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An international journal of news from the stellarator community
Editor: James A. Rome Issue 169 August 2020
E-Mail: Phone: +1 (865) 482-5643
On the Web at
Feature extraction and prediction
of radiative collapse in
Large Helical Device using
sparse modeling
The features of radiative collapse have been extracted
from high-density plasma experiments in the Large Helical
Device (LHD Toki, Japan) with a sparse modeling
technique. The extracted features have been used to
explore the underlying physics of radiative collapse and to
develop a machine learning predictor of the collapse.
In stellarator-heliotron plasmas, radiative collapse is one
of the most critical issues that limit the operational density.
The well-known Sudo scaling law for the density limit
suggests that the balance between heating power and radiative
power loss is a key, together with robust confinement
capability such as plasma volume and magnetic field [1].
However, contributions of other operational conditions
(e.g., impurity contamination, wall conditions) to the
occurrence of radiative collapse are not expressed in the
Sudo scaling law.
In the present study, a machine-learning classifier that distinguishes
plasmas in the close-to-collapse state (in which
radiative collapse is likely to occur) and in the stable state
has been constructed based on experimental data from
LHD. In the experiment, a hydrogen and deuterium gaspuff
was used as fueling, and the magnetic configuration
was fixed at the magnetic axis position Rax of 3.6 m, with
B = 1.375 T or 2.75 T. The surveyed line-averaged density
and heating power range up to 1.5 × 1020 m3 and 15 MW,
respectively. The data was classified into stable and closeto-
collapse states according to the density exponent
which is a criterion of thermal instability [2]. Here, the
dots indicate time derivatives.
Using the constructed classifier, features of radiative collapse
have been extracted using exhaustive search (ES), a
sparse modeling technique. Sparse modeling is one of the
frameworks of data-driven science; it exploits the inherent
sparseness in all high-dimensional data to extract the maximum
amount of information from the data [3]. In ES, all
possible combinations of input parameters are compared
with each other to find the optimal set.
As a result of feature extraction, line-averaged electron
density , line emissions of C IV and O V, and electron
temperature at the plasma edge have been identified
as key parameters of radiative collapse. Using those
parameters, collapse likelihood has been calculated, corresponding
to distance from the boundary between stable
and close-to-collapse states obtained by machine learning.
Figure 1 shows a typical discharge with radiative collapse
in LHD. In this discharge, the collapse likelihood
increased and reached 1.0 (100%) before the plasma collapsed.
P ·
rad  Prad
n ·
e  ne
= -----------------------
Te edge
In this issue . . .
Feature extraction and prediction of radiative
collapse in Large Helical Device using sparse
The features of radiative collapse have been
extracted from high-density plasma experiments in
the Large Helical Device (LHD Toki, Japan) with a
sparse modeling technique. The extracted features
have been used to explore the underlying physics of
radiative collapse and to develop a machine-learning
predictor of the collapse. ......................................... 1
NIFS-SWJTU Joint Project (NSJP) for CFQS
The origins of an international joint project to design,
build, and operate a stellarator with quasi-axisymmetry,
the Chinese First Quasi-axisymmetric Stellarator
(CFQS) are reviewed. ............................................ 2
Stellarator News -2- August 2020
The collapse likelihood has been verified with about 500
discharges in LHD, and more than 85% of radiative collapses
have been predicted successfully at least 30 ms
before occurrence. Also, using the extracted parameters,
mechanisms of occurrence of radiation collapse have been
explored focusing on radiation loss of light impurities at
the plasma edge, especially outside the last closed flux
This work is supported by the National Institute for Fusion
Science Grant administrative budget NIFS18KLPP051,
and the JSPS KAKENHI Grant Numbers JP19J20641 and
Tatsuya Yokoyama,1,2 Hiroshi Yamada,1 Suguru Masuzaki,3,4
Junichi Miyazawa,3,5 Kiyofumi Mukai,3,5 Byron J. Peterson,3,5
Naoki Tamura,3,5 Ryuichi Sakamoto,3,5 Gen Motojima,3,5
Katsumi Ida,3 Motoshi Goto,3,5 Tetsutaro Oishi,3,5
Masahiro Kobayashi,3,5 Gakushi Kawamura,3,5
and the LHD Experiment Group3
1 Graduate School of Frontier Sciences, The University of Tokyo
2 JSPS Research Fellow
4 Kyushu University
[1] S. Sudo et al. Nucl. Fusion,30(1), 11–21, 1990.
[2] B. J. Peterson et al., Plasma Fusion Res. 1, 045–045,
[3] Y. Igarashi et al., J. Phys. Soc. Jpn 87, 044802 (2018).
NIFS-SWJTU Joint Project
The National Institute for Fusion Science (Japan) and
Southwest Jiaotong University (China) signed a Memorandum
of Understanding (MoU) on 3 July, 2017, to begin
an international joint project to design, build, and operate a
stellarator with the quasi-axisymmetry. The name of the
device was decided to be the Chinese First Quasi-axisymmetric
Stellarator (CFQS). We have published several
papers describing the physics design elements and the
engineering design results. The web site for this project is
The purpose of this article is not to describe the device
design or the experimental program. Readers may visit the
web site, and succeeding articles will appear in Stellarator
News and in other places. Instead we discuss the origin of
this joint project between NIFS and SWJTU, and the reasons
for adopting the quasi-axisymmetric stellarator as the
device in the program. Because we do not intend to give a
complete record of the research histories of the stellarator
community, some important stellarator programs may not
be mentioned. We hope to receive comments and requests
for amendments to any unintentional inaccuracies in the
We believe that the NSJP is very important in the long and
unbroken stream of stellarator research. The stellarator
concept, developed by the famous Lyman Spitzer, was
pursued in a series of magnetic confinement programs at
the Princeton Plasma Physics Laboratory (PPPL) in the
1950s and the 1960s. Stellarator of all types produce rotational
transform by means of external coils with little or no
toroidal plasma current. The stellarator family includes
several unique devices called Asperators at Tohoku University
in Japan, which had a very strong three-dimensional
shaping of the magnetic axis to contribute to the
creation of the rotational transform. [It should be noted
that without the aid of computers, early stellarators probably
had no closed flux surfaces.] At the University of Wisconsin,
Madison (UW), an Interchangeable Module
Stellarator (IMS) was constructed using a pioneering
design with modular coils rather than using a continuous
helical conductor winding.
When the experimental results of the T-3 tokamak at the
Kurchatov Institute in the Union of Soviet Socialist
Republics (USSR) were reported with a record high electron
temperature, many fusion laboratories in the world
made a decision to employ this idea in their research on
magnetic confinement. In an impressive effort, PPPL converted
its Model C stellarator into the ST tokamak. During
Fig. 1 An example of a collapsed discharge in LHD: (a)
density exponent and collapse likelihood, (b) line-averaged
electron density and electron temperature at plasma edge,
(c) diamagnetic energy and radiated power.
Stellarator News -3- August 2020
the 1970s and 1980s, the major line of development of
magnetic confinement research was led by tokamak
devices. In this phase of magnetic confinement research,
tokamaks had a great advantage of being able to heat the
plasma using the confining toroidal current for ohmicheating
(OH). OH has a very good heating efficiency and
requires a relatively simple and cheap hardware structure.
In parallel with this big tokamak world, there were two
continuous streams of stellarator research at Kyoto university
in Japan (Heliotron experiments) and IPP in Germany
(Wendelstein experiments). They continued fundamental
fusion experiments with a series of stellarator devices.
However, they had to wait until the technology for external
plasma heating was developed before stellarators could
be competitive with tokamaks using OH. Positive experimental
results with electron cyclotron heating (ECH) on
these devices were followed by many new stellarator
experiment proposals all over the world. ATF (Advanced
Toroidal Facility) in Oak Ridge, U.S.A., the Compact
Helical System (CHS) at NIFS, Japan, and Wendelstein 7-
AS (W7-AS) at IPP, Germany were all started around
1988. The H-1 heliac and TJ-II heliac joined the community
as well. The first stellarator with a complete configuration
optimization, the Helically Symmetric Experiment
(HSX) at UW also started configuration design in 1990.
Construction of two major devices, LHD and W7-X was
started at this time.
In Japan, the major role of CHS was to understand stellarator
confinement physics in the Heliotron type magnetic
configuration developed in a series of experiments at
Kyoto. In addition, a new type of magnetic configuration
study with poloidal field control, which was introduced
from the ATF program, was an important subject. This
poloidal field control scheme has become the most powerful
tool to control the position of the magnetic axis in LHD
and other stellarators. Such pioneering works are necessary
before starting much larger size experiments such as
LHD. When the LHD experiment started in 1998, the main
experimental research activities at NIFS were handed over
to LHD from CHS. The next role of the CHS team was to
find out the next step of the compact stellarator experiment.
At that time, the standard computational configuration
optimization technique was widely adopted in
stellarator magnetic configuration design; one example
was the pioneering design work for HSX. Because one of
research targets of the CHS program is to study the confinement
physics in a low-aspect-ratio stellarator, we
chose an optimization with quasi-axisymmetry. In this
stellarator optimization work, we had a happy opportunity
of collaborating with Prof. J. Nührenberg and Prof. P.
Merkel who pioneered stellarator optimization. After completing
the physics and engineering design, an experimental
program of CHS-qa was proposed in 2000, but
unfortunately this plan was not accepted by NIFS as a next
step of the CHS experiment.
PPPL began designing a National Compact Stellarator
Experiment (NCSX) with quasi-axisymmetry in 1998 and
succeeded in initiating device construction in 2003. However,
after working for 5 years to manufacture the device,
the program was canceled. These two programs would
have been major experimental activities in the stellarator
world because quasi-axisymmetry is one of very new and
challenging topics in stellarator research in the 2000s.
Although the LHD experiments and the tireless construction
of W7-X continued during this decade, we lost one
step of a new generation of stellarator concept development.
In 2015, NIFS received an inquiry from a university in
China about the possibility of the transfer of the CHS
device for learning and doing research on a stellarator
experiment. Because the main line of the fusion development
in China is tokamak research, there was no stellarator
experiment running in China at this time. However,
discussions of the strategy of fusion development in China
are very similar to those of other countries; namely, it is
important to study stellarator physics now, even though
the present main line is tokamak research. Such a comprehensive
understanding is supported especially by top-level
fusion scientists in China. University experimentation is
an appropriate venue for starting a new but important program
in fusion research in China. The university is Southwest
Jiaotong Universtiy (SWJTU), located in Chengdu
city of Sichuan province. Jiaotong in Chinese means
“transportation,” and this word is given to the top-level
technical university in China because the technology of
transportation (railway) used to be the university’s most
important role. NIFS leaders decided that it was a good
idea to assist stellarator research in China and work
together in order to establish strong stellarator research
activities in Asia. The name of the device was at that time,
the Chinese First Stellarator (CFS).
After further discussions about the cost of transferring
CHS and preparing the experimental environments as well
as the experimental programs, a different idea emerged;
construction of a new device with an advanced stellarator
design would be more appropriate for a new project at the
university. NIFS agreed to modify the program and created
an MoU for starting a new international joint project,
the NIFS-SWJTU Joint Project (NSJP). The device name
was modified to Chinese First Quasi-axisymmetric Stellarator
(CFQS). In the MoU, the role of NIFS is to lead the
design work for the device and the research program, as
well as to contribute to the heating and diagnostic systems
of the experiments. The role of SWJTU is jointly design
the device, to construct the device and experimental facilities,
and conduct the experiments in collaboration with
Stellarator News -4- August 2020
NIFS and other international researchers. The magnetic
configuration design, data, and physics and engineering
experience and design work from the CHS-qa design programs
were fully utilized. For more than 15 years a host of
calculations and discussions have been conducted for stellarator
optimization in general, and for the quasi-axisymmetric
stellarator in particular, but in theory only! It is time
to validate these theoretical efforts against real quasiaxisymmetric
plasmas in real experiments. The first priority
of the program was to start the experiment as soon as
possible without spending more time on discussions. We
wanted to restore the lost 15 years. We thought that the
important tasks to complete before starting the experiment
are reliable (robust) engineering designs and the adequate
estimation of the necessary accuracy of the device.
The construction of the mockup coil for the MC4 modular
coil, which has the highest complexity of the three-dimensional
shape, was started in 2018, and we are now entering
the manufacturing phase for the four different types of
modular coils. The manufacturing of the vacuum chamber
is just starting. Future articles in Stellarator News will
include an introduction of the research environment in the
University and the city of Chengdu, as well as a more
detailed report on the CFQS device design and manufacturing.
Shoichi Okamura
Research Enhancement Strategy Office
National Institute for Fusion Science
Toki, Japan
The NIFS-SWJTU Joint Project team.

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