Two-dimensional beam emission spectroscopy forhydrogen isotope negative neutral beam in Large
Helical Device
メタデータ

言語: English
出版者:
公開日: 2021-07-14
キーワード (Ja):
キーワード (En):作成者: Kobayashi, Tatsuya, YOSHINUMA, Mikiro, IDA,
Katsumiメールアドレス:所属:

URL

http://hdl.handle.net/10655/00012584
This work is licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 3.0
International License.

1

Two-dimensional beam emission spectroscopy forhydrogen isotope negative neutral beam in Large
Helical Device
T. Kobayashi1,2 , M. Yoshinuma1 , and K. Ida1
1

National Institute for Fusion Science, National Institutes of Natural Sciences, Toki 509-5292,

Japan
2

The Graduate University for Advanced Studies, SOKENDAI, Toki 509-5292, Japan

E-mail: kobayashi.tatsuya@nifs.ac.jp

Abstract.

A new beam emission spectroscopy (BES) system that has improved lines of sightis installed in LHD, and routine measurement has been started in the 21st LHD experimentcampaign in 2019–2020. The new system is optimized for hydrogen isotope experiments byequipping a rotatable large-diameter interference filter to be compatible with either the hydrogenor the deuterium beam emission component. An avalanche photo diode detector array having 8
× 8 pixels is used for obtaining a radial–vertical image of electron density fluctuation covering the
mid-radius to the plasma periphery. Spatial resolution and wavenumber cutoﬀ are derived fromequilibrium reconstruction and plasma kinetic profiles. Obtained fluctuation data is presented
for a low field high beta discharge. The spatiotemporal structure of the fluctuations is clearlyshown by Fourier correlation analyses.

1. Introduction

Cross field anomalous transport in magnetically confined plasmas is one of the key
issues in fusion development [1]. Multi-scale fluctuation interaction and consequent

2
flow structure formation has been pointed out to be essential in determining turbulenceenergy redistribution in the wavenumber space for more than a decade [2]. To clarify
underlying physics of the cross field anomalous transport and the nonlinear structureformation, direct measurement of turbulent fluctuation is mandatory.
Beam emission spectroscopy (BES) is one of the active local density fluctuation
diagnostics installed in many diﬀerent plasma fusion devices including tokamaks[3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13] and stellarators [14, 15, 16, 17, 18, 19]. Owing to its easily
accessible range of visible light wavelength with commercial optics and applicabilityof commonly equipped heating neutral beams as the probing beam, BES systems are
successfully operated in many diﬀerent situations. In particular, multi-channel andmulti-dimensional measurement system with good locality and high spatiotemporal
resolution is universally composed for unveiling the multi-scale interaction of microscale turbulences and meso- and macro-scale plasma activities. One of the prototypicalapplications of BES systems is for determining the role of turbulence in the L-H
transition. See, e.g., [20]. Recently, a dynamic interaction among magnetic islands,
heat pulses, and turbulences is clearly depicted by a BES system in DIII-D [21].
One of the diﬃculties in installing a BES system having good resolutions is tofind lines of sight as parallel as possible to the magnetic field line. For realizing thisrequirement, a tangential view to torus with an acceptable brightness is mandatory.
Finding lines of sight that satisfy those conditions is often challenging particularly inlarge superconducting devices having wide cryostat structures, such as the large helical3device (LHD).
A new BES system has been installed in LHD, and routine measurement has been
started in the 21st LHD experiment campaign in 2019–2020. Compared to previous BES
systems in LHD [17, 18, 19], the radial resolution is improved approximately by 60 %,and the angle between the line of sight and the beam vector is reduced by 37 % thatenlarges the spectrum separation of the beam emission component from the backgroundHα /Dα line. The angles between the lines of sight and the local magnetic field lines are
6.73 ± 2.6 degrees in average, which enables us to achieve the wavenumber resolutionof k⊥ < 0.6 cm−1 . The new system is optimized for hydrogen isotope experimentsby equipping a rotatable large-diameter interference filter to be compatible with either
the hydrogen or the deuterium beam emission component. An avalanche photo diodedetector array having 8 × 8 pixels is used for obtaining a radial–vertical image covering
the mid-radius to the plasma periphery. In this paper, we elaborate the diagnostic
capability of the new BES system using obtained electron density fluctuation data.
The rest of the paper is organized as follows: Section 2 describes the hardware
setup of the new BES system. Then, fluctuation measurement capability is discussed in
section 3 by examining the spatial resolution and wavenumber cutoﬀ. Section 4 presents
the measurement results. The summary is given in section 5.

4
2. Hardware setup

In this section, we describe the hardware properties constructing the new BES systemwith emphasis on its capability for fluctuation measurement in hydrogen isotope
experiment.

2.1. System overview
The system overview is illustrated in Fig. 1. The objective optics are installed in the
LHD 6-O port, where a commercial camera lens (Mamiya F/2.8, f = 300 mm) is utilized
to obtain the magnification of ∼ 15. Behind the camera lens, a 16 × 16 channel opticalfiber array of a diameter of 0.8 mm is installed to obtain a 20 × 20 cm2 radial–vertical(R − Z) image of the plasma fluctuation. The two-dimensional fiber array is led toa large-diameter interference filter spectrometer (Bunkou-Keiki CLF-400) by opticalfiber bundles through two junction panels inside and outside the LHD hall aiming forflexible fiber arrangement. The light image is converted to the parallel light by theentrance collimate camera lens (F/2.8, f = 400 mm) for utilizing the single largediameter interference filter of a diameter of ∼ 160 mm. The angle between the normal
vector to the filter surface and the parallel light can be externally tunable for varying thetransmitted central wavelength. The filtered light image is directly coupled on an 8 ×
8 pixels avalanche photo diode camera (Fusion Instrument Kft. APDCAM-10g) by theexit focal camera lens (F/2.8, f = 400 mm), where 4 fiber images are coupled to one APD
element having 1.6 × 1.6 mm2 shape as shown in Fig. 2. In APDCAM-10g, two 4 × 8

10 4

(.

6 2 8 481
5

LHD HallLHD
f = 300 mm, F/2.8
Camera lens

6-O port

16x16 channel
optical fiber array(800 µm core diameter)

=
=
=
==
=

Junction panelPC
4 to 1binning

APDCAM-10g
8x8 pixel S8550-02

CLF-400

Clara
CCD

CLP-100

=
=
=
==
=
PC
Junction panel

Figure 1. Schematic of the BES system in LHD.

•

S

m
i

pixels APD detector arrays (Hamamatsu S8550-02) are used. The frequency bandwidth

•

)

22

e

D :
Psignalgto noise ratio
22:
is tuned to be 100 kHz for obtaining a betterin the22
low frequency
F
22
Arange. Sampling time is set to be 200 kHz so far. One of the advantages of APDCAM10g is that the exit fiber ports are equipped on the APD element surface. Some fiber

spots are coupled to the exit fiber ports in order to monitor the transmitted spectrum
by a conventional lens-grating spectrometer installed behind (Bunkou-Keiki CLP-100),
which consists of a set of F/2, f = 100 mm camera lenses and an 1800/mm grating. In
addition, the emission spectrum without filtering is always monitored. The detector of
the lens-grating spectrometer is a Peltier-cooled charge-coupled device (CCD) camera(Clara, Andor) having a 1392×1040 pixel array with a 6.45 × 6.45 µm2 pixel size.

6
1.6x1.6 mm 2

D

G
Exit fiber
port
Hamamatsu
S8550-02

B

E

Figure 2. Schematic of the APD array arrangement.

•
•

S

:
1
F
2.2. Viewing configuration and optical system

F

Schematic view of the lines of sight is shown in Fig. 3 (a). One of the three neutralbeam (NB) injection heating with the negative ion source (NB #3) is used as the probe
beam of the system. An in-vessel stainless steel mirror is installed to build lines of sightas parallel as possible to the local magnetic field line for obtaining a better wavenumber
resolution. In order to protect the stainless steel mirror surface, a mechanical shutter
system is also installed. The actuator of the mirror shutter is installed from the LHD
6-T port, where an air motor driving system with a rotary vacuum feedthrough androtational shafts of totally 2.8 m long is utilized. The distance between the objective
optics and the focal point is approximately 5 m, and a single spot diameter at the focal
point is 1.3 cm. Angles between the lines of sight and the beam vectors are in therange of 150.6 − 153.6 degrees. The neutral beam is injected with the beam energyof 120 − 180 keV and the beam source of either hydrogen or deuterium, anticipating

:F 8

123

7
(b)

(a)

Magnetic surface

f=-108 deg.

a99

NB #3
Mirror & shutter
f=-108 deg.

Shutter
actuator

LoS

16x16
LoS arrayYX

6-O port

6-T port#156774, t = 4.75 s• .(LoS)
6 E87(a)DE5E8
8Etop8torus
10-view and (b)Son the poloidal
D• Figure: 8 3. Schematic78:
of the lines of sighton the•a
VL 57 5 7 86E A O•
85 8 8 :H
84
6• -ABB 8 D E
cross section at ϕ = −108 degrees overlaid with the eﬀective minor radius.

the beam emission component having Doppler blue shifts of 6.46 − 11.51 nm from theHα /Dα line.
The two-dimensional array shape of the lines of sight is designed on the poloidal
cross section at the toroidal angle of ϕ = −108 degrees. Figure 3 (b) shows the schematicof the lines of sight on the poloidal cross section at ϕ = −108 degrees overlaid with theeﬀective minor radius reﬀ , the most frequently used minor radial coordinate in LHD
obtained according to the plasma volume [22]. The plasma boundary is defined by
the eﬀective minor radius inside which 99 % of the plasma stored energy is confined,
a99 . It is found that the radial region roughly from the mid-radius to the edge plasmaboundary is covered by the two-dimensional array. The major radial position and thevertical position of the lines of sight on the poloidal cross section at ϕ = −108 degrees,(R, Z), are used as the nominal coordinate of the measurement. Note that the actual

8measurement location is determined by the line averaged eﬀective minor radius weighted
by the beam density and the electron density as discussed below.
The lifetime of the excited beam atoms is approximately 6 − 7 ns in the LHD
parameter range [23, 5]. The excited beam atom can penetrate deeper into the plasma
with the high beam velocity of ∼ 4 × 106 m/s. Because the beam is not injected directlyin the radial direction but in the tangential direction, the mean radial traveling extent
in the lifetime is less than ∼ 1.3 cm.

2.3. Rotatable filter spectrometer system
Since the neutral beam injection with the negative ion source has no multiple charged
ions, only the fundamental Doppler shifted component need be taken care of. To
minimize contaminations of impurity emissions or bremsstrahlung emissions, it isbeneficial to use a narrow bandpass interference filter for this situation.

In LHD

deuterium/hydrogen experiments, the ion source for the neutral beam operation ispreferentially chosen to match the plasma source gas.

Therefore, the transmitted

central wavelength must be tunable according to the neutral beam source. To meetthis requirement, a rotatable filter spectrometer system is designed [24].
Figure 4 (a) shows the rotation angle dependence of the transmitted central
wavelength.

The full width at the half maximum (FWHM) of the transmittancespectrum is shown by shaded areas. Those data are obtained by a bench test [24].
The transmitted central wavelength from the exit fiber port B is more blue shifted9#156774 (Hydrogen), t = 4.7-4.8 s(a)(c) θ = -12.5 deg.

Port GPort B

Port GHa-D B 58
B
E
p
SVf
g ce

.

f

Port B

gd
Sgf

f b
gd

Of
g
Hn t
Port B
Port Gbf 5 cDeuterium
Da
xH
lH
% 8
G
b
/
Hydrogen
) (78
(78
fG
1 B
.
o
t
Ga
/xH
o
t
8 E
)%
. o
t
yH
OfG
Figure 4. Specifications of the rotatable narrow bandpass filter spectrometer: (a) rotation angle
7B
0
Go
t
θ dependence of the transmitted central wavelength with the full width at the half maximum
Hp
k ri
vp
fG
(FWHM) of the transmittance spectrum shown by shaded areas for the exit fiber ports B and#154759 (Deuterium), t = 3.5-5.3 s(b)(d) θ = -7.5 deg.

g

G, (b) rotation angle setting required for hydrogen and deuterium neutral beams as a functionof the injection beam energy, and (c,d) transmission characteristics for diﬀerent rotation angles(θ = −12.5 deg. and θ = −7.5 deg.) overlaid with typical beam emission spectra for hydrogenand deuterium neutral beams, respectively.

compared to that from the exit fiber port G because of a larger eﬀective incident angleof the light to the filter which depends on the image position. Since the APD elements
locate between those exit fiber ports, the transmitted wavelength of light focused on
APD elements is a value between two wavelength curves in Fig. 4 (a). Necessary
wavelength depends both on the neutral beam ion species and on the neutral beamenergy. Therefore, rotation angle setting is given for each of those conditions [Fig. 4(b)]. The most frequently used beam energy is Eb ∼ 165 keV, where corresponding
setting angles for the hydrogen beam and the deuterium beam are −12.5 degrees and10−7.5 degrees, respectively. The transmittance spectra for those rotation angle settings
are shown in Figs. 4 (c) and (d), overlaid with typical emission spectra around thebeam emission components with hydrogen beam and deuterium beam, respectively. It
is shown that the shapes of the transmittance spectra from port B and port G with
diﬀerent rotation angle settings are almost identical, as is systematically demonstrated
in [24]. The beam emission components locate between the transmittance spectra fromport B and port G. Note that detector columns at the port G side (the right sidecolumns on Fig. 2) suﬀer a reduction of signal intensity because the beam emission
component lies at the edge of the transmission curve not at the flattop region with therotation angle settings in Figs. 4 (c) and (d). To compensate this eﬀect, we apply asignal calibration using a density ramp up discharge as discussed in subsection 4.2. In
the case of the deuterium discharge [Fig. 4 (d)], not only the beam emission component
but also impurity emission lines (likely OV emissions from the edge region) exist in thetransmitted range of wavelength, which worsens the locality of the BES signal. The
plasma facing components were not well conditioned in that discharge, because it was
immediately after an unplanned vacuum opening. In particular, approximately 40 % of
the transmitted light is estimated to be contaminated by those impurity emission lines
according to the measured spectrum, therefore we have to abandon to use this data
for analysis. An advantage of the new BES system is that the data quality is always
checked by the monitor spectrometer.

11
3. Fluctuation measurement capability

In this section, the fluctuation measurement capability of the new BES system is
examined by calculating the radial resolution and the wavenumber cutoﬀ from thereconstructed three-dimensional equilibrium and measured kinetic profiles for thehydrogen discharge # 156774.

3.1. Radial resolution
The radial resolution of the BES lines of sight is analyzed on a simplified model
illustrated in Fig. 5. The axis along the line of sight is defined as z, and local polar
coordinates (rF , θF ) are defined on each poloidal cross section along the line of sight.
We consider variations in the neutral beam density nb and the electron density ne along
the line of sight. In addition, an electron density variation on the poloidal cross section
is taken into account, where the neutral beam density remains constant. The lightemission intensity from the sampling volume is proportional to the volume integral of
nb ne ,∫ z ∫ aF ∫ 2π

I=
0

0

0

nb ne rF dθF drF dz,(1)

where aF is the local radius of the sampling volume cylinder. The electron density
distribution in the sampling volume is approximated up to the first order terms as






∂reﬀ
∂reﬀ
 ,
cos θF+ sin θF
ne = n̂e 1 − rF L−1
ne∂R rF =0
∂Z rF =0(2)

where Ln−1e ≡ −n̂−1e ∂ne /∂reﬀ |rF =0 is the inverse density gradient length and n̂e = ne |rF =0 .
Since the variation in the electron density is treated as symmetric, the integrated value

12
z
(a)

(b)

Z
aF
qF r
F

R

z

LoS

(c)

(d)

nb

ne

ne
nb
z

R, Z

Figure 5. Schematic view of a sampling volume (a) along a line of sight (LoS) and (b) on the
cross section perpendicular to the line of sight; models of the electron density profile and theneutral beam profile (c) along the line of sight and (d) on the cross section perpendicular to theline of sight.

is simply given as
I = πa2F∫ z
0

nb n̂e dz.

(3)

The mean radius of the sampling volume is given by the weighted integral of theeﬀective minor radius reﬀ by nb ne :r̄eﬀ =

1 ∫ z ∫ aF ∫ 2π
reﬀ nb ne rF dθF drF dz
I 0 0 0(4)

The local eﬀective minor radius in the sampling volume is given as




∂reﬀ
∂reﬀ
,
reﬀ = r̂eﬀ + rF cos θF+ sin θF
∂R rF =0
∂Z rF =0(5)

13where r̂eﬀ = reﬀ |rF =0 . Now substituting Eq. (5) into Eq. (4) gives∫z

1
0 r̂eﬀ nb n̂e dz
2∫z− a2F L−1n (∇reﬀ ) ,
n
n̂
dz
4
b
e
0

r̄eﬀ =

(6)

where


2



2

∂reﬀ
∂r
 +  eﬀ
 .
(∇reﬀ )2 = ∂R rF =0
∂Z rF =0

(7)

The first and second terms in Eq.(6) correspond to the mean eﬀective minor radius along
the line of sight and the correction term due to simultaneous variations of the eﬀective
minor radius and the electron density in the sampling volume, respectively.
Similarly, the deviation of the eﬀective minor radius from its mean value, i.e., theradial resolution, is derived as
1 ∫ z ∫ aF ∫ 2π
(reﬀ − r̄eﬀ )2 nb ne rF dθF drF dz(δreﬀ ) =I 0 0 0
2

∫z

=

2
1
1
0 (r̂eﬀ − r̄eﬀ ) nb n̂e dz
4∫z+ a2F (∇reﬀ )2 − a4F L−2
ne (∇reﬀ ) .
4
8
n
n̂
dz
0 b e

(8)

The first and second terms reflect variations in the eﬀective minor radius along theline of sight and perpendicular to the line of sight, respectively. The third term is theeﬀective sampling volume shrinking due to the electron density variation.
Since the gradient length of the electron density and the scale length of the eﬀective
minor radius are much longer than the sampling volume radius, the correction terms
in Eqs. (6) and (8) are negligibly small for all the lines of sight even in the peripheral
density gradient region. Therefore, those terms are neglected in the rest of this paper.
Calculations of the measurement position and the radial resolution aredemonstrated using the actual discharge data. Figure 6 (a) shows the radial profiles of14
reff [m]#156774, t = 4.7-4.8 s

(a)

(b)
z ~ 0 [m]Tenenb,vac [1014 m-3](c)nb [1014 m-3]

]
C
itkl
9
d
rkowg
d
baI
b
d
n s fl
zV
d
n s
-).
2

(d)

d

Figure 6. (a) Radial profiles of the electron density and the electron temperature measured by
the Thomson scattering system, (b) reconstructed eﬀective minor radius on the midplane, (c)vacuum neutral beam density profile, and (d) neutral beam density profile attenuated by plasma.
Thin lines in (b-d) show the leftmost and the rightmost lines of sight passing through slightly
above the midplane on the poloidal cross section at ϕ = −108 deg.

the electron density and the electron temperature determined by a Thomson scatteringsystem [25]. In this discharge, a significant hollow electron density profile is formed.
Spatial distribution of the eﬀective minor radius is displayed in Fig. 6 (b). The neutralbeam injection profile in vacuum is given by a neutral beam simulation code as shownin Fig. 6 (c). The plasma–beam interaction is calculated accounting for the beam
stopping cross section depending on the beam energy, the electron density, the electron
temperature, and the impurity contents [26]. The obtained neutral beam attenuation
profile is shown in Fig. 6 (d).
Figure 7 shows distributions of the eﬀective minor radius, the electron density, andthe neutral beam density along the lines of sight with slightly above the midplane and

C
c M
aI

15

z

#156774, t = 4.7-4.8 s
(a)

1
p
it
.

(b)

R = 4.20 m(c)

4.11 m4.00 mFigure 7. Distributions of (a) the eﬀective minor radius, (b) the electron density, and (c) theneutral beam density along the lines of sight passing through slightly above the midplane andR = 4.00, 4.11, and 4.20 m on the poloidal cross section at ϕ = −108 deg.

R = 4.00, 4.11, and 4.20 m in the nominal coordinates. All three cases show similar
beam density profile shapes with shifted central positions. As the nominal radial position
moves outward, the eﬀective minor radius increases and its deviation along the line ofsight becomes larger. Variation in the electron density is particularly substantial at theedge line of sight.
Substituting obtained values to Eqs. (6) and (8) provides the mean eﬀective minor
radius and the radial resolution for each line of sight. They are exhibited in Figs. 8(a) and (b) as a function of the nominal coordinates (R, Z). The mean eﬀective minor
radius is larger at lines of sight having larger nominal R, but slightly changes in the

. ,4

i

16
(a)

(b)

(c)

(d)

#156774, t = 4.7-4.8 s

12 1
t
f
1 1
on u91
on
* a
9 o
o s
* *
Z
1

1
1

on u
n u x

g
D
dR
21*

Figure 8. Distributions of (a) the mean eﬀective minor radius, (b) the deviation of the eﬀective
minor radius, line integrations of (c) the neutral beam density multiplied by the electron density,and (d) the neutral beam density for all lines of sight plotted in the nominal coordinates.

Z direction. The radial resolution is mostly less than 3 cm, and worsens at the outer
bottom lines of sight. Integrals of nb ne and of nb along the lines of sight are shown in
Figs. 8 (c) and (d). Large signal intensities are expected in the outer top lines of sight.

3.2. Fiber binning
To increase signal intensity, lights from four sampling volumes are binned and coupled
to one APD pixel, which would worsen the radial resolution. The mean eﬀective minor
radius with the fiber binning, r̄eﬀ,bin , is given as1

r̄eﬀ,bin = ∑NN ∫ z ∫ aF ∫ 2π∑

00
j=1 Ij j=1 0∑N ∫ z0 r̂eﬀ,j nb,j n̂e,j dz= j=1,∑N ∫ zj=1 0 nb,j n̂e,j dz

reﬀ,j nb,j ne,j rF dθF drF dz
(9)

lr

11 1
u
11 1
c
11 1
m

17
where the suﬃx j denotes the fiber numbering for an APD pixel and N = 4 is thenumber of the fiber binning. The mean deviation of the eﬀective minor radius fromr̄eﬀ,bin is given as1

2(δreﬀ,bin ) = ∑NN ∫ z ∫ aF ∫ 2π∑

j=1 Ij j=1 0

00(reﬀ,j − r̄eﬀ,bin )2 nb,j ne,j rF dθF drF dz

∫z
2
N
1 ∑
j=1 0 (r̂eﬀ,j − r̄eﬀ,j ) nb,j n̂e,j dz+(r̄eﬀ,j − r̄eﬀ,bin )2 .
∫∑NzN
j=1 0 nb,j n̂e,j dz
j=1

∑N

=

(10)

The first term shows the averaged radial deviation in all lines of sight on the APD pixel ofinterest, and the second term corresponds to deviation of the mean eﬀective minor radiifrom r̄eﬀ,bin . Here, all the correction terms in Eqs. (6) and (8) are neglected. Figure 9shows the mean eﬀective minor radius and the radial resolution under the fiber binningfor each detector channel plotted by the corresponding mean nominal coordinates. Here,symbols at the fifth row and the fifth column, the sixth row and the fourth column, andthe sixth row and the fifth column from the top left corner are not aligned with theregular spacings. Those points are composed by the 3 fibers-to-1 detector binning, andthe remaining fiber channels are injected to exit fiber ports B and G and directly tothe monitor spectrometer. The eﬀect of the fiber binning is particularly clear in theradial resolution plot at the top inner positions, where the radial resolution before thefiber binning was finest. While, the radial resolution remains almost unchanged at thepositions where δreﬀ before the fiber binning was larger than the sampling volume radius
aF of 0.65 cm.

18
(a)

(b)

#156774, t = 4.7-4.8 s

Figure 9. Distributions of (a) the mean eﬀective minor radius and (b) the deviation of theeﬀective minor radius under the 4 spots-to-1 detector binning plotted in the mean nominal
coordinates.
(a)

(b)

#156774, t = 4.7-4.8 s

Figure 10. Distributions of (a) the angle between the line of sight and the magnetic field lineand (b) its deviation plotted in the nominal coordinates.

3.3. Angle between line of sight and magnetic field line
The angle between the line of sight and the magnetic field line and its deviation on
1

7

5

2

2

1

7

the line of sight, denoted as α and δα, respectively, are calculated in the same ways
to the eﬀective minor radius. Distributions of α and δα are shown in Figs. 10 (a) and(b), respectively. Most of the lines of sight have α < 8 degrees with small deviations ofδα < 2 degrees. Those angles determine the wavenumber cutoﬀ as discussed below.

19
3.4. Wavenumber cutoﬀ
Volume integral of a temporally and spatially varying electron density in the sampling
volume acts as a spatial lowpass filter, causing a fluctuation amplitude reduction in the
BES signal. The amplitude reduction rate trivially depends on the fluctuation spatial
structure. Here, the hardware wavenumber cutoﬀ of the system is derived. The situationthat is considered is illustrated in Fig. 11. A plane wave of the electron density having
the parallel and perpendicular wavenumbers to the magnetic field direction, k|| and k⊥ ,is given as the test wave. Using the angle between the line of sight and the magnetic
field line to be α, the wavenumber components parallel and perpendicular to the line ofsight, kz and kx , are given as




kx







=

kz

cos α − sin α
sin α

cos α





k⊥



,

(11)

k||

where the direction x is taken to be the direction of the wave propagation perpendicular
to the line of sight. The fluctuation part of the BES signal intensity is proportional tothe volume integral of the electron density multiplied by the beam density denoted as
I˜j (t) ∝∫ z ∫ aF ∫ 2π000

= |ñe |e−iωt∫ z0nb (z)|ñe |e−iωt+ikx x+ikz z rF dθF drF dz
nb (z)eikz z dz

∫ a ∫ 2π00eikx x rF dθF drF ,(12)where |ñe | is the amplitude of the electron density fluctuation, ω is the intrinsic frequencyof the wave, and i is the imaginary unit. Signal intensity with the fiber binning is thengiven asI˜BES (t) =

N
∑
j=1

I˜j (t)20∝ |ñe |e

−iωt



∫ z
0

nb (z)e

ikz z

dz 

N ∫ a ∫ 2π
∑

j=1 0

0


ikx xje

rF,j dθF,j drF,j  ,(13)where diﬀerences among the binned lines of sight in the z direction are negligibly small
and therefore are not taken into account for simplicity. The integral in the z direction
and the term in the square brackets in Eq. (13) are called the parallel integral and theperpendicular integral, respectively. They and their product are shown in Fig. 12 as afunction of the perpendicular wavenumber and the angle between the line of sight and themagnetic field line. Here, the parallel wavenumber is given by the gyrokinetic ordering
to be k|| ∼ ρ∗ k⊥ , where ρ∗ ≡ ρt,i /a99 is the relative ion gyroradius and ρt,i is the ion
gyroradius. Reduction of the fluctuation amplitude due to the volume integral becomessignificant when the wave phase substantially changes in the direction of interest. The
amplitude cutoﬀ due to the perpendicular integral is significant when the perpendicular
wavelength is comparable to the binned sampling volume size at k⊥ ∼ 1 cm−1 . This
cutoﬀ wavenumber in the perpendicular integral is almost independent on the line ofsight angle α.
When the line of sight is perfectly aligned on the magnetic field direction, α = 0,
the parallel integral is very weak because of its small parallel wavenumber. However,once the line of sight angle becomes finite, the perpendicular phase variation aﬀects thephase distribution along the line of sight through Eq. (11), which strongly limits theobservable perpendicular wavenumber range. As a result, the amplitude cutoﬀ due tothe parallel integral show a strong α dependence as shown in Fig. 12 (b). The productof both integrals is shown in Fig. 12 (c). The perpendicular wavenumber that results in

21

z

a

(a)

(b)

B

y
aF
z q F rF
! !$

x

%

C $A>BD %A>BD %EFEFGF9

EFEFGF9

!"

!%
!$

!∥

LoS

56

1 < >BC $ EFEFG

2

Figure 11. Schematic view of a sampling volume and a magnetic field line (a) along a line of

!" L

Kx

- .crossSsection perpendicular to the line of sight. Wavenumber vector
sight (LoS) and (b) on the
GTV
7G

components are also displayed.

(a)

(b)

r
(c)

0 .5

de

ca

. 3
y

2-0

ri = 1.66 mm (Edge)

B D:8D5| amplitudePnk of thei perpendicular*
Hk
Figure 12.
Fluctuation
reductionsasce
a function
wavenumber

i
DB C
78

|
P
n
< 8B
l h
H5= :5 78
d between
M < theMrssight andathe magnetic_n field line
Hα byp(a) theoperpendicular
5= :5
and the angleline of< 8B B: *H
integral, (b)cthe parallel
integral, andbold curve in (c)*i (c) their product.
I1A .gmt presents the M
wavenumber cutoﬀ.

< 8B
<
oMz

22
(b)

#156774, t = 4.7-4.8 s(a)Figure 13. The wavenumber cutoﬀ (a) plotted as a function of the angle between the line ofsight and the magnetic field line and (b) plotted for all lines of sight in the nominal coordinates.

the half decay of the fluctuation amplitude, being referred to as the wavenumber cutoﬀ,
is overlaid by the black thick curve.
The wavenumber cutoﬀ is plotted as a function of α in Fig. 13 (a). As shown above,α < 8 degrees holds for most of the lines of sight, which provides the wavenumber cutoﬀ
of k⊥ > 0.6 cm−1 . The wavenumber cutoﬀ is plotted for each binned line of sight in
Fig. 13 (b).
Wavenumber coverage of the BES system is compared to other fluctuation
diagnostics, the phase contrast imaging (PCI) [27], and the Doppler back scattering(DBS) [28] diagnostics in Fig. 14. The PCI and the DBS have lower boundaries in their
wavenumber coverage, while the BES has an upper boundary. The BES complements
the smaller wavenumber range that cannot be encompassed by the PCI and the DBS.
The BES coverage is mostly out of the so-called turbulence range, typified by regimesof the ion temperature gradient (ITG) modes or the trapped electron modes (TEM),
but is rather proper for MHD turbulences or long-wavelength fluctuations as shown in
Fig. 14. The neutral beam with the negative ion source in LHD used as the probe beam

23
BES
m=5

m=10

m=20

DBS
PCI
ITG & TEM

Figure 14. Observable wavenumber range of BES shown with covering ranges of the phase
contrast imaging (PCI) diagnostics and the Doppler back scattering (DBS) diagnostic in LHD
as well as typical wavenumber ranges for the ion temperature gradient (ITB) mode, the trappedelectron mode (TEM), and coherent MHD modes with some poloidal mode numbers m.

of BES has an extremely low level of beam source oscillation, which helps to diagnose
low frequency density fluctuations.

4. Measurement results

The new BES system was routinely operated from the 21st LHD experiment campaign
in 2019–2020. One of the best results was obtained in an experiment aiming to clarify
a confinement mode transition phenomena in a low magnetic field condition. A setof fluctuation analyses was applied to the data and basic properties were successfully
drawn.

4.1. Target discharge
Figure 15 is the time evolution of the discharge parameters and the BES signals IBES for
the target shot # 156774. Fueling from the gas puﬀ and the neutral beams with positive

24
ion source (NB #4 and #5) as well as the wall recycling is performed by deuterium gas,
while the neutral beams with the negative ion source (NB #1 to #3) are operated
with hydrogen gas. The deuterium content of the plasma is between 60 % to 75 %.
The confinement mode transition occurs at t ∼ 4 s indicated by an abrupt increaseof the density ramp up pace. The discharge is performed in a low toroidal magnetic
field condition with Bt = −1 T and an inward shifted magnetic axis configuration ofRax = 3.6 m. An intrinsic error field is compensated by an external coil field. The
probe beam (NB #3) is injected from the beginning of the discharge and breaks down
at t ∼ 5 s. Throughout the discharge, the line averaged density ramps up from 1.5 to
4×1019 m−3 , which is useful for the BES signal calibration. The bottom panel shows thetime evolution of the emission light spectrum. The beam emission component appears
at λ ∼ 645 nm when both the plasma and the probe beam are present, and vanishes
after the break down of the NB #3. Impurity emissions are not distinguishably large
due to intensive wall conditioning by the boronization. The BES signals from channels
2 (mid-radius) and 50 (edge) show corresponding time evolution. Note that even after
the break down of the NB #3, the BES signal intensities remain nonzero, possibly
due to non beam emission components, including nonzero impurity emissions or thebremsstrahlung emission.

25#156774

0
0
0
0
0

(a)
probe

NB #1 (H)NB #2 (H)NB #3 (H)4 NW

NB #4 (D)NB #5 (D)(b)

D puff [arb.u.](c)ch50 (R=4.17m, Z=0.07m)
ch2 (R=4.00m, Z=0.07m)

Ha & Da
Beam emission(R=4.11m, Z=-0.02m)(d)

Figure 15. Time evolutions of (a) the NBI port through powers, (b) the line averaged density,
the diamagnetic plasma stored energy, and the gas puﬀ sequence, (c) the BES signal intensities
of channels 2 and 50, and (d) the beam emission spectrum. The NB # 3 is the probe beam of
the BES system.

4.2. Linearity between the BES intensity and the line averaged electron density
The BES intensity is expected to be proportional to the integral of the electron density
and the beam density along the line of sight,∫

nb ne dz. Here, linearity between those

two values are examined. Figure 16 compares the BES intensity and
BES channels 2 and 50. Calculation of∫∫

nb ne dz for the

nb ne dz is presented in subsection 3.1. Values

obtained by a moving averaging with a time window of 0.1 s from 3.5 s to 5.3 s areplotted. A value from 4.9 s to 5.0 s is excluded because the probe beam breaks down in
the time period. The last three points with∫nb ne dz = 0 correspond to values without

the NB #3 injection. Dashed lines in Fig. 16 present the linear fitting of the points when

26
(b)

#156774, t = 4.7-4.8 s

(a)
ch50

ch2
Beam-off(c)(d)

Figure 16. (a) Relation between the BES signal intensities and the neutral beam density
multiplied by the electron density integrated on the lines of sight for the BES channels 2 (midradius) and 50 (edge), (b) the linear correlation coeﬃcient, (c,d) the intersection a0 and theslope a1 of the linear fitting plotted in the nominal coordinates. Dashed lines in (a) are thelinear fittings for symbols.

the probe beam is injected. Both of the BES channels show almost perfect linearities.
Points for the BES channel 50 without the NB #3 injection do not meet the intercept of
the fitting line. This implies that the BES signal has an oﬀset possibly due to emissions
caused by the probe beam injection. Correlation coeﬃcients for the BES channels 2
and 50 are 0.995 and 0.997, respectively. Very high linearity is a common feature in
all channels as shown by Fig. 16 (b), where the correlation coeﬃcients are plotted as afunction of the mean nominal coordinates. Linear fitting coeﬃcients, the intercept a0
and the slope a1 , are also plotted in Figs. 16 (c) and (d).
Utilizing obtained linear fitting coeﬃcients, the BES signals can be translated into

27
the electron density. The line averaged electron density on the line of sight is given as∫

nb ne dzne,LoS = ∫
.
nb dz

(14)

This value is a good approximation of the local electron density if ne can be regarded
as constant on the line of sight, i.e.,∫∫nb ne dz ∼ ne nb dz. The high linearity allows

substitution of the numerator to the linear regression,ne,BES =a0 + a1 IBES
∫
.
nb dz

(15)

The reconstructed electron density profiles are plotted with the Thomson measurementin Fig. 17 for diﬀerent time periods. Here, fitted electron density profiles and theiruncertainties obtained based on a machine learning technique [29] are plotted. The
horizontal errors show the radial resolution δreﬀ , while the vertical errors indicate theelectron density variation along the line of sight. The reconstructed profiles agree with
the Thomson measurement except for the edge peak location, where the density variation
along the line of sight is substantial as shown by Fig. 7 (b).

4.3. Fluctuation analysis
Fourier correlation analyses are applied to the BES data to obtain the basic
spatiotemporal information of fluctuations. Figure 18 shows the time evolution of thesquared cross coherence defined as
γ 2 (t, f ) =|⟨S ∗ Sref ⟩t |2,∗
Sref ⟩2t⟨S ∗ S⟩2t ⟨Sref(16)

where S and Sref are the Fourier components of the BES signals at an arbitrary channel
and at the reference channel, respectively. The Fourier transform is performed with the

28#156774

Figure 17.

(a) t = 3.5-3.6 s(b) t = 3.9-4.0 s(c) t = 4.3-4.4 s(d) t = 4.7-4.8 s

Fitted electron density profiles measured by Thomson scattering (red) andreconstructed electron density profiles by the beam attenuation calculation (blue) and by the
BES measurement (black) for diﬀerent time periods of (a) t = 3.5 − 3.6 s, (b) t = 3.9 − 4.0 s, (c)t = 4.3 − 4.4 s, and (d) t = 4.7 − 4.8 s.

5 ms Turkey window and the ∆t = 2.5 ms time interval. Moving time averaging isdefined for an arbitrary quantity evolving in time Ψt as ⟨Ψ⟩t = (2N + 1)−1∑N

i=−N Ψt+i∆twith a factor of N = 7. The reference channel is chosen to be the BES channel 49, atthe top row and the seventh column from the top left corner of the two-dimensional
array in Fig. 9 (a). The squared cross coherence is calculated for the radial channel
array at the second row.
Far before the confinement mode transition occurring at t ∼ 4 s, only a weakcoherent mode appears at f ∼ 5 kHz. After the confinement mode transition, avariety of fluctuation activities are triggered. First, a low frequency coherent modeat f ∼ 1.4 kHz is observed in all the BES channels. In addition, a broadband frequency

29g#156774(a) reff = 0.34 m
PNB [MW](b) reff = 0.38 m(c) reff = 0.41 m(d) reff = 0.45 m(e) reff = 0.49 m(f) reff = 0.53 m(g) reff = 0.57 m(h) reff = 0.61 m

Figure 18. Time evolutions of the squared cross coherence at diﬀerent radial positions of thesecond row of the two-dimensional array: (a) reﬀ = 0.34 m, (b) reﬀ = 0.38 m, (c) reﬀ = 0.41 m,(d) reﬀ = 0.45 m, (e) reﬀ = 0.49 m, (f) reﬀ = 0.53 m, (g) reﬀ = 0.57 m, and (h) reﬀ = 0.61 m.
Reference signal is taken from the top row of the two-dimensional array at reﬀ = 0.57 m.

component in f = 2 − 10 kHz is seen in the edge channels, whose coherence gradually
increases in time and radial width expands in t > 4.5 s. Shortly before the transition,
both the low frequency and broadband fluctuation components seem to appear in somechannels, although not as significant as those after the transition. Since the density
is slowly ramped up before the transition as well, driving sources for those modes are
possibly related to the density and/or the edge density gradient. Even after the break30
down of the probe beam NB #3, a weak coherence remains in the edge channels, likely
due to edge broadband emissions. A similar fluctuation spectrum is obtained from themagnetic probe array placed on the vacuum vessel wall, suggesting that the observed
density fluctuations are caused by MHD activities.
Detailed discussion on the fluctuation properties is performed on time averaged
spectrum in t = 4.70 − 4.97 s, the latter phase of the improved confinement period.
Figures 19 (a)-(c) show the power spectrum density, the squared cross coherence, and thecross phase, respectively, as a function of the frequency. Positive cross phase corresponds
to the phase delay with respect to the reference channel. The spectral peaks are largest at
the outermost radius, and gradually decays as the measurement position moves inward.
The squared cross coherence is largest at the second outermost radius, i.e., the position
closest to the reference channel at reﬀ ∼ 0.57 m. The squared cross coherences of
the higher frequency peaks decay quicker than that of the lowest frequency peak at
f = 1.4 kHz. The phase diﬀerence is nonzero in the entire frequency range, showing
radial phase propagations.
Figures 19 (d)-(f) show the radial profiles of the power spectrum density, the squared
cross coherence, and the cross phase, respectively, for spectral peaks at f = 1.4 kHz,
2.8 kHz, and 4.2 kHz. The peak values of the power spectrum density are larger thanthe photon noise level. High squared cross coherence of the f = 1.4 kHz peak prevails
over the observable radial range, while the coherent fluctuations of higher frequencies
are mostly localized at the edge region. Smooth outward propagation of the fluctuation

31#156774, t = 4.70-4.97 s, θ=0.190.03 rad

(a)

(d)

Photon
noise

(b)

(e)

(c)

(f)

Figure 19. Frequency dependences of (a) the power spectrum densities, (b) the squared crosscoherences, and (c) the cross phases at diﬀerent radial positions and (d-f) their radial profiles
for spectral peaks at f = 1.4 kHz, 2.8 kHz, and 4.2 kHz.

phase is seen for all three frequency peaks, while the phase propagation velocity diﬀers
from each other.

Since no discontinuous phase inversion is seen, observed radial

structures may not be the so-called common modes due to the edge beam attenuation.
Poloidal structure of the fluctuation modes at reﬀ ∼ 0.47 (the seventh column of thetwo-dimensional array) is displayed in Fig. 20. The squared cross coherence and the crossphase are calculated with respect to the same reference signal of the BES channel 49, thetop row and the seventh column of the two-dimensional array. Since the radial positionsof the poloidal array are very close to each other, the power spectrum density levels
are nearly identical as shown in Fig. 20 (a). The squared cross coherence decreases and32#156774 , t = 4.70-4.97 s, reff = 0.470.09 m(a)Photon noise(d)(b)

Exponential fit
(e)
(c)

(f)

Figure 20. Frequency dependences of (a) the power spectrum densities, (b) the squared crosscoherences, and (c) the cross phases at diﬀerent poloidal angles and (d-f) their poloidal angle
profiles at spectral peaks at f = 1.4 kHz, 2.8 kHz, and 4.2 kHz.

the phase diﬀerence increases as the measurement position is apart from the reference
channel, indicating preferential phase propagations in one direction [Figs. 20 (b) and(c)].
Detailed poloidal structure is presented in Figs. 20 (d)-(f) for spectral peaks at
f = 1.4 kHz, 2.8 kHz, and 4.2 kHz. The peak values of the power spectrum density arealmost independent on the poloidal angle [Figs. 20 (d)]. The poloidal correlation lengthof the fluctuating mode can be derived from the squared cross coherence profile shownin Figs. 20 (e). By performing the exponential fitting to the squared cross coherence
profiles except for the reference channel, the e-folding poloidal angles are obtained to

33
be 7.35, 0.573, and 3.34 radians for fluctuations at f = 1.4 kHz, 2.8 kHz, and 4.2 kHz,
respectively. The fluctuations at f = 1.4 kHz and 4.2 kHz are global modes because
the correlation remains high in the poloidal location isolated by π. Meanwhile, thefluctuation at f = 2.8 kHz shows a much smaller correlation angle of ∼ π/11, presenting
a local mode feature.
Similarly, performing the linear fitting to the phase profiles gives an estimation of
the poloidal mode structure. Note that the general MHD mode structures in LHD aredescribed in the Boozer coordinate system, therefore the fitting in the real coordinate
does not necessarily provide an accurate determination of the poloidal mode number[30]. Nevertheless, it is worthwhile to obtain the approximated numbers in the real
coordinate. The poloidal mode structure of the fluctuation at f = 4.2 kHz is wellapproximated by m = −4 structure, where the negative number corresponds to the mode
propagation in the electron diamagnetic direction. The fluctuation at f = 2.8 kHz seems
to have a poloidal mode number of m ∼ −1, while for the fluctuation at f = 1.4 kHz,
−1 < m < 0 is a possible estimation. A non integer m is not realistic. Low m
modes only provides a small phase diﬀerence in diﬀerent BES channels, therefore phase
contaminations due to the radial variation of the BES channel position or the real
coordinate–Boozer coordinate transformation may become meaningful. To obtain moreplausible poloidal mode numbers using the BES data, further corrections required, which
is one of the unresolved issues for the future.
Finally, two-dimensional images of the electron density fluctuation pattern are

34
t = 4.75 + dt [s]Be-dia.

Figure 21.

(a) dt = 0 [µs](b) dt = 10 [µs](c) dt = 20 [µs](d) dt = 30 [µs](e) dt = 40 [µs](f) dt = 50 [µs](g) dt = 60 [µs](h) dt = 70 [µs](i) dt = 80 [µs]Time evolution of two-dimensional electron density fluctuation images in thefrequency range of 2 − 10 kHz. Frames are separated by 10 µs each.

shown in Fig. 21. Signals from all BES channels are translated to the electron density byEq. (15), and are processed by a digital bandpass filter with the transmitted frequency
band of f = 2 − 10 kHz for drawing out the turbulent nature. Snapshots are shownwith a 10 µs interval. For the sake of better visualization, a spline interpolation isapplied in both the R and Z directions. Although it is not very unambiguous, there
are density clumps and holes propagating downward, i.e., the electron diamagnetic
direction. The amplitude of the electron density fluctuation is ∼ 0.1 × 1019 m−3 inaverage, corresponding to ∼ 2 % of the equilibrium electron density.

35
5. Summary

A new beam emission spectroscopy system, which has improved lines of sight andoptimized rotatable interference filter spectrometer for hydrogen isotope experiments,
was installed in LHD. An avalanche photo diode detector array having 8 × 8 pixels
was used for obtaining a radial–vertical image of electron density fluctuation covering
the mid-radius to the plasma periphery. Spatial resolution and wavenumber cutoﬀ
were calculated from equilibrium reconstruction and plasma kinetic profiles. Obtained
fluctuation data was presented for a low field high beta discharge, and the spatiotemporal
structure of the fluctuations was successfully shown.
The BES system introduced here is the only diagnostic system that can measure
the local electron density without a lower wavenumber cutoﬀ in LHD. Radial–vertical
two-dimensional array is useful to image the low frequency electron density fluctuation
mainly for global MHD activities.

By operating the BES with turbulent density

fluctuation measurement systems such as DBS or PCI, most of the wavenumber range
can be covered, which is planned in the near future.

Acknowledgments

The authors acknowledge all the members of the LHD Experiment Group for theirassistance. The authors also thank H. Nakano, Y. Fujiwara, M. Kisaki, K. Tanaka,
T. Tokuzawa, M. Nakata, Y. Suzuki, C. Suzuki, M. Emoto, K. Yamasaki, C. Moon,
T. Oishi, S. Kado, S. Kobayashi, G. R. McKee, Z. Yan, D. Dunai, W. Hu, V. Olevskaia,

36
M. Osakabe, T. Morisaki, and S. Sakakibara for strong support and useful discussions.
This work is partly supported by the National Institute for Fusion Science grants(ULHH033) and by the Grant-in-Aid for Scientific Research of JSPS (15H02336,
17K14898).

37
References[1] Ch P Ritz, R V Bravenec, P M Schoch, Roger D Bengtson, J A Boedo, J C Forster, Kenneth W
Gentle, Y He, R L Hickok, Y J Kim, et al 1989 Phys. Rev. Lett. 62 1844
[2] P H Diamond, S I Itoh, K Itoh, and T S Hahm 2005 Plasma Phys. Control. Fusion 47 R35[3] R J Fonck, P A Duperrex, and S F Paul 1990 Rev. Sci. Instrum. 61 3487–3495[4] G R McKee, C Fenzi, R J Fonck, and M Jakubowski 2003 Rev. Sci. Instrum. 74 2014–2019[5] M W Shafer, R J Fonck, G R McKee, and D J Schlossberg 2006 Rev. Sci. Instrum. 77 10F110[6] G R McKee, R J Fonck, D K Gupta, D J Schlossberg, M W Shafer, R L Boivin, and W Solomon
2007 Plasma Fusion Res. 2 S1025–S1025[7] A R Field, D Dunai, R Gaﬀka, Y-c Ghim, I Kiss, B Meszaros, T Krizsanoczi, S Shibaev, andS Zoletnik 2012 Rev. Sci. Instrum. 83 013508[8] Y-c Ghim, A R Field, D Dunai, S Zoletnik, L Bardóczi, A A Schekochihin, and MAST Team 2012
Plasma Phys. Control. Fusion 54 095012[9] D R Smith, R J Fonck, G R McKee, and D S Thompson 2012 Rev. Sci. Instrum. 83 10D502[10] M Lampert, G Anda, A Czopf, G Erdei, D Guszejnov, Á Kovácsik, G I Pokol, D Réfy, Y U Nam,and S Zoletnik 2015 Rev. Sci. Instrum. 86 073501[11] M Lampert, S Zoletnik, J G Bak, Y U Nam, and KSTAR Team 2018 Phys. Plasmas 25 042507[12] Y Y Li, J Fu, B Lyu, X W Du, C Y Li, Y Zhang, X H Yin, Y Yu, Q P Wang, M von Hellermann,
et al 2014 Rev. Sci. Instrum. 85 11E428[13] R Ke, Y F Wu, G R McKee, Z Yan, K Jaehnig, M Xu, M Kriete, P Lu, T Wu, L A Morton, et al2018 Rev. Sci. Instrum. 89 10D122[14] S Kobayashi, S Kado, T Oishi, T Kagawa, S Ohshima, T Mizuuchi, K Nagasaki, S Yamamoto,
H Okada, T Minami, et al 2010 Rev. Sci. Instrum. 81 10D726[15] S Kobayashi, S Ohshima, H Matsuda, X X Lu, D Kokubu, K Ida, T Kobayashi, M Yoshinuma,
S Kado, T Oishi, et al 2016 Rev. Sci. Instrum. 87 11E519

38[16] T Oishi, S Tanaka, S Kado, M Yoshinuma, K Ida, S Okamura, and CHS group 2004 Rev. Sci.
Instrum. 75 4118–4120[17] S Kado, T Oishi, M Yoshinuma, and K Ida 2010 Rev. Sci. Instrum. 81 10D720[18] T Oishi, S Kado, K Ida, M Yoshinuma, H Nakano, and K Yamazaki 2010 Rev. Sci. Instrum. 81
10D719[19] M Ono, K Ida, M Yoshinuma, H Nakano, T Kobayashi, and C Moon 2016 Plasma Fusion Res. 111402115–1402115[20] Z Yan, P Gohil, G R McKee, D Eldon, B Grierson, T Rhodes, and C C Petty 2017 Nucl. Fusion
57 126015[21] K Ida, T Kobayashi, M Ono, T E Evans, G R McKee, and M E Austin 2018 Physical review letters
120 245001[22] C Suzuki, K Ida, Y Suzuki, M Yoshida, M Emoto, and M Yokoyama 2012 Plasma Phys. Control.
Fusion 55 014016[23] I H Hutchinson 2001 Plasma Phys. Control. Fusion 44 71[24] V Olevskaia, T Kobayashi, K Ida, M Yoshinuma, and W Hu 2019 Plasma Fusion Res. 14 1305118–
1305118[25] I Yamada, K Narihara, H Funaba, T Minami, H Hayashi, T Kohmoto, and LHD ExperimentGroup 2010 Fusion Sci. Tech. 58 345–351[26] K Ida, M Yoshinuma, T Kobayashi, Y Fujiwara, J Chen, I Murakami, M Kisaki, M Osakabe, and
LHD Experiment Group 2019 Plasma Fusion Res. 14 1402079[27] K Tanaka, C A Michael, L N Vyacheslavov, A L Sanin, K Kawahata, T Akiyama, T Tokuzawa,and S Okajima 2008 Rev. Sci. Instrum. 79 10E702[28] T Tokuzawa, H Tsuchiya, T Tsujimura, M Emoto, H Nakanishi, S Inagaki, K Ida, H Yamada,
A Ejiri, K Y Watanabe, et al 2018 Rev. Sci. Instrum. 89 10H118[29] K Fujii, C Suzuki, and M Hasuo 2019 IEEE Trans. Plasma Sci. 47 3305–3314[30] S Sakakibara, H Yamada, and LHD Experiment Group 2010 Fusion Sci. Tech. 58 471–481