD simulation in a heliotron
configuration with a large pressure gradient to
reveal the nonlinear dynamics of a collapse phenomenon.
Qualitative agreement with the experiments was
achieved.The growth of the ballooning-like resistive
modes results in energy relaxation in about 1 ms. The
coexistence of the edge linear modes and the core
pressure drop is also reproduced. .......................... 6
All Wendelstein 7-X coils successfully tested
All planar and non-planar coils for W7-X have passed
electrical, cryogenic, and mechanical tests. Assembly
of the device is progressing well, although the tight
assembly conditions are challenging. ..................... 9
Stellarator News -2- August 2009
current limiters. This material is available from Nexans, as
rods, cylinders, or plates. While its properties are lackluster
at 77 K, they are very good at 20–30 K.
Bulk YBCO is being developed mainly as a material to be
used in bearings, in the USA (Boeing), Europe (Nexans),
and Japan (ISTEC), among others. The characteristics of
this material are nothing less than spectacular at temperatures
up to 60–65 K. YBCO has limited current density
capabilities at 77 K, good enough for tapes, but not for
high-field magnet applications, which need to be operated
in subcooled liquid nitrogen.
The most impressive performance of YBCO pucks has
been a 17 T magnet at 29 K without a background field
[8]. For B-2212, the MIT group has built a 3 T magnet at 4
K, and a 1 T insert in a 19 T background [9].
These materials are available at costs of 15 €/cm2
(150 k€/m2).
B. Modeling of HTS bulk material
The interaction of HTS bulk material with magnetic fields
is very nonlinear and complex. In this section two methods
that simplify the complex behavior are described. These
methods are used in the remainder of the paper to analyze
interactions between tiles of HTS monoliths and the magnetic
field.
Using the simple Bean model of superconductivity, the
HTS monoliths are assumed to be at critical current density.
As the external field is raised, currents are generated
on the surface of the monoliths to prevent penetration of
the field to the bulk. The current density is a function of
the temperature of the monolith and the local applied field.
The “skin” current thickness increases with increasing
magnetic field. As the field decreases, edge currents flow
in the reverse direction on the surface, locally trapping
some magnetic field.
If the current density capability of the monoliths is large
and the thickness of the skin currents is small compared
with the size of the monoliths, the monoliths can be
described as “diamagnetic” elements.
Two methods have been used to describe the diamagnetic
model of the HTS monoliths. The first assumes that the
magnetic field is parallel to all surfaces of the monolith.
The second one assumes that the magnetic permeability μ
of the HTS monoliths is very small. While either method
works, the second one is easier to implement, as applying
the boundary conditions to all surfaces of the monoliths is
time consuming.
We have used μ = 0.001 in the remainder of this paper to
describe the HTS monoliths.
C. Estimate of forces/currents in HTS monolith
The interaction between HTS monoliths and magnetic
field can be divided into two effects. The first is the surface
currents that exclude the external magnetic field from
the superconductor. It is straightforward to estimate the
value of these currents. The surface current density excited
by the presence of the field is simply
K = B/μ0,
where B is magnetic field external to the surface of the
monoliths. The critical current densities of YBCO are on
the order of 109–1010 A/m2. Thus, to expel a field of 5 T,
the thickness of the current carrying layer is less than 0.01
m (1 cm). It is expected that the value of the field outside
the surface of the monolith is comparable to the applied
field, B0 (the assumption being that the main effect of the
HTS monoliths is to “globally” turn the direction of the
magnetic field). These currents exist even if the wide surface
of the monolith is aligned with the magnetic field, in
which case one would not expect the direction of the field
to be modified.
The second effect is due to the interception of fields perpendicular
to the wide surface of the monolith. Assuming
that the tiles have a dimension of the average diameter of
the tiles, the magnetic moment generated by the presence
of the monolith is
where δ is the angle between the main normal to the
monolith and the applied magnetic field.
The main difficulty with these simple models arises
because of interactions with adjacent tiles, which generate
local magnetic fields. This makes it necessary to solve the
problem using multidimensional models.
The torque that a monolith will experience in the presence
of an externally applied magnetic field B0 is on the order
of
The forces/torques are very large and must be supported.
In order to quantify the forces, the full multidimensional
effects must be calculated.
D. Effect of gaps between monoliths
The magnetic field does not have to follow the main surface
of the superconducting monoliths in the gaps between
monoliths; that is, the magnetic field can “escape” through
these regions.
One option to avoid the effect of the gaps between monoliths
is to stack multiple layers of monoliths, such that they
m π2
4μ0
∼ --------B0a3 cosδ
τ m × B0 π2
4μ0
--------B0 2 = ∼ a3 sinδcosδ
Stellarator News -3- August 2009
are staggered. Although the field can still escape through a
gap, it is intercepted by the monolith behind.
The impact of the staggered layer of monoliths also
requires numerical calculation. This is described in the
next section.
3. Use of HTS monolith for toroidal field ripple
cancellation
The quantitative work was complex. Simpler geometries
were investigated and are reported here. A simple geometry
using helical coils for a cylindrical configuration
proved to provide none of the simplifications that a twodimensional
(2D) model would have. That is, the helical
geometry still needs a 3D model for analysis.
In the remainder of this section we describe calculations
that are directly relevant to tokamaks. It is possible to
build a simple 2D model representing the use of monoliths
for ripple control.
The simple model is shown in Fig. 1. The model uses a
toroidal field (TF) system with only 8 coils, with relatively
large ripple. The outer legs of the coils are at 6 m. The ripple
calculations for these coils are performed at a radius of
4 m.
The throat of the magnet is assumed to be continuous, with
discrete legs in the outboard side. The symmetry of the
problem was used to decrease the size of the required
mesh. The planes with boundary conditions of normal
magnetic fields are shown. It is assumed that the model is
2D, with coils extending in the direction out of the plane.
Thus, the model is directly applicable to the midplane
region of tokamaks.
A. Single layer of monoliths with 16 azimuthal monoliths
The commercial code VectorFields from Opera-2D software
is used to model this system. The problem is solved
with multiple adaptations of the grid until 0.1% accuracy
of the solution is achieved.
Contours of constant magnetic field are shown in Fig. 2.
The top shows the results for no monoliths, while the bottom
shows the results for one layer with large tiles. The
case shown in the bottom part of Fig. 2 has 16 monoliths,
with the centerline of one of the monoliths corresponding
to the shadow of the TF coils. Both a substantial perturbation
of the field in the region of the tiles, and the effect of
the gap are readily seen. As described above, the field
tends to “squeeze out” between the monoliths.
The effects of smaller tiles and multiple layers are
described in the next section.
B. Multiple layers
There are 8 tiles between each pair of TF coils, or 64 tiles
around the device. For the geometry chosen for the example,
the monoliths are about 30 cm in width. In all cases,
the thickness of the monoliths is assumed to be 0.02 m (2
cm).
Fig. 1. Schematic of geometry used to calculate the effect
of multiple HTS monoliths on the toroidal field ripple in
tokamaks. Fig. 2. (Contours of constant magnetic field for the tokamak
case with 8 coils. Top: no HTS monoliths (base case).
Bottom: 16 HTS monoliths.
Stellarator News -4- August 2009
The first layer of monoliths occurs at 4.8 m, and each subsequent
layer is placed at 5 cm intervals, that is, the separation
between layers is 0.03 m (3 cm). The gap between
the tiles has been varied from about 0.01 m (1 cm) to about
0.04 m (4 cm).
Figure 3 shows the resulting field profiles for the cases of
1 and 3 layers of 0.3 m monoliths. It is interesting to note
the dark regions of high-intensity magnetic field between
some tiles. The field is not prevented from penetrating
between tiles by the presence of monoliths downstream,
but instead “squeezes out” between the tiles in a staircaselike
pattern. However, it is clear that the magnetic field
ripple has been decreased, as the contours of constant
magnetic field look more axisymmetric.
Figure 4 shows the magnetic field along an arc at 4 m,
along the toroidal direction. Shown in Fig. 4 is a half-distance
between coils, using the symmetry properties of the
model. The field is sinusoidal. No higher harmonics are
visible in the field, showing that the local field from the
individual monoliths has been “washed out.”
Corresponding values of peak-to-peak ripple are shown in
Fig. 5 as a function of the number of layers. The field ripple
is about 7% with no correction by the monoliths, and
decreases exponentially as the number of layers increases.
The exponent is about 0.5. Between 4 and 5 layers are
required in order to reduce the ripple to <1%.
Also shown in Fig. 5 is the ripple for the case with a
smaller gap between monoliths. In the results up to now
the toroidal gap between monoliths has been 0.5°, corre-
Fig. 3. Contours of constant magnetic field (a) for the case
of a single layer of 0.3 m monoliths and (b) for the case of 3
layers of monoliths with 3 cm between layers.
(a)
(b)
Fig. 4. Magnetic field magnitude as a function of the toroidal
angle for the case of 3 layers of 0.3 m monoliths, corresponding
to the case shown in Fig. 3(b).
Fig. 5. Peak-to-peak ripple at 4 m as a function of the
number of layers, for two cases of gaps between monoliths.
Stellarator News -5- August 2009
sponding to about 0.04 m between tiles. The point indicated
with 0.1° between monoliths in Fig. 5 corresponds to
about 0.008 m between tiles.
Although the results are for infinitely long monoliths, the
results are expected to be relevant even for tiles of limited
extent in the poloidal direction.
The thickness of the current-carrying layer can be determined
from these results. It is on the order of 1 cm, so the
assumption of perfectly diamagnetic monoliths, although
not exact, does provide good insight into the performance
of the monoliths for shaping fields in toroidal geometries.
4. Stellarator geometry
The complex geometry of the stellarator is presently being
investigated using the same model. Figure 6 shows the
model that is being implemented in VectorFields.
Acknowledgment
Suggestions and feedback from Hutch Neilson are appreciated.
L. Bromberg, J.V. Minervini, J.H. Schultz
Plasma Science and Fusion Center
Massachusetts Institute of Technology
Cambridge MA, USA
E-mail: brom@psfc.mit.edu
A. Boozer, T. Brown, P. Heitzenroeder, and M. Zarnstorff
Princeton Plasma Physics Laboratory
Princeton University, Princeton NJ, USA
References
[1] C. D. Beidler, E. Harmeyer, F. Herrnegger, et al., “The
Helias reactor HSR4/18,” Nucl. Fusion, 41 (2001)
1759.
[2] A. Sagara, and O. Motojima, “LHD-type reactor design
studies,” Fusion Technol., 34 (1998) 1167–73.
[3] M. Wanner, J.-H. Feist, H. Renner, J. Sapper, F. Schauer,
H. Schneider, V. Erckmann, H. Niedermeyer, W7-X
Team, “Design and construction of Wendelstein 7-X,”
Fusion Eng. Des. 56–57 (2001) 155–162.
[4] B. E. Nelson, L. A. Berry, A. Brooks, et al., “Design of
the National Compact Stellarator Experiment (NCSX).”
Fusion Eng. Des. 66–68 (2003) 169-174.
[5] F. Najmabadi and A. R.Raffray, “The ARIES-CS compact
stellarator fusion power plant”, Fusion Sci. Technol.
54 (2008) 655–72.
[6] X. R. Wang, A. R. Raffray, L. Bromberg, J. H. Schultz,
L. P. Ku, J. F. Lyon, et al., “ARIES-CS Magnet Conductor
and Structure Evaluation,” Fusion Sci. Technol.,
54 (2008) 818–837.
[7] T. Brown, L. Bromberg, M. Cole “Results of compact
stellarator engineering trade studies,” Symposium of
Fusion Engineering, San Diego, June 2009.
[8]
[9] M. Tomita and M. Murakami, “High-temperature superconductor
bulk magnets that can trap magnetic fields
of over 17 Tesla at 29 K,” Nature 421 (2003) 517–20.
[10] L. Bromberg, private communication (unpublished).
Fig. 6. Helical geometry with tiles along three surfaces, for
future investigation of field shaping.
Stellarator News -6- August 2009
Nonlinear simulation of a collapse
event in LHD
1. Introduction
Controlling the collapse phenomena which take place in
toroidal experiments is one of the key issues for the development
of fusion sciences. Such collapse phenomena usually
proceed on a magnetohydrodynamic (MHD) time
scale, sometimes accompanied by precursory oscillations,
and are in general harmful to confinement. Because the
collapse phenomena are governed by highly nonlinear processes,
it is necessary to make use of nonlinear numerical
simulation techniques.
In recent high-performance helical experiments such as
the super-dense core (SDC) state of the Large Helical
Device (LHD) [1], a collapsing event with an abrupt flushing
of the core density has been observed under certain situations.
This event is termed a core density collapse
(CDC) [2]. CDCs are typically observed in the reheating
stage during which the plasma beta gradually increases
after a pellet injection series. The crash phase of the CDCs
is characterized by a rapid fall of the central density and its
expulsion toward the edge. CDCs are sometimes accompanied
by precursors in the outer region [3]. Further
increase of the plasma beta is limited by the CDC in some
cases. The CDC is phenomenologically understood at
present, whereas the detail mechanism, in particular the
nonlinear dynamics of the crash phase, has not yet been
clarified.
In this study, we aim at providing a qualitative understanding
of the nonlinear dynamics of a collapse phenomenon
in a heliotron plasma with a large pressure gradient
(characteristic of the SDC state of LHD) by means of a
nonlinear MHD simulation.
2. Simulation model
The governing equations for the simulation are the nonlinear,
resistive, compressive equations,
, (1)
, (2)
, (3)
, (4)
where the density ρ, fluid velocity v, magnetic field B, and
the pressure p are developed. The current density j and the
electric field E are evaluated by
, (5)
. (6)
In Eqs. (1)–(6), the dissipation terms are included as the
resistivity η and the viscosity μ. These terms are assumed
to be uniform constants for simplicity. All spatial derivatives
are expressed numerically using a fourth-order central
difference scheme, and together with the time
integration were solved using the fourth-order Runge-
Kutta method. The simulations are executed in full toroidal
three-dimensional geometry using the helical-toroidal
coordinate system that is used in the HINT code [4]. The
helical period h is set at 10/2 to follow the LHD configuration.
The numbers of the numerical grid are 62 × 146 for
the poloidal cross section, and 500 for the toroidal direction.
The simulation geometry includes the region out of
the separatrix, which is treated as an initially biased lowpressure
plasma.
The initial condition for the simulation is given by the
numerical solution of the HINT2 code [5]. In particular,
the profile of the equilibrium models an average experimental
configuration of LHD during outward-shifted operation
with an SDC. Note that the unit of the time of the
simulation roughly corresponds to 1 s of the experiment.
The simulation starts by adding tiny random perturbations
to the velocity components of the initial equilibrium.
Then, the spontaneous time development of the MHD system
is solved by vector-parallel calculation on a supercomputer.
3. Simulation result
For high resistivity, η =10-4, the system tends to be unstable
for some resistive instabilities. Al-though such unrealistically
high resistivity may exaggerate the linear growth
rate of the resistive instability modes compared to the
experiments, these simulation results can help us obtain a
basic understanding of the nonlinear behavior of the resistive
modes. The structure of the linear eigenmode is
shown in Fig. 1 with the contour of the perturbations in the
pressure at the horizontally elongated poloidal cross section.
The mode component is poloidally localized in the
outer region with the intermediate (m ~ 15) components,
where m is the poloidal mode number. Such a ballooninglike
nature is seen at any toroidal location. Moreover, the
mode structure is almost identical for all of the horizontally
elongated plane. This implies that the low-n components,
where n is the toroidal mode number, are not so
significant in this case.
∂t
∂ρ = –∇•(ρv)
∂t
∂ ρv ( ) ρvv ( ) ∇p – J B × μ ∇2 v 13
= –∇• + + + --∇(∇•v)
+μ ∇2v 13
+ --∇(∇•v)
∂t
∂B = –∇×E
∂t
∂p = –∇•(pv) – (γ – 1)(p∇•v + ηj2)
j = ∇×B
E = –v × B + ηj
Stellarator News -7- August 2009
As the amplitude of the perturbations becomes large, the
configuration is deformed spontaneously into a visible
scale, and the growth is saturated. The time development
of the overall system is plotted with the change in total
kinetic energy in Fig. 2. One can see that the growth and
the relaxation of the instability repeat three times in about
t = 500τA. The corresponding change in the pressure profile
shows disordering by the instability in the edge region.
Moreover, the central pressure also drops as time goes on.
This behavior is clearly shown in Fig. 2 in the trace of
maximum pressure. The most rapid drop in pressure is
observed at around t = 335τA. The system reaches its final
relaxed state just after this rapid pressure drop. In the final
state, the pressure profile forms a wide tail in the peripheral
region.
The collapsing process is more clearly visualized by a
two-dimensional contour plot of the pressure profile in a
horizontally elongated poloidal cross section, as shown in
Fig. 3. The structure is destroyed in the peripheral region,
reflecting the linear eigenmode structure. The convection
motions of the eigenmodes form a number of finger-like
structures in the unstable region. The disordered region is
extended inward. However, the bulk of the plasma is not
displaced away, despite the rapid fall at t ~ 335τA. This is a
remarkable contrast to our previous simulation for the
spherical tokamak case [6], where the rapid fall of the core
pressure is caused by a secondary induced internal lowm/
n instability.
The period of the core pressure fall at around t = 335τA is
characterized by some qualitative transitions of the system.
The most salient feature of this period is the disordering
of the magnetic field structure. The system maintains
nested flux surfaces in the core region before t = 335τA,
but some of these flux surfaces are abruptly lost at around
t = 335τA. As the core pressure drop ends, the flux surfaces
gradually reappear. Such a disordered magnetic
structure can cause a flattening of the pressure profile in a
wide region due to the parallel equilibration motion of
MHD. Therefore, the disordering of the magnetic structure
can be considered to be the direct cause of the core pressure
collapse.
This insight can be supported by another observation of
the simulation result concerned with the plasma flow
structures. To find the place where the plasma loss due to
this mechanism occurs extensively, the internal energy
flux |pV| is plotted in Fig. 4(a) using color contours on top
of the pressure profile, which is indicated by the gray contours.
One can see that such plasma outlets are mainly
located at the roots of the fingers. Another simple analysis
shows that the direction of the energy flux is almost parallel
to the magnetic field. The neighboring magnetic structure
is also shown in Fig. 4(b). The magnetic flux surfaces
are hard to find except in the regions between the islands
or their ruins. In Fig. 4(b), one can see a couple of wellformed
surfaces at R = 4.24 m and 4.30 m on the equator
(Z = 0), putting the ruins of the ι = 2/3, 5/8, and 4/7 islands
between them, with the outlets corresponding to the disordered
region. Thus, within the MHD framework, the magnetic
and flow structures show that the core pressure can
be expelled away through the disordered or reconnected
field lines. Note that the spots of the outlets are seen apart
from the original linear eigenmode ones, which are indicated
with the red and blue contours in Fig. 4.
Fig. 1. The linear eigenmode structure. Perturbations in the
pressure are plotted with color contours. The puncture plot
of magnetic field for the initial condition is also shown.
Fig. 2. Time development of the total kinetic energy normalized
by the initial plasma thermal energy and the maximum
pressure.
Fig. 3. Deformation of the pressure profile on a horizontally
elongated poloidal cross section at t = 335τA.
Stellarator News -8- August 2009
4. Discussion and summary
The simulation results described here can be compared in
several ways with the experimental observations of the
CDC in LHD. First, the time scale of the crash phase of
the CDC is of the order of sub-milliseconds, which is comparable
to the whole relaxation process of the simulation
result. As mentioned above, the resistivity for the simulation
is assumed to be much larger than a realistic one, and
the linear growth of the resistive modes may thus appear
to be more rapid. However, since the nonlinear behavior
(including the loss mechanism of the core pressure) is
dominated by the convection term of the MHD fluid, the
time scale should not be much affected by the value of the
resistivity. Second, the coexistence of the edge precursors
and the core collapse in the experiment can be reasonably
explained by the simulation result. The core collapse is not
directly caused by the linear mode activities, but results
from the flattening of the pressure gradient due to the disordering
of the magnetic structure. Under this scenario, the
role of the precursor modes is only to trigger the flushing
of the core pressure. The magnitude and the time constant
of the collapse are governed by global parameters such as
the pressure gradient. Third, the experimental observation
that only the density drops, leaving the temperature profile
unchanged, appears to show that the process is governed
not by a conductive process, but by a convective one. The
simulation, which solves an almost pure convective process,
supports that observation.
In summary, we have demonstrated the nonlinear dynamics
of a heliotron plasma with a large pressure gradient
during a collapse event induced by a ballooning-like resistive
instability with an intermediate wave number. It is
clear that the flushing of the core pressure is triggered by
edge instabilities through the disordering of the magnetic
field structures. The simulation result provides us with a
basic understanding of the nonlinear behavior of the resistive
modes. The identification of the mode structures
between the experiment and simulation is a subject of our
ongoing research. The recent stability analysis for the
LHD-SDC plasma [7] shows that the configuration is
almost stable for the ideal modes. Therefore, control of the
resistive modes will be important. More systematic analyses
of the resistive modes will be performed in the next
step of this study.
This work was presented at the 22nd IAEA Fusion Energy
Conference (Geneva, 2008, TH/P9-17) and will be published
in Nuclear Fusion [8] in more detail.
Naoki Mizuguchi
National Institute for Fusion Science
Toki, Gifu 509-5292, Japan
E-mail: mizu@nifs.ac.jp
References
[1] N. Ohyabu et al., Phys. Rev. Lett. 97, 55002 (2006).
[2] R. Sakamoto et al., Plasma Fusion Res. 2, 047 (2007).
[3] S. Ohdachi et al., 22nd IAEA Fusion Energy Conf.,
(Geneva, 2008) EX/8-1Rb.
[4] K. Harafuji et al., J. Comput. Phys. 81, 169 (1989).
[5] Y. Suzuki et al., Nucl. Fusion. 46, L19 (2006).
[6] N. Mizuguchi et al., Nucl. Fusion 47, 579 (2007).
[7] Y. Narushima et al., Joint Conf. 17th Int. Toki Conf.
and 16th Int. Stellarator/Heliotron Workshop (Toki,
2007), P1-053.
[8] N. Mizuguchi et al., Nucl. Fusion 49, to be published
(2009).
Fig. 4. Poloidal profiles of the plasma pressure energy flux
at t = 335τA. (a) Contours of the absolute value of the
energy flux |pV| (orange), perturbations in the pressure in
the linear eigenmode (red and blue), and net pressure
(gray). (b) Magnification of the box in (a) without the pressure
but with the puncture plot of the magnetic field lines.
The original locations of the rational surfaces for ι = 2/3, 5/
8, and 4/7 are also specified (green).
Stellarator News -9- August 2009
All Wendelstein 7-X coils successfully
tested
The last of the superconducting Wendelstein 7-X (W7-X)
coils has successfully passed cryogenic tests at CEA
Saclay near Paris. The 50 non-planar and 20 planar coils
of W7-X are the heart of the device and technically the
most demanding components. The non-planar coils produce
the helically twisted magnetic field, responsible for
the confinement of the plasma. For experimental flexibility,
the radial plasma position and the helical twist of the
magnetic field lines can be modified by the planar coils.
In 1998, the contract for the production of the non-planar
coils was placed with a consortium of two companies,
Babcock-Noell in Germany and Ansaldo in Italy. The planar
coils were manufactured by TESLA in the UK. The
production of the coils went through many ups and downs:
various technical problems, in particular with the electrical
insulation, had to be solved during the production; but also
quite substantial modifications, especially on the casings
and the support blocks, have been implemented. During
the cold tests in Saclay the superconductor performed better
than expected, showing no degradation due to bending
inside the coils or welding of the aluminium alloy jacket.
However, the electrical insulation of the non-planar coils
in the header area, where the winding pack layers are connected
and the connections to the power supplies are
made, had to be reworked on several coils.
The tests at Saclay demonstrated that the specifications
were achieved. The tests at around 5.7 K included several
current cycles. For each coil type at least one temperatureinduced
quench was provoked by increasing the temperature
to at least 6.2 K until the conductor quenched. In addition
to confirming that the coils achieved the specified
current and the thermally induced quench safety margin,
the thermal cycles revealed weaknesses of the electrical
insulation. Subsequent high-voltage tests at Paschen conditions
showed in such cases breakthrough voltages below
the specified values. After reworking of the critical areas,
the necessary voltages could be achieved for all coils.
Completing the acceptance test, the last non-planar coil
was used to experimentally verify the stability of the
cable-in-conduit superconductor with respect to mechanical
disturbances. An open question with respect to the W7-
X design was whether the energy released during possible
stick-slip events, originating from the sliding elements
within the extremely highly loaded mechanical support
structure, could in the worst case induce a quench in the
superconducting cable. Therefore, qualification of the sliding
support elements included mechanical tests to ensure a
sufficiently large number of magnetic field load cycles
without any stick-slip. In addition, the so-called mechanical
quench (MQ) test was developed to investigate the
effect of such a stick-slip in case it still occurs in spite of
all the precautions (Fig. 1). The MQ test assembly consisted
of a pendulum which, via a transfer rod, applied a
defined energy to the electrically charged coil inside the
cryostat. The amplitudes and the frequency spectrum of
the impact response were calculated to be comparable to
the various stick-slip possibilities in the coil support elements.
The results of this test are very comforting: even
the highest impact energies corresponding to improbable
simultaneous stick-slip events, combined with the lowest
stability margin of the conductor expected during W7-X
operation at a field of 3 T on-axis could not induce a
quench. This suggests that even if stick-slip occurs, no
quench of any superconducting coil is to be expected.
Altogether, the assembly of W7-X is progressing well.
Some problems result from the extremely tight space conditions
inside the cryostat, which require quite resourceintensive
collision analyses regarding positioning of the
helium pipe work and superconducting bus system, as well
as the thermal superinsulation covering the inside of the
outer cryostat vessel and the outside of the ports. Also, the
application of the electrical insulation to the cable joints
turned out to be much more difficult and time-consuming
under real, very tight assembly conditions as compared to
the qualification of these assembly steps at the work
bench. At present, assembly work is progressing on four of
the five magnet modules. Figure 2 shows the torus hall and
the current state of assembly.
Fig. 1. MQ test setup. The superconducting coil is hit by
different pendulum weights via a transfer rod that is fed
through the cryostat wall and the thermal LN2-shield. The
transfer rod is sealed against the cryostat wall with a double
bellows system with intermediate vacuum. The pendulum,
hanging from the pendulum frame, is released from
different heights. The dead stop frame limits the movement
of the transfer rod and the attached coil.
Stellarator News -10- August 2009
W7-X Newsletter:
Coordination: Prof. a. D. Dr. Robert Wolf
Contact: Dr. Andreas Dinklage
E-mail: andreas.dinklage@ipp.mpg.de
Fig. 2. View into the torus hall with one magnet module sitting on the machine base (at present only temporarily) and
another one alongside. On the right one lower shell of the outer cryostat vessel can be seen.