F-P6 Deep learning for tomographic reconstruction of imaging diagnostics

3rd Asia-Pacific Conference on Plasma Physics, November 5th, 2019, Crowne Plaza Hefei, Hefei, ChinaNaoki Kenmochi1, Masaki Nishiura1,2, Kaori Nakamura1, Kenji Ueda1 , Zensho Yoshida1

1Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Japan2National Institute of Fusion Science, Toki, Japan

Generating pairs of local-emissivity and line-integrated images that simulate the experimental system

Training the generative model which generates the local-emissivity profiles from the line-integrated images

Application for the He II-emission imaging diagnostic

[1] D. R. Ferreira et al., Fusion Sci. Technol. 74, 47 (2018).

[2] I. Goodfellow et al., in Proc. NIPS, 2672 (2014).

[3] N. Kenmochi et al., Plasma Fusion Res. 14, 1202117 (2019).

[4] P. Isola et al., arXiv:1611.07004 (2016).

[5] Z. Yoshida et al., Plasma Fusion Res. 1, 008 (2006).

[6] Z. Yoshida et al., Phys. Rev. Lett. 104, 235004 (2010).

[7] K. Nakamura et al., Rev. Sci. Instrum. 89, 10D133 (2018).

[8] M. Nishiura et al., Nucl. Fusion 59, 096005 (2019).

Email: kenmochi@ppl.k.u-tokyo.ac.jp

References

Introductionp Conventional tomography employs a simple model of internal structure, and the model

parameters are easily evaluated by inverting the integrated observables.p The limited accessibility of diagnostics or the influence of nonlocal optical effects (such as

backscatter from the chamber walls) can cause a lack of data, resulting in numerical instabilities in the inversion problem.

!" #, % = !' exp −, - #, % − -.-'

/ 0 #, %012'

34

Levitation magnet

Levitation magnet

1.0

0.8

0.6

0.4

0.2

0.0

Refl

ecta

nce

806040200

Incident angle [degree]

FB450-10 IF1(z=-0.2m) IF1(z=0.0m) 0.2m right from TS port (z=0.0m) 2.45GHz port (z=0.0m) fit_reflectance_Height_X

Local emissivity Line-integrated image

Line-integrated without reflection Reflection

The reflection from the walls at z=0m is dominant.

Image-quality metricspStructural similarity (SSIM)pNormalized root-mean-square

error (NRMSE)pPeak signal-to-noise ratio (PSNR)

� Here, SSIM reaches a maximum value of 1.0 when the two images are equal (Note that one can recognize the difference between two images if the SSIM value is less than 0.9).

Tomographic reconstruction of imaging diagnostics[3]

The Ring Trap 1 (RT-1) device is a laboratory magnetosphere that is realized by a levitated superconducting ring magnet in vacuum [5, 6].

üThe levitated coil weights ~100kg, which is made of Bi-2223 superconductor

üRadius of levitated coil�r=0.375 m

üRadius of vacuum chamber�R=1.0 m

real ?or

fake ?

Generator

Discriminator

The Ring Trap 1 (RT-1) experiment

Generative Adversarial Networks

Model function of Local-emission profile

-: Magnetic flux-.: - at r where ne becomes maximum at z=0-': - at wall of vacuum vessel (r=1.0m)

HeII (468.7 nm) emission profile(experimentally obtained)

0: Magnetic field strength012': Magnetic field strength at z=0

ü A GAN learns a loss that tries to classify whether output images are real or fake, while simultaneously training a generative model to minimize this loss.

ü A “conditional GAN” (cGAN) learns a conditional generative model, applying the same generic approach to problems that would traditionally require very different loss formulations [4].

ü We used the TensorFlow 1.13.1 implementation of cGAN named “pix2pix” [4].

ü We applied this reconstruction technique to the He II 468.6 nm imaging diagnostic of Coherence Imaging Spectroscopy (CIS) [7] from RT-1.

ü To train the network to reconstruct images, we generated pairs of local-intensity profiles and line-integrated images that simulate the optics of the CIS system.

ü We generated the local emissivity using typical model functions for the electron-density and temperature profiles of RT-1 [8].

ü We selected a total of 6500 pairs of images randomly as input for the training, which spanned one million iterations.

ü We also generated another set of 1300 samples using the same strategy, which we employed as a validation set to avoid overfitting.

ü Note that this particular reconstructionwas not part of either the training set or the validation set.

ü They show that the network can produce reconstructions with high accuracy.

ü We applied it to images obtained by the CIS from RT-1. ü For helium plasmas, the CIS measured the spectral intensity, ion temperature,

and flow velocity of He+. ü The 10 kW input power of electron-cyclotron heating (ECH) sustained the target plasma. ü We applied 9.4 kW of ion-cyclotron-resonance-frequency (ICRF) heating

to the double-loop antenna 0.1 sec after the start of the ECH injection and maintained it up to the termination of the discharge.

ü The He+ intensity increases, especially along the magnetic field lines near the L-magnet. ü This result corresponds that the heated He+ ions around the double-loop antenna

on the high-field side near the center stack move to the upper region of the L-magnet along the magnetic field lines.

1

2

3

p Deep-learning convolutional neural networks (CNNs) have been applied at JET to reconstruct the 2D plasma profile with satisfactory accuracy [1].

p Although the learning process is automatic, numerous manual processes are necessary to design an effective loss function.

p A Generative Adversarial Network (GAN) has been proposed to learn the loss function automatically via an adversarial process [2].

n We have built a method using cGAN and used it to obtain the local emissivity from line-integrated images [3].

M. Nishiura, Z. Yoshida, N. Kenmochi, T. Sugata, K. Nakamura, S. Katsura, K. Shirahata, C. Michael1, J. Howard1

Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8561, Japan1Plasma Research Laboratory, Australian National University, Canberra 2601, Australia

EXPERIMENTAL ANALYSIS OF SELF-ORGANIZED STRUCTURE AND TRANSPORT ON MAGNETOSPHERIC PLASMA DEVICE RT-1

AbstractThe dipole plasma exhibits strong heterogeneities in field strength, density, temperature, etc., while maintaining the holistic balance. Enquiring into the

internal structures, we reveal the fundamental self-organizing mechanisms operating in their simplest realization (as commonly observed in astronomicalsystems). Three new findings are reported from the RT-1 experiment: (i) Creation of a high-energy electron core (similar to the radiation belts in planetarymagnetospheres) is observed for the first time in a laboratory system. High-energy electrons (3 – 15 keV), produced by an electron cyclotron heating(ECH), accumulate in a “belt” located in the low density region (high-beta value ~ 1 is obtained by increasing the high-energy component up to 70% of thetotal electrons). (ii) The dynamical process of the “inward diffusion” (a spontaneous mechanism of creating density gradient) has been analyzed byperturbing the density by gas injection. (iii) By a system of coherence-imaging spectroscopy, the profiles of the ion temperature and flow velocity havebeen measured. The effect of the ion cyclotron resonance frequency (ICRF) heating has been visualized. These results advance our understanding oftransport and self-organization not only in dipole plasmas, but also in general magnetic confinement systems relevant to fusion plasmas.

22-27 October, 2018IAEA-FEC2018, Gandhinagar,India

E-mail: nishiura@ppl.k.u-tokyo.ac.jp

1. Introduction

2. Self-organized plasma formation due to up-hill diffusion and high energy electron core formation

RT-1(ring trap 1) enables us to study themagnetosphere plasma physics and one of newconcepts for nuclear fusion device. In the RT-1device, the existence of high energy electronaround a few 10 keV and the diversity of plasmashave been observed [1].

The increase of beta value (> 1) and iontemperature gives us the novel plasma physics aswell as an interesting topic to understand thenature of the background physics. The electronbeta has already achieved around ~0.7. (in thispresentation local electron beta be>1)

Fig. 1 (a) Top and (b) cross sectional views of RT-1.The transmission lines L#1 and L#2 for 8.2 GHzECRH and three interferometer chords are shown.

8x10-3

6

4

2

0

Dia

mag

netis

m (W

b)

1.21.00.80.60.40.20.0

Line average density (x1018 m-3)

8.2GHz cut off L#1 horn-X, L#2 wg-O, H L#1 horn-X, L#2 wg-O, He L#1 horn-X, L#2 wg-X, H (40kW) L#1 horn-X, L#2 wg-X, D (40kW)

Conventional operationregime

Extended operationregime

DH

Fig.3 Extended തne and Wp for H, D, and He (Wpand തne ) in the dipole configuration by thelevitated superconducting coil of RT-1. Theconventional (gray area) and extendedoperational regimes are plotted.

5. Summary

Acknowledgment: This work was supported by the NIFS Collaboration research program (NIFS15KOAH034),

and JSPS KAKENHI Grant No 17H01177.

As one of discharge scenarios to increase the ion beta,• an ion cyclotron range of frequencies (ICRF) heating system has been implemented. The ICRF

experiment requires the high density target plasmas by using an electron cyclotron heating(ECRH) to obtain a good matching between an antenna and plasmas.

• A collision between electrons and ions increases the ion temperature by ECRH.4. ICRF Heating and its effect in dipole confinement

References[1] Hasegawa, A., Comments Plasma Phys. Contr. Fusion 11 (1987) 147.

[2] Yoshida, Z., Adv. Phys. X 1 (2016) 2.

[3] Persoon, A. M., et al., JGR: Space Phys. 118 (2013).

[4] Nishiura, M., et al., Nucl. Fusion 55 (2015) 053019.

[5] Kawazura, Y. et al., Phys. Plasmas 22 (2015) 112503.

[6] Nishiura, M., et al., Nucl. Fusion 57 (2017) 086038.

[7] Nishiura, M., et al., Plasma and Fusion Res.

[8] Stix T.H. 1992 Waves in Plasmas(New York: American Institute of Physics) pp342-3.

[9] Kenmochi, N., et al. Rev. Sci. Instruments 89 (2018) 10C101.

[10] Howard, J., et al., JINST 10 (2015) P09023.

[11] Nakamura, K., et al. Rev. Sci. Instruments (2018) in press.

[12] Howard, J., et al., Plasma Phys. Control. Fusion 38 (1996) 489.

-0.4

-0.2

0.0

0.2

0.4

Z (m

)

1.00.80.60.40.20.0R (m)

2MHzDouble loop antenna

Levitation coil

View planefor spectroscopy

IC resonance

DP

He+

He2+, D+

C2+

H+

Fig. 2. Double-loop antenna and the current direction (left figure). Poloidal cross section of RT-1 with ion cyclotron resonance layers for main and impurity ions in the case of RF frequency of 2 MHz, and Poloidal field lines. DP is the probe position for edge electron temperature measurement. The position of the double loop antenna is indicated.

Magnetosphere plasma in RT-1.

3. Self-organized plasma and up-hill diffusion

Coherence imaging cell• BBO crystal(α-cut: 15mm,

45°-cut: 3mm)• Two polarizer plates

Interference filter• Target ion : HeII

Levitating coil

Coherence imaging cell

Interference filter (468nm)

L1 lens L2 lens L3 lens

Camera (Canon EOS 70D)

FIG. 4. Measured profiles of (a) the electron density and (b)the high-energy electrons. The spontaneous belt structure ofhigh energy electrons is observed in outer radial location.

The reconstructed density at the maximum exceeds the cut off density, and therefore, the up-hill diffusion grows up the density.

ne(1.4s) - ne(1.1s)

FIG. 6. Difference of the electron density. The density profile at t = 1.4 s is subtracted from t = 1.1 s. The increase in the density is observed at r = 0.55 m.

FIG. 5. Time evolution of the line-integrated densities where the chords of the interferometers pass through the inner and the outer edge regions (r=0.45, 0.62, and 0.7m are the innermost radii of the chords). The innermost chord IF1 observed the constant electron density from t = 1.1 to 1.4 sec.

The results are summarized as follows: (i) The population of the high-energy electrons (which contribute to the highbeta) has strongly heterogeneous profile; they tend to localize in a low-density region and create a belt structure. (ii)The strongly peaked density profile is self-organized by the up-hill diffusion. By actively modifying the density profilewith gas injection, the dynamical process of the up-hill diffusion, driven by density fluctuations in the drift-frequencyregime, has been elucidated. (iii) The CIS diagnostic visualized the effect of the ICRF heating. The ion temperatureand flow were enhanced at the locations where the He+ emission is intense in the EC heating.

The observed toroidal flow velocity is expressed as the sum of drift velocities,

𝑉𝑜𝑏𝑠 = 𝑚𝑣∥2

𝑅2𝑹 × 𝑩𝑞𝐵2

−𝑚𝑣⊥2

2𝑩 × 𝛻𝑩𝑞𝐵3

−𝛻 𝑛𝑘𝑇𝑖 × 𝑩

𝑞𝑛𝐵+𝑬⊥ × 𝑩𝑞𝐵2

Levitation magnet

ICRF ON

ICRF OFFHe+ ions were heated globally in the plasma confinement region. The ion flow velocity was accelerated near the levitation magnet. These parameters are effectively enhanced at the locations where the He+

emission is intense in the EC heating.

FIG. 8. Line-integrated emission intensity, temperature, and flow velocity of He+ in the case of ICRF off (upper line) and on (lower line). The ICRF heating increases the He+ intensity and the ion temperature.

FIG. 7. Coherence imaging spectroscopy for 2D profile.

Dominant

To obtain the local ion flow in a poloidal cross section, the line-integrated flow velocity of He+ is reconstructed by the velocity tomography method [12]. The result at the equatorial plane is plotted in FIG. 9. The local flow has two peaks at the inner and outer areas.

FIG. 9. Local flow velocity of He+ reconstructed from the line-integrated flow velocity.

M. Nishiura, Z. Yoshida, N. Kenmochi, T. Sugata, K. Nakamura, S. Katsura, K. Shirahata, C. Michael1, J. Howard1

Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa 277-8561, Japan1Plasma Research Laboratory, Australian National University, Canberra 2601, Australia

EXPERIMENTAL ANALYSIS OF SELF-ORGANIZED STRUCTURE AND TRANSPORT ON MAGNETOSPHERIC PLASMA DEVICE RT-1

AbstractThe dipole plasma exhibits strong heterogeneities in field strength, density, temperature, etc., while maintaining the holistic balance. Enquiring into the

internal structures, we reveal the fundamental self-organizing mechanisms operating in their simplest realization (as commonly observed in astronomicalsystems). Three new findings are reported from the RT-1 experiment: (i) Creation of a high-energy electron core (similar to the radiation belts in planetarymagnetospheres) is observed for the first time in a laboratory system. High-energy electrons (3 – 15 keV), produced by an electron cyclotron heating(ECH), accumulate in a “belt” located in the low density region (high-beta value ~ 1 is obtained by increasing the high-energy component up to 70% of thetotal electrons). (ii) The dynamical process of the “inward diffusion” (a spontaneous mechanism of creating density gradient) has been analyzed byperturbing the density by gas injection. (iii) By a system of coherence-imaging spectroscopy, the profiles of the ion temperature and flow velocity havebeen measured. The effect of the ion cyclotron resonance frequency (ICRF) heating has been visualized. These results advance our understanding oftransport and self-organization not only in dipole plasmas, but also in general magnetic confinement systems relevant to fusion plasmas.

22-27 October, 2018IAEA-FEC2018, Gandhinagar,India

E-mail: nishiura@ppl.k.u-tokyo.ac.jp

1. Introduction

2. Self-organized plasma formation due to up-hill diffusion and high energy electron core formation

RT-1(ring trap 1) enables us to study themagnetosphere plasma physics and one of newconcepts for nuclear fusion device. In the RT-1device, the existence of high energy electronaround a few 10 keV and the diversity of plasmashave been observed [1].

The increase of beta value (> 1) and iontemperature gives us the novel plasma physics aswell as an interesting topic to understand thenature of the background physics. The electronbeta has already achieved around ~0.7. (in thispresentation local electron beta be>1)

Fig. 1 (a) Top and (b) cross sectional views of RT-1.The transmission lines L#1 and L#2 for 8.2 GHzECRH and three interferometer chords are shown.

8x10-3

6

4

2

0

Dia

mag

netis

m (W

b)

1.21.00.80.60.40.20.0

Line average density (x1018 m-3)

8.2GHz cut off L#1 horn-X, L#2 wg-O, H L#1 horn-X, L#2 wg-O, He L#1 horn-X, L#2 wg-X, H (40kW) L#1 horn-X, L#2 wg-X, D (40kW)

Conventional operationregime

Extended operationregime

DH

Fig.3 Extended തne and Wp for H, D, and He (Wpand തne ) in the dipole configuration by thelevitated superconducting coil of RT-1. Theconventional (gray area) and extendedoperational regimes are plotted.

5. Summary

Acknowledgment: This work was supported by the NIFS Collaboration research program (NIFS15KOAH034),

and JSPS KAKENHI Grant No 17H01177.

As one of discharge scenarios to increase the ion beta,• an ion cyclotron range of frequencies (ICRF) heating system has been implemented. The ICRF

experiment requires the high density target plasmas by using an electron cyclotron heating(ECRH) to obtain a good matching between an antenna and plasmas.

• A collision between electrons and ions increases the ion temperature by ECRH.4. ICRF Heating and its effect in dipole confinement

References[1] Hasegawa, A., Comments Plasma Phys. Contr. Fusion 11 (1987) 147.

[2] Yoshida, Z., Adv. Phys. X 1 (2016) 2.

[3] Persoon, A. M., et al., JGR: Space Phys. 118 (2013).

[4] Nishiura, M., et al., Nucl. Fusion 55 (2015) 053019.

[5] Kawazura, Y. et al., Phys. Plasmas 22 (2015) 112503.

[6] Nishiura, M., et al., Nucl. Fusion 57 (2017) 086038.

[7] Nishiura, M., et al., Plasma and Fusion Res.

[8] Stix T.H. 1992 Waves in Plasmas(New York: American Institute of Physics) pp342-3.

[9] Kenmochi, N., et al. Rev. Sci. Instruments 89 (2018) 10C101.

[10] Howard, J., et al., JINST 10 (2015) P09023.

[11] Nakamura, K., et al. Rev. Sci. Instruments (2018) in press.

[12] Howard, J., et al., Plasma Phys. Control. Fusion 38 (1996) 489.

-0.4

-0.2

0.0

0.2

0.4

Z (m

)

1.00.80.60.40.20.0R (m)

2MHzDouble loop antenna

Levitation coil

View planefor spectroscopy

IC resonance

DP

He+

He2+, D+

C2+

H+

Fig. 2. Double-loop antenna and the current direction (left figure). Poloidal cross section of RT-1 with ion cyclotron resonance layers for main and impurity ions in the case of RF frequency of 2 MHz, and Poloidal field lines. DP is the probe position for edge electron temperature measurement. The position of the double loop antenna is indicated.

Magnetosphere plasma in RT-1.

3. Self-organized plasma and up-hill diffusion

Coherence imaging cell• BBO crystal(α-cut: 15mm,

45°-cut: 3mm)• Two polarizer plates

Interference filter• Target ion : HeII

Levitating coil

Coherence imaging cell

Interference filter (468nm)

L1 lens L2 lens L3 lens

Camera (Canon EOS 70D)

FIG. 4. Measured profiles of (a) the electron density and (b)the high-energy electrons. The spontaneous belt structure ofhigh energy electrons is observed in outer radial location.

The reconstructed density at the maximum exceeds the cut off density, and therefore, the up-hill diffusion grows up the density.

ne(1.4s) - ne(1.1s)

FIG. 6. Difference of the electron density. The density profile at t = 1.4 s is subtracted from t = 1.1 s. The increase in the density is observed at r = 0.55 m.

FIG. 5. Time evolution of the line-integrated densities where the chords of the interferometers pass through the inner and the outer edge regions (r=0.45, 0.62, and 0.7m are the innermost radii of the chords). The innermost chord IF1 observed the constant electron density from t = 1.1 to 1.4 sec.

The results are summarized as follows: (i) The population of the high-energy electrons (which contribute to the highbeta) has strongly heterogeneous profile; they tend to localize in a low-density region and create a belt structure. (ii)The strongly peaked density profile is self-organized by the up-hill diffusion. By actively modifying the density profilewith gas injection, the dynamical process of the up-hill diffusion, driven by density fluctuations in the drift-frequencyregime, has been elucidated. (iii) The CIS diagnostic visualized the effect of the ICRF heating. The ion temperatureand flow were enhanced at the locations where the He+ emission is intense in the EC heating.

The observed toroidal flow velocity is expressed as the sum of drift velocities,

𝑉𝑜𝑏𝑠 = 𝑚𝑣∥2

𝑅2𝑹 × 𝑩𝑞𝐵2

−𝑚𝑣⊥2

2𝑩 × 𝛻𝑩𝑞𝐵3

−𝛻 𝑛𝑘𝑇𝑖 × 𝑩

𝑞𝑛𝐵+𝑬⊥ × 𝑩𝑞𝐵2

Levitation magnet

ICRF ON

ICRF OFFHe+ ions were heated globally in the plasma confinement region. The ion flow velocity was accelerated near the levitation magnet. These parameters are effectively enhanced at the locations where the He+

emission is intense in the EC heating.

FIG. 8. Line-integrated emission intensity, temperature, and flow velocity of He+ in the case of ICRF off (upper line) and on (lower line). The ICRF heating increases the He+ intensity and the ion temperature.

FIG. 7. Coherence imaging spectroscopy for 2D profile.

Dominant

To obtain the local ion flow in a poloidal cross section, the line-integrated flow velocity of He+ is reconstructed by the velocity tomography method [12]. The result at the equatorial plane is plotted in FIG. 9. The local flow has two peaks at the inner and outer areas.

FIG. 9. Local flow velocity of He+ reconstructed from the line-integrated flow velocity.

withoutICRF

withICRF

Input, output, and target images for the network

ü We generated the line-integrated images from the local emissivity, assuming toroidal symmetry for the RT-1 plasmas.

ü We took account of reflections from the chamber walls and the levitation magnet (L-magnet).

ü We also employed the CIS optics to simulate the results, using the optical-engineering program ZEMAX.

Coherence Imaging Spectroscopy for 2D profile

Reflectance of chamber walls of RT-1

Tomographic reconstruction with CNN in JET[1]

Generator

real/fakepair ?

Generator

Discriminator

Real pairs

Fake pairs

line-integrated images local-emissivityTraining data

3D Ray tracing of the CIS optics

Measurement of reflectance of chamber walls

normalized root-mean-square error20 (NRMSE). Table Ishows the kinds of results that can be expected withthese metrics.

The examples in Fig. 5 have not been carefully selectedto yield particularly good results, and in practice, it mightbe possible to obtain even better results. For example,

Fig. 5. Three reconstructions from pulse #92213 at t = 49.7 s (top), t = 49.9 s (middle), and t = 50.0 s (bottom). Originalreconstruction (left) versus neural network (right).

FULL-PULSE TOMOGRAPHIC RECONSTRUCTION WITH DEEP NEURAL NETWORKS · FERREIRA et al. 51

FUSION SCIENCE AND TECHNOLOGY · VOLUME 74 · JULY –AUGUST 2018

Lagrange multipliers take a significant amount of com-putation time. The total run time depends on the actualdata, but with the code available at JET, it can take morethan 1 h to produce a reconstruction. This makes itimpractical to compute more than a few reconstructionsper pulse. There is hardly an opportunity to see how theradiation profile develops across an entire pulse.

To appreciate the computational effort involved,consider the following. The bolometer system at JEThas a sampling rate of 5 kHz. For the purpose of noisereduction, a window average of 5 ms is usually applied,which corresponds to 25 samples. Subsampling by afactor of 25 yields an effective sampling rate of200 Hz; so, in principle, it should be possible to haveas many as 200 reconstructions per second of pulse time.For a pulse of about 30 s, this means a total of 6000reconstructions; at an average of 1 h per reconstruction, thiswould require 250 days.

Clearly, another way to compute the reconstructions foran entire pulse should be found. The following sectionsdescribe how a deep neural network was devised and trainedon existing tomograms to produce the same results. A smallamount of error is more than compensated for by a largecomputational speedup (both to be quantified below). Withthis approach, it becomes possible to analyze the time evolu-tion of the radiation profile in great detail. The pulsesdiscussed at the end of this paper, which illustratedisruptions and impurity transport, are only a few examplesof what can be done.

II. DEEP NEURAL NETWORKS

Deep learning7,8 is having a tremendous impact in fieldssuch as image processing and natural language processing. Inparticular, convolutional neural networks (CNNs) have beenvery successful at classifying input images into a set of outputclasses. This has been demonstrated in the recognition ofhandwritten digits,9 in the classification of Web images,10

and in the annotation of online videos,11 to cite only a fewapplications.

In general, CNNs have a common overall structure,which is depicted in Fig. 2. This comprises the following:

1. an input layer, which receives an image, amultichannel image (in case of color images),or a set of video frames

2. one or more convolutional layers, where multiplefilters (in the form of a sliding window) areapplied to the same input; each filter produces adifferent feature map

3. a subsampling layer after each convolution, oralternatively, some form of subsampling appliedduring the convolution itself, namely, by makingthe sliding window stride in larger steps acrossthe input

4. one or more densely connected layers at the endto perform classification based on the featuresextracted by the convolutional layers

Fig. 1. (a) Lines of sight for the vertical and horizontal cameras and (b) a sample tomographic reconstruction for pulse #89065 att = 47.8 s.

48 FERREIRA et al. · FULL-PULSE TOMOGRAPHIC RECONSTRUCTION WITH DEEP NEURAL NETWORKS

FUSION SCIENCE AND TECHNOLOGY · VOLUME 74 · JULY –AUGUST 2018

Lines of sight Conventional CNN

SSIM NRMSE PSNR[dB]

Mean 0.9393 0.0631 25.957

Std.dev. 0.0224 0.0165 2.546

Generator

SummaryWe have developed a new tomography method using a cGANand have demonstrated its efficiency by converting a line-integrated image into local emissivity. n Calculation of the line-integrated image from the local emissivity is generally easier than the calculation of the opposite relation. n In the present work, we have taken into account backscattering from the chamber walls,

which makes even the line-integrals involved; hence conventional inversion methods do not apply. n This method can be applied to other diagnostics in other machines

where reconstruction is difficult because of restrictions on measurements or complexities of the inversion problem.

Levitation magnet

Lifting magnet

023501-6 Nishiura et al. Rev. Sci. Instrum. 88, 023501 (2017)

FIG. 9. Contours of the electric field E✓ excited by the double-loop antennain helium plasma. L-magnet indicates the levitation magnet. The antennas arelocated outside the LCFS. The contours of the power absorption area for He2+

are also plotted. The ion cyclotron layers for H+, He2+, and He+ are depicted.

FIG. 10. E✓ (closed circles) vertically measured by the EO sensor alongR = 0.72 m in helium plasma. The ICRF power is 7 kW. The separatrix(dashed line) is located at (R, Z) = (0.72 m, 0.35 m). The input parameterfor the simulation was the measured antenna current (252 A).

being measured as 185 V/m in the hydrogen–helium mix-ture and 95 V/m in the helium plasma. The antenna currentat 2 MHz was 280–296 A, 1.2 times higher than at 3 MHz.Therefore, E✓ was increased by the higher RF input power andelectron density. Again, the electric fields were peaked at theLCFS. The local measurement of RF electric fields clarified anunexpected wave excitation during ICRF heating of the mag-netosphere plasmas. The EO sensor system is a powerful toolfor studying wave physics in plasmas. However, the underlyingwave physics and the relation between the observed electricfields and the ion heating efficiency require further carefulinvestigation.

IV. DISCUSSION ON RF ELECTRIC FIELDS EXCITEDIN PLASMAS

E✓ measured along the Z direction shows a local maxi-mum near the LCFS. The peaked profile of the measured E✓

FIG. 11. E✓ measured by the EO sensor in helium plasmas. The helium gaspressures were 2.1 mPa (closed circles) and 4.4 mPa (open circles).

FIG. 12. E✓ measured by the EO sensor in plasmas. The fill gas pressures aremixed hydrogen at 8.0 mPa and helium at 0.6 mPa (closed circles) and heliumat 4.6 mPa (open circles).

in Fig. 10 cannot be replicated by the TASK/WF2 code. Wenow attempt to interpret the measured E✓. The signal of theEO probe might cause incomplete separation of E✓ from theradial and vertical E components (Er and Ez, respectively);however, the measured Er and Ez components were one orderof magnitude lower in sensitivity than E✓ and were insensitiveto the ✓ direction.

To evaluate the interference effect in the measured E✓, wecalculated the RF electric fields by the TASK/WF2 code. Themain structures of the levitation magnet and the vacuum vesselof RT-1 were entered into the simulation model. The spatialstructure was divided into non-structural meshes for the finiteelement method, and the wave equation of the electric fieldwas given by the Maxwell equation in plasma18

r ⇥ r ⇥ E +1c2

@

@t2E =�µ0

@

@t

⇣J + Jext

⌘,

where J is the perturbed current induced by an RF field and Jextis the external current density. This solution gives the fields andstructures of electromagnetic waves in plasmas. The excitationof electromagnetic waves is modeled by feeding Jext to theantenna.

Contours of the Eθexcited by the double-loop antenna