Plasma and Fusion Research: Regular Articles

Volume 17, 2402042 (2022)

Data-Driven Control for Radiative Collapse Avoidancein Large Helical Device∗)
Tatsuya YOKOYAMA1,2) , Hiroshi YAMADA1) , Suguru MASUZAKI3,4,5) , Byron J. PETERSON3,4) ,Ryuichi SAKAMOTO1,3) , Motoshi GOTO3,4) , Tetsutaro OISHI3,4) , Gakushi KAWAMURA3,4) ,Masahiro KOBAYASHI3,4) , Toru I TSUJIMURA3) , Yoshinori MIZUNO3) , Junichi MIYAZAWA3,4) ,Kiyofumi MUKAI3,4) , Naoki TAMURA3,4) , Gen MOTOJIMA3,4) and Katsumi IDA3,4)
1)

Graduate School of Frontier Sciences, The University of Tokyo, Chiba 277-8561, Japan
Research Fellow of Japan Society for the Promotion of Science, Tokyo 102-0083, Japan
3)
National Institute for Fusion Science, National Institutes of Natural Sciences, Gifu 509-5292, Japan
4)
The Graduate University for Advanced Studies, SOKENDAI, Gifu 509-5292, Japan
5)
Advanced Fusion Research Center, Research Institute for Applied Mechanics, Kyushu University,Fukuoka 816-8580, Japan
2)(Received 13 December 2021 / Accepted 6 March 2022)
A radiative collapse predictor has been developed using a machine-learning model with high-density plasmaexperiments in the Large Helical Device (LHD). The model is based on the collapse likelihood, which is quantified by the parameters selected by the sparse modeling, including n̄e , CIV, OV, and T e,edge . The control system
implementing this model has been constructed with a single-board computer to apply this predictor model tothe LHD experiment. The controller calculates the collapse likelihood and regulates gas-puﬀ fueling and boosts
electron cyclotron resonance heating in real-time. In density ramp-up experiments with hydrogen plasma, highdensity plasma has been maintained by the control system while avoiding radiative collapse. This result hasshown that the predictor based on the collapse likelihood has the capability to predict a radiative collapse inreal-time.
c 2022 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: Large Helical Device (LHD), radiative collapse, density limit, stellarator-heliotron plasmas, sparsemodeling, data-driven science, plasma control, collapse avoidance
DOI: 10.1585/pfr.17.2402042

1. Introduction
The sudden termination of plasma is a critical risk ofa fusion reactor. The most known phenomenon is disruption, which is the major collapse in tokamak plasma.
In stellarator-heliotron plasma, where no disruption occurs since the plasma current is not required to sustain theplasma, radiative collapse is the major cause of plasma termination in a high-density regime. The operational density
is limited by radiative collapse. Improvement of density
limit is an essential issue in fusion energy development because of the advantages of high-density operation for improving confinement for mitigating the divertor heat load.
The best-known density limit is the Sudo density [1].
[1020 m−3 ] = 0.25P0.5 B0.5 a−1 R−0.5 .
nSudoe(1)Here, P is the absorbed heating power (MW), B is the magnetic field strength on the plasma axis (T), a is the averageminor radius (m), and R is the major radius (m).
The data-driven approach using machine learningtechniques as recently attracted significant attention in theauthor’s e-mail: yokoyama.tatsuya17@ae.k.u-tokyo.ac.jp∗) This article is based on the presentation at the 30th International Toki
Conference on Plasma and Fusion Research (ITC30).

study of disruption prediction, which is a critical phenomenon in a tokamak [2–5]. Some of these data-driven
studies have been applied to the real-time prediction of disruptions in tokamak devices [6, 7].
In our previous studies [8, 9], the collapse likelihood,which shows the probability of the occurrence of radiative collapse, was estimated based on experiment data in
Large Helical Device (LHD) [10]. To estimate the likelihood, a linear support vector machine (SVM) [11] wastrained with the plasma parameters selected by exhaustive
search (ES) [12]. A linear SVM, which is a supervisedmachine learning technique, was employed as a basic twoclass classifier to distinguish “close-to-collapse” discharge
data from “stable” data. In the ES, all possible combinations of parameters were evaluated and compared witheach other by F1 score [13], which is one of the metrics
commonly used in classification problems. The ES is oneof the sparse modeling techniques. Sparse modeling is oneof the frameworks of data-driven science and it exploits theinherent sparseness in all high-dimensional data to extractthe essence of the data [14]. As a result of ES, a combination of key four parameters, n̄e , CIV, OV, and T e,edge , hasbeen selected from 15 candidate parameters (see Table 12402042-1

c 2022 The Japan Society of Plasma
Science and Nuclear Fusion Research

Plasma and Fusion Research: Regular Articles

Volume 17, 2402042 (2022)

Fig. 1 Schematic diagram of the collapse avoidance control system.

in [9]). Moreover, the proximity of radiative collapse wasquantitatively estimated as the “collapse likelihood” using
these four key parameters.
In this study, a predictor model of radiative collapse
based on the collapse likelihood has been applied to control fueling and heating the LHD plasma to avoid radiative collapse. The remainder of this paper is organized asfollows. In section 2, the experimental setup of collapse
avoidance is described. The result and discussions of collapse avoidance experiments are presented in section 3. Finally, section 4 presents the conclusion.

2. Development of a Collapse Avoidance Control System
The predictor model based on the collapse likelihood
has been applied to a real-time feedback control system
for the operation of the LHD. The collapse likelihood wasquantitatively evaluated to take the continuous value fromzero to one using the key parameters extracted by the ES[8]. Figure 1 shows a schematic diagram of the control system. A single-board computer, Raspberry Pi 4 Model B,
with quad-core CPU, 8 GB RAM, and general-purpose input/output (GPIO) interface, has been used as a controller1 .
Since Raspberry Pi does not have any analog input/output
interfaces, an analog-digital converter with 24-bit resolution2 has been used to convert an input analog signal intoa digital signal. The controller calculates the collapse likelihood based on the input signals and compares the likelihood with the threshold value, which is given by the GUIinterface, in real-time. On average, the controller calculates the likelihood every 8 ms, which is limited by thetransmission speed of the Raspberry Pi. When the likelihood exceeds the threshold, an alarm signal is sent out.
The alarm signal is turned oﬀ when the likelihood falls below the threshold.
When the alarm signal is sent from the controller, thegas-puﬀ control system turns oﬀ the fueling and additional
power is injected by the electron cyclotron heating (ECH).
According to the result of ES-SVM, reducing plasma den1 https://www.raspberrypi.org/products/raspberry-pi-4-model-b/
2 lhttps://www.seeedstudio.com/Raspberry-Pi-High-Precision-ADDA-Board.html

sity and raising edge temperature will eﬀectively reduce
the likelihood, i.e., to prevent the occurrence of collapse[8]. Therefore, gas-puﬀ fueling and ECH have been employed as actuators of the control system. The gas puﬀ isone of the main fueling sources in LHD [15]. As ECH,
77 GHz gyrotrons for the fundamental O-mode heatingand 154 GHz for the second-harmonic X-mode heating areavailable. These are controlled by a real-time interlock system [16, 17]. Note that the time duration where ECH canbe turned on is limited by its technical capability and theinterlock system to avoid a blank injection.
The signals of plasma parameters selected by the feature extraction are input to the controller, i.e., n̄e , CIV, OV,and T e . As T e , T e,edge measured using the Thomson scattering measurement has been used in the dataset. However, its
time resolution is 30 Hz, which is lower than the requirement of the control system. Therefore, T e,edge has been
replaced by T e,ECE , which is obtained through the electron
cyclotron emission (ECE) measurement with the channel
that detects 146.5 GHz. The T e,ECE corresponds to the electron temperature near the center of the plasma, and is only
available in experiments with Bt =2.75 T. Here the change
in the parameter requires the recalculation of the decisionfunction and the collapse likelihood. The SVM has been
trained again with n̄e , CIV, OV, and T e,ECE using available data in the training dataset. The decision function andthe collapse likelihood for the control system, fctrl (x) andLikelihoodctrl , are calculated as follows:−1.89
CIV1.31 OV−0.129 T e,ECE,fctrl (x) = exp (2.10)n̄−0.600e(2)Likelihoodctrl
=1

 .
1 + exp −14.9 log10 fctrl (x) + 0.283(3)

The performance of Likelihoodctrl has not changed significantly from the result of the previous study [8]. In
the discharge with control described below (#168701), theLikelihoodctrl first reached the threshold 11 ms later thanthe original likelihood. This delay is smaller enough than
the averaged prediction margin of 90 ms.

2402042-2

Plasma and Fusion Research: Regular Articles

Volume 17, 2402042 (2022)

3. Collapse Avoidance in LHD

early phase was successfully avoided by turning gas puﬀ
oﬀ and boosting ECH. In this case, likelihood thresholdhas been set as 0.9, shown by the dashed horizontal line in
the top panel of Fig. 2. The change in the plasma toward
the collapse in the early ramp-up phase was detected about
65 ms before its occurrence, which is earlier enough for amargin of 30 ms for the control. In the discharge with control, the gas puﬀ was turned oﬀ within 10 ms after the controller detected the collapse. Meanwhile, the boost ECH
was injected about 20 ms later when the controller detected
the collapse, while it was earlier than the collapse.
In the latter part of the discharge with control, the radiative collapse has been avoided only by turning on/oﬀ
gas puﬀ and n̄e was developed above 1.2 × 1020 m−3 . In
this phase, the ECH was unavailable because of the technical limitation of duration time. When the change of NBI
heating power occurred at around 5.3 s and 6.3 s, the predictor detected the occurrence of the radiative collapse, andthe high-density plasma was successfully sustained by thecontrol. When the collapses were avoided, the recoveriesof electron temperature T e,edge and diamagnetic energy Wp
were observed.
The oscillation of the control signal, i.e., the oscillation of the likelihood, is mainly caused by the oscillationof T e,ECE signal. Even a small oscillation is amplified by
the strong dependence on T e,ECE . It remains unclear how
turning on/oﬀ of gas puﬀ with intervals shorter than theconfinement time scale of about 100 ms aﬀects avoiding
collapse.

3.1

Collapse avoidance experiments

The collapse avoidance with the control system has
been attempted in density ramp-up experiments in LHD.
Figure 2 shows two typical discharges in hydrogen plasma,with and without collapse avoidance control. In these discharges, the plasma has been sustained by gas-puﬀ fuelingand NBI heating. ECH has been used to initiate plasma,
while two 154 GHz gyrotrons have been reserved for boost
injection.
In the discharge without control, shown by the dashedblue line, a radiative collapse occurred in the early phaseof the density ramp-up at around 3.6 s. In this case, the gas
puﬀ was injected at a constant until a preset time (about4.5 s).
On the other hand, in the discharge with control,
shown by the solid red line, the radiative collapse in the3.2 Discussions on collapse avoidanceRadiative collapse is likely to occur when n̄e is high;thus, reducing n̄e is one possible way to avoid radiative collapse. However, the likelihood recovery was not accompanied by the decrease in n̄e , as shown in Fig. 2. This is also
seen in Fig. 3, indicating the trajectory of the discharges
with and without control on the contour of the collapse

Fig. 2 The discharges with and without collapse avoidance control in hydrogen plasma, shown by red and blue lines,respectively. The dashed horizontal line in the top panel
and the dotted vertical line show the threshold value andthe time when the likelihood exceeded the threshold atfirst, respectively.

Fig. 3 The trajectory of the discharges (solid) with control, (dotted) without control, and (chain) with only ECH control
on the color contour which shows the likelihood of radiative collapse against line averaged density and otherextracted parameters.

2402042-3

Plasma and Fusion Research: Regular Articles

Volume 17, 2402042 (2022)

4. Conclusion

Fig. 4 The temporal changes of n̄e , Hα line emission, and thevoltage signal that controls the gas puﬀ in the discharge
with collapse avoidance control system (#168701).

likelihood against line averaged density and the term ofother extracted parameters. The likelihood shown in Fig. 3
is calculated with T e,edge and diﬀerent from the likelihood
used in the real-time control. In the discharge without control, shown by the dotted line in Fig. 3, once plasma enteredthe unstable (red) region, plasma went toward collapse.
In the discharge with control, it is seen that the plasma
returns from the unstable (red) region to the stable (blue)
region by the control, as shown in the solid line. Figure 4
shows that n̄e kept increasing (dn̄e /dt > 0), even while thegas-puﬀ fueling was turned oﬀ. During this time, recycling
was reduced but not extinguished, as shown by Hα line
emission in Fig. 4. This suggests that the fuel was suppliedby the recycling from the vessel wall when the plasma wasreturning to the stable region.
In the latter phase of the controlled discharge, theplasma stayed in the stable region near the boundary while
increasing the density. After the heating stopped at around7.3 s, the plasma went into the unstable region and terminated. This result shows that regulating gas-puﬀ fuelingis eﬀective in keeping plasma in the stable region. It also
demonstrates that the control system can achieve a higher
plasma density.
In other discharges with hydrogen plasma, collapse
avoidance with only boost ECH has been attempted. In
these cases, the collapse in the early phase has not been
avoided. The chain line in Fig. 3 shows a discharge wherecollapse avoidance with only boost ECH has been attempted. In this discharge, the boost ECH was injected
at 3.53 s and stopped at 3.6 s by the interlock. As shown inFig. 3, the plasma state never returned to the stable region
in this discharge. The possibility of avoiding radiative collapse with only boost ECH by changing operational conditions, such as oﬀ-axis injection, is under investigation.

In this study, a real-time collapse avoidance control
system has been developed based on the result of the datadriven approach on radiative collapse. Collapse likelihood
has been quantified using the SVM trained with the plasma
parameters selected by ES, which is one of the sparse modeling techniques. The control system calculates the collapse likelihood in real-time; it actuates gas puﬀ and ECH
for fueling and additional heating, respectively.
The control system has been applied to density rampup experiments in hydrogen plasma in LHD to show thatthe predictor based on the collapse likelihood has the capability to predict a radiative collapse in real-time. Consequently, the radiative collapse in the initial density ramp-up
phase has been avoided, and the control system has maintained high-density plasma. This is the first case to control stellarator-heliotron plasma to avoid radiative collapse
based on the machine-learning results.
The discharges, where the plasma was about to collapse but was avoided to collapse, are good examples thatreveal the radiative collapse mechanism. Further investigation focusing on plasma behavior, when the collapse wasavoided, is underway.

Acknowledgements
The authors are grateful to the LHD experiment groupfor the excellent support of this work. This work issupported by the National Institute for Fusion Sciencegrant administrative budgets NIFS21KLPP068, and JSPS
KAKENHI Grant Numbers 17H01368, 19J20641, and20K20426.
[1] S. Sudo et al., Nucl. Fusion 30(1), 11 (1990).
[2] A. Murari et al., Nucl. Fusion 60(5), 056003 (2020).
[3] C. Rea et al., Fusion Sci. Technol. 76(8), 912 (2020).
[4] K.J. Montes et al., Nucl. Fusion 61(2), 026022 (2021).
[5] J. Kates-Harbeck, A. Svyatkovskiy and W. Tang, Nature568(7753), 526 (2019).
[6] C. Rea et al., Nucl. Fusion 59(9), 096016 (2019).
[7] W. Hu et al. Nucl. Fusion 61(6), 066034 (2021).
[8] T. Yokoyama et al., J. Fusion Energy 39(6), 500 (2020).
[9] T. Yokoyama et al., Plasma Fusion Res. 16, 2402010(2021).
[10] A. Iiyoshi et al., Nucl. Fusion 39(9Y), 1245 (1999).
[11] C. Cortes and V. Vapnik, Machine Learning 20(3), 273(1995).
[12] Y. Igarashi et al., J. Phys.: Conf. Series 699(1), 012001(2016).
[13] C. Van Rijsbergen, Information Retrieval. (Butterworths,London, 1979).
[14] Y. Igarashi et al., J. Phys.: Conf. Series 1036, 012001(2018).
[15] J. Miyazawa, K. Yasui and H. Yamada, Fusion Eng. Des.
83(2), 265 (2008). Proceedings of the 6th IAEA Technical
Meeting on Control, Data Acquisition, and Remote Participation for Fusion Research.
[16] T.I. Tsujimura et al., Fusion Eng. Des. 153, 111480 (2020).
[17] T.I. Tsujimura et al., Nucl. Fusion 61(2), 026012 (2021).

2402042-4