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Published by Oak Ridge National Laboratory
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Editor: James A. Rome Issue 156 April 2017
E-Mail: jamesrome@gmail.com Phone (865) 482-5643
On the Web at http://web.ornl.gov/info/stelnews
Confirmation of the magnetic
topology of W7-X
The ability to control edge magnetic topology is of great
interest to the magnetic-confinement fusion community.
The Wendelstein 7-X (W7-X) stellarator (in Greifswald,
Germany) is no exception to this statement; simulations
have suggested that unwanted stray magnetic fields (error
fields) may degrade the performance of its island divertor.
Specifically, magnetic fields with Fourier harmonics of
m/n = 1/1 resonate with the m/n = 5/5 island divertor,
breaking its five-fold stellarator symmetry. Although the
first experimental campaign (OP1.1) on W7-X did not
directly address the m/n = 1/1 error field, efforts were
made to begin to address the possible presence of error
fields with n = 1 character. In the article “Confirmation of
the topology of the Wendelstein 7-X magnetic field to better
than 1:100,000” (published November 30, 2016 in
Nature Communications [1]), key results from flux surface
measurements of W7-X are described. These are under a
Creative Commons license, which allows them to be
reproduced if credit is appropriately given. The article
itself is open access and can be found here: http://
www.nature.com/articles/ncomms13493.
That article describes flux surface measurements of the
W7-X OP1.1 configuration, and of a special configuration
with iota near 0.5 which was used to determine the amplitude
and phase of the n = 1, m = 2 field error. More measurements
and details can be found in the papers by Otte et
al. [2] and Lazerson et al. [3].
Island chains and error fields
An island chain can appear on any magnetic surface with a
rational value of iota. In practice, island chains with a
detectable and operation-relevant size appear only for loworder
rational values of iota, and only if there is a Fourier
component of the magnetic field that has matching (i.e.,
resonant) toroidal and poloidal mode numbers, n and m, so
that = n/m.
W7-X is designed to reach iota of 1 at the outermost flux
surface in the main configuration. It is a five-fold periodic
device, with a pentagon-like shape, and has an n = 5 Fourier
component to its magnetic field, so that an n = m = 5
island chain appears at the plasma edge, this island chain
is used in W7-X to establish an island divertor for particle
and power exhaust, a crucially important part of a fusion
device.
The quality of these islands is thus very important for the
success of the project. Unwanted error fields may break
the 5/5 islands and limit the operation capabilities of the
device. We describe these error fields in relative terms,
bmn= Bmn/B0, where B0 is the average magnetic field
strength in the confinement region, and Bmn is the amplitude
of the m, n Fourier component of the error field. In
the search for error fields, we focus on the toroidal (n)
numbers since only n = 5 and multiples thereof should be
present, whereas a broad spectrum of poloidal (m) numbers
is present in W7-X.
Of particular concern is the n = 1 component, which would
create an n/m = 1/1 island chain; this could result from,
e.g., a slightly misplaced coil module and would lead to
asymmetric divertor loading.
In this issue . . .
Confirmation of the magnetic topology of W7-X
The n = 1, m = 2 field error in W7-X has been measured
to be less than 1:100,000 and agrees well with
that expected from the as-built, as-installed coil geometry.
These results were recently published in Nature
Communications and are summarized here. .......... 1
The new era has begun: The first deuterium
plasma in LHD on March 7, 2017
The LHD launched its new phase of research with
deuterium plasmas on March 7, 2017, after several
years of preparation and device upgrades. ............ 4
Stellarator News -2- April 2017
How we measured the error field
Island chains are sensitive indicators of small changes in
the magnetic field topology, since they are physical manifestations
of resonances in the magnetic topology. The
radial full width w of an island chain is related to a resonant
magnetic field component through [4]
(1)
For the configuration chosen for error field studies here,
iota is nearly constant from the inner to the outer magnetic
surfaces, so a sizable island chain will result from even a
very small resonant error field. See Fig. 1.
In the complete absence of error fields, a small n = 5, m =
10 island chain would appear at the iota = 1/2 location at a
distance of around 25 cm from the innermost magnetic
surface, but in the presence of even a small n = 1 error
field, an n = 1, m = 2 island chain will appear.
The B21 error field is too small to create an island structure
large enough to be measured clearly. This is in part due to
the good news that it is small, and in part due to iota being
so close to 1/2 that the electron beam comes very close to
its launch position (the electron gun) after two toroidal
transits, thus running the risk of hitting the back of the
electron gun and disappearing. Such shadowing effects are
well-known nuisances and are particularly severe near
rational values of iota. We have a new electron gun design
for OP1.2 that should minimize this problem.
It was nevertheless possible to indirectly measure the B21
field error, despite this shadowing problem, by adding an n
= 1 error field with a well-defined amplitude and phase,
using the set of five trim coils [5]. The primary purpose of
these coils is to trim away the unwanted n = 1 error field
components, but the trim coils are used here to create an
extra n = 1 error field and thus generate an n/m = 1/2
island chain wide enough to be measurable.
By scanning the phase and amplitude of the imposed,
well-defined error field, measuring the island phase and
width (Fig. 2), and comparing to Eq. (1), we find that an
n/m = 1/2 island with a width of about 4 cm must be present,
even in the absence of trim-coil-induced fields.
Entering the other known quantities for this configuration
we arrive at:
To our knowledge, this is an unprecedented accuracy, both
in terms of the as-built engineering of a fusion device, as
well as in the measurement of magnetic topology. This
value is well within the range that can be corrected with
the trim coils.
Fig 1. The iota profile is shown for the special configuration
developed for field error detection. Iota varies only minimally
around the resonant value of 1/2. The x-axis is a
measure of the minor radial size (in meters) of the magnetic
flux surface, i.e., a pseudo-radial coordinate.
Source: Nature Communications [1].
bmn
d
dr
----- w2m
16R0
------------ w 4
R0bmn
md
dr
-----
= = --------------
Fig. 2. Measured island chains for different coil current settings.
For the special iota ~ 1/2 configuration, the n = 1, m = 2
island size and phase was measured with the standard fluorescent
rod flux surface measurement technique. Here two
conglomerate images with several nested surfaces are
shown for two different phases of a purposely added n = 1
field structure with the same amplitude. Although the shadowing
problem leads to gaps, the trained eye can still detect
the changes in size and phase of the m = 2 island. In part b)
evidence of a smaller n = 2, m = 4 structure can be seen as
well, indicated with green arrows. Source: Nature Communications
[1] (slightly augmented version of the published figure).
b21
d
dr
----- w2m
16R0
------------ 0.15m–1 0.04m · 2 2
16 5.5m
------------------------------
= = = 5.4 10–6
Stellarator News -3- April 2017
The as-built coil forms and their as-installed locations
have been implemented numerically in our codes and used
to calculate the size, phase, and location of the intrinsic
1/2 island chain resulting from the B21 component. These
data agree very well with our fully independent direct
measurements of the magnetic topology. The agreement
regarding amplitude is shown in Fig. 3.
The now experimentally validated numerical model of the
coil system allows us to identify the primary source of the
measured error field: It is caused primarily by imperfections
in the placement and shapes of the planar coils. For
the special magnetic configuration chosen here, the planar
coils produce a much larger fraction of the magnetic field
than they do in configurations used for plasma operation;
this is because iota, which is generated only by the nonplanar
coils, was lowered so dramatically. The W7-X standard
configuration has iota = 1 at the plasma edge and has
no planar coil current. At first glance, one may argue that
what we measured is not directly related to the error fields
for later operation in the standard configuration and hence
not particularly relevant. But what we measured is highly
relevant because it confirms the metrology measurements
to a very high accuracy. These measurements tell us that
the b11 relative error caused by imperfections in the magnetic
coil system is also expected to be small, likely close
to or somewhat below a previous metrology-based estimate
of 1.1 104, which is also well within the correction
capabilities of the trim coils. Moreover, it is an
independent confirmation of what we already expected
from metrology measurements: That W7-X was built with
the required accuracy.
Of course, we plan to measure the b11 error field in OP1.2,
in a configuration with iota near 1, whose magnetic field is
overwhelmingly dominated by the nonplanar coils and is
very close to those that are used for plasma operation [5].
Erratum for Nature Communications paper
In the Nature Communications paper (but not here), there
were a few typos and typesetting errors in the text and the
affiliations in the W7-X team; the author affiliations were
corrected on line after publication in an erratum [6]. Of
note: there are unfortunately a few instances where Bmn
was written but bmn was meant. These remain in the paper,
as it was not practical to correct them given the rules for
such corrections in Nature journals, and it is clear from the
context which of the two terms was meant.
[1] T. Sunn Pedersen et al., Confirmation of the topology
of the Wendelstein 7-X magnetic field to better than
1:100,000, Nature Commun. 7, 13493 (2016).
[2] M. Otte et al., Setup and Initial Results from the Magnetic
Flux Surface Diagnostics at Wendelstein 7-X,
Plasma Phys. Contr. Fusion 58, 064003 (2016).
[3] S. Lazerson et al., First measurements of error fields on
W7-X using flux surface mapping, Nucl. Fusion 56,
106005 (2016).
[4] A. H. Boozer, Non-axisymmetric magnetic fields and
toroidal plasma confinement, Nucl. Fusion 55, 025001
(2015).
[5] S. A. Bozhenkov et al., Methods for measuring 1/1
error field in Wendelstein 7-X stellarator, Nucl. Fusion 56,
076002 (2016).
[6] T. Sunn Pedersen et al., Erratum: Confirmation of the
topology of the Wendelstein 7-X magnetic field to better
than 1:100,000, Nature Commun. 8, 14491 (2017)
Sergey Bozhenkov, Matthias Otte, Thomas Sunn Pedersen, Max
Planck Institute for Plasma Physics, Greifswald, Germany
Samuel Lazerson, Princeton Plasma Physics Laboratory, Princeton,
NJ, USA
On behalf of our co-authors and the W7-X Team
Fig. 3. The measured island widths (circles) are compared
directly to those predicted from numerical calculations that
take the as-built, as-installed geometry of the W7-X coil set
into account (triangles). Excellent agreement is seen. The
offset from zero in the linear fits indicates the intrinsic 4 cm
island width. If no intrinsic error field were present, the
points would line up with the dotted lines. Source: Nature
Communications [1].
Stellarator News -4- April 2017
The new era has begun: The
first deuterium plasma in LHD
on March 7, 2017
The Large Helical Device (LHD) launched its new phase
of research with deuterium plasmas on March 7, 2017,
after several years of preparation not only for device
upgrades but also for administrative procedures.
A commemorative ceremony was held on March 7, 2017,
with approximately 150 guests [including members of the
Diet, the Ministry of Education, Culture, Sports, Science
and Technology (MEXT), local governments, local residents’
associations, NIFS collaborators, and other people]
in attendance.
The Director General of NIFS, Prof. Yasuhiko Takeiri,
delivered the ceremonial address, followed by the initiation
of the sequence by pushing the button to successfully
produce the first deuterium plasma heated by ECH. By the
way, the button had been kept from the ceremony for the
first plasma of LHD conducted in March 1998.
The first light of the deuterium plasma is shown in Fig. 1,
and its waveform (much simplified from a usual waveform
of LHD, for the purpose of the ceremony) is shown in Fig.
2.
After the successful production of the first deuterium
plasma, the Kusudama, a decorative paper ball for festive
occasions in Japan, was opened collaboratively by distinguished
guests (Fig. 3). The vertical banner reads, “Celebration
(in red): Deuterium first plasma production.” The
congratulatory speeches continued, including a speech by
Dr. David Gates (Princeton Plasma Physics Laboratory);
congratulatory messages from distinguished international
collaborators were introduced.
In the deuterium experiment in LHD, higher performance
of plasma confinement is envisaged, and further advanced
research will be conducted to facilitate not only helical
systems research but also worldwide fusion research. We
appreciate your further support and interest, and invite you
to utilize the LHD as one of the major advanced international
platforms for fruitful collaborative research.
Tomohiro Morisaki and Masaki Osakabe
for LHD Experiment Group
National Institute for Fusion Science (NIFS), Japan
Fig. 1. The first deuterium plasma in LHD (#133301).
Fig. 2. A waveform of the first deuterium plasma.
Fig. 3. Opening of the “Kusudama.”