J. Plasma Fusion Res. SERIES, Vol. 9 (2010)

Correlation of low-frequency fluctuations measured by the gold neutral beamprobe and end plates in GAMMA 10
Yoshiaki MIYATA, Masayuki YOSHIKAWA, Masanori MIZUGUCHI, Youhei OONO, Fumiaki
YAGUCHI, Nanako MATSUDA, Hidetaka MURATA, Makoto ICHIMURA, Tatsuya MURAKAMI
and Tshuyoshi IMAI
Plasma Research Center, University of Tsukuba(Received: 30 October 2009 / Accepted: 26 February 2010)

The electrostatic instability due to the density gradient was observed in many magnetic confinement devices.
The electrostatic instability and radial particle flux due to the instability were also observed by using heavy ion
beam probe (HIBP) in GAMMA 10. The potential fluctuation of the end plates settled at both side of GAMMA 10
was measured for the first time. The correlation between the potential fluctuation measured by HIBP and thepotential fluctuation of end plates was assessed. We found that the measurement of end plates potential is usefulmeasuring technique of radial fluctuation profile.
Keywords: heavy ion beam probe, electrostatic probe, mirror device, potential fluctuation, drift wave instability

1. Introduction

In magnetic confinement fusion plasmas, the particle
and energy are important issues because the transports
cause the decreasing of the density and the temperature.
The formation of structures of inhomogeneous
magnetized plasma has been one of issues in modern
physics. The plasma particle and thermal energy run
away across the confinement magnetic field as a result of
the turbulence fluctuation due to the thermal force andinstabilities in plasmas. The particle and thermaltransports can’t be explained in terms of neoclassicaltransport theory which handles the effect only the
coulomb collision for the particle trajectory. The
elucidation of the anomalous transport which leads to theimprovement of the energy confinement time is one of
the main issues. The fluctuations due to the instabilities
cause the transports [1]. The ion temperature gradientmode is a branch of the drift wave called the universal
instability caused by the density gradient [2-4]. The drift
waves have been observed in many devices due to theplasma density gradient. Therefore, the study of themechanisms of both the transport and the suppression
leads to the reduction of the transports and the potential
fluctuations [5].
Figure 1 shows schematic view of GAMMA 10. The
x-axis and the y-axis are perpendicular to the magnetic
field in the horizontal and vertical directions, respectively.
The z-axis is parallel to the magnetic field. In the tandem
mirror GAMMA 10, the lengths of central, anchor andplug/barrier cells are 6.0m, 4.8m and 2.5m, respectively.
Magnetic field strength at the mid-plane of the central
cell is 0.41T in the standard operation and mirror ratio is

ECRH

Fig.1

ICRF

ECRH

ICRF

ICRF

ECRH

Schematic view of the GAMMA 10 tandem mirror.
Magnetic coil set and magnetic flux tube withheating systems, as well as the axial profiles ofmagnetic field (solid curve) and potential (dashedcurve) are illustrated.

5. The anchor cells are located at both sides of the central
cell and consist of minimum-B mirror field which is
produced by a base ball coil. The magnetic field strengthis 0.61T at the mid-plane of the anchor cell and mirror
ratio is 3. The plug/barrier cells are located at both endsof GAMMA 10, where the electron confinement
potentials and ion confinement potentials are produced.
The plasma is created by plasma guns, and heated andsustained using ion cyclotron range of frequency (ICRF)
heating systems. There are three types of oscillators
named RF1, RF2 and RF3. The waves excited with RF1
and RF2 systems take on the plasma production and ion
heating in the central cell, respectively. The ion andelectron axial confinement potentials are produced using
electron cyclotron resonance heating (ECRH) at bothsides of GAMMA 10. We use the heavy ion beam probe

author’s e-mail: miyata@prc.tsukuba.ac.jp84©2010 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchY. Miyata et al., Correlation of Low-Frequency Fluctuations Measured by the Gold Neutral Beam Probe and End Plates in GAMMA 10(HIBP) for potential measurement of core plasma at
central cell in GAMMA 10. The electrostatic fluctuations
are ever observed by HIBP during ICRF heating [6, 7].
The plasma touches the end plates along with themagnetic field. The end plates made of stainless steel aresettled at both end sides of GAMMA 10. In this paper, thepotential fluctuation of the end plates was measured forthe first time. The correlation between the potential
fluctuation measured by HIBP and that of end plates wasassessed.

End Cell

X Axis#5#4#3#2 End Plate#1

Z AxisOuter Mirror
ThroatMagnetic Field Line

2. Gold neutral beam probe

We use a gold neutral beam probe (GNBP) system
for measuring the plasma potential. Figure 2 shows
schematic view of GNBP. The features of GNBP areusing the neutral primary beam and the negative gold ion
by Cs sputtering [8]. The energy and the incident angle ofthe primary beam passing the plasma center are about 12
keV and 40 degrees, respectively. Typical primary beam
current is obtained 2 μA using the Faraday Cup. The
GNBP system has two incident angle electrostatic
deflectors of the vertical and the horizontal directions. A
parallel plate type electrostatic energy analyzer with theincident angle of 45 degrees is installed on the x-y plane.
In the analyzer, the micro-channel plate detector of 32
anodes which is mounted along y direction is utilized forthe beam detector. The detected positive secondary beam
is derived from the neutral primary beam ionized at theionization position. The electron-impact ionization
process is dominant in a case of the ionization of the
primary beam. The secondary beam current depends onthe electron distribution function at the ionization
position. The density fluctuation is obtained from theperturbation of the detected beam intensity, and thepotential fluctuation is obtained from the perturbation of
the plasma potential. It is possible to measure thepotential, density fluctuations and their phase difference

Fig.3

divided plates. (Here, the Y-Axis is in theperpendicular direction to the plane).

at the arbitrary point simultaneously by GNBP.

3. End Plate measurement

The end plates consist of some divided plates. The
end plates are divided into five sections in radial direction
and are connected to ground though the cement resistor.
The end plate #1, #2, #3 and #4 cover the region of radiuscompared at central cell ~5.5, 5.5~7.8, 7.8~11 and 11~16cm, respectively. The #1, #2 and #3 end plates are divided
into four. The #4 and #5 end plates are divided into eightsections in circumferential direction and normallyconnected. Figure 3 shows schematic view of end platesystem. The 1 MΩ of cement resistor is connected to eachplate. The end plate potential is affected by changing of
this resistance value. Then it is possible to control theradial potential profile in GAMMA 10. The floating
potential of each end plate by using the 50 Ω of pick-up
resistor is measured. The electron mainly flows into theend plates because the electron is lighter than the ion. The
floating
potentialisusually
negativeandsignificantly-decreased to negative during the formationof axial confinement potential by using the local electron
heating.
The end plates are used for controlling the radialpotential profile. The high-performance analog-digitalconvertor (ADC) was installed to the end plates. The
established ADC has the resolution of 16 bits and it ispossible to measure 16 channels simultaneously. The
sampling frequency of waveforms is 333 kHz. It is easy
to assess the correlation between the fluctuation measured
by GNBP and end plates because both measurement
equipment use the same ADC. It is possible to measure
the radial fluctuation profile and assess the correlation byloading the end plates of radial position. The fluctuationof end plate potential was analyzed by using the sample
of 512 points and haning window.

GAMMA 10
Vacuum Vessel

Fig.2

Gold neutral beam probe system in the central cellof the GAMMA 10 tandem mirror. In the case of avertically directed beam sweep for radial potential
profileobservations

inasingleSchematic view of end plates settled at both sideof GAMMA 10. The end plates consist of somedischarge,

ionization points move in the vertical direction due

4. Results and Discussions

to the incident angle changes. (Here, the z-axis isin the perpendicular direction to the plane).
85

Y. Miyata et al., Correlation of Low-Frequency Fluctuations Measured by the Gold Neutral Beam Probe and End Plates in GAMMA 10500

1Fig. 4a

4

0.8

3

0.6

2

0.4
Line Density

1

0.2

Diamagnrtism
0
50

75

75

100
125
Time[ms]

End Potential[V]Fig. 4cFig.475

Potential Fluctuation Level[rel.unit]
4

2 10

4

1 10

4

0

5

10
15
Radius[cm]20

Potential Fluctuation Level[rel.unit]

Frequency[Hz]

3 10

1000

Fig. 6b
100

10

1

0

5

10
15
Radius[cm]20

fluctuation had the peak near 10 kHz every time. The
fluctuation near 10 kHz was identified by electrostatic
probe (ESP) established in circumferential direction. The
observed fluctuation was estimated as the drift-type
fluctuation with the azimuthally mode number of 3.
Because the fluctuation rotated right-handed to themagnetic field line. We calculated the mode number by
the phase difference between two ESPs separated incircumferential direction. Previous research hassuggested that the drift-type fluctuation occurs strongly ina high plasma pressure case at central cell [9]. Figure 6ashows the frequency profile of this drift-type fluctuationfrom 136.2 to 143.8 ms in radial position. These results
show the drift-type fluctuation rotates in the same
frequency in radial direction. Figure 6b shows the profile
of radial potential fluctuation level measured by GNBP
from 136.2 to 143.8 ms. The potential fluctuation had thesame level in radial direction. These results show thedrift-type fluctuation has global structure in radial
direction.
The fluctuation of end plates potential was analyzed
on the same plasma shot. Figure 7 shows the fluctuation
spectrum of #1 end plate potential at 134.7 ms. The
fluctuation of end plate potential had the peak near 10
kHz every time in the same way as the potential
fluctuation measured by GNBP. Figure 8a shows thefrequency profile of this potential fluctuation measured

150

150

central cell. The solid and dotted curves are the
and

4

4 10

143.8 ms.

diamagnetism measured by diamagnetic loop in thedensity4

fluctuation level measured by GNBP from 136.2 toa) Time evolution of the electron line density

line

4

radial position. b) Profile of radial potential

measured by microwave interferometer and theelectron

4

1 10
2 10
3 10
Frequency[Hz]measured by GNBP from 136.2 to 143.8 ms in#1 EndPlate#2 EndPlate#3 EndPlate#4 EndPlate
100
125
Time[ms]0

Fig.6 a) Frequency profile of this drift-type fluctuation

-100

-300
50

1

4

0

0

-200

10

Fig. 6aR=1.5[cm]R=5.1[cm]R=13.1[cm]050134.7[ms]Spectrum of potential fluctuation measured by

4 10

200
100

100

GNBP near the central cell at 134.7 ms.

300

0
150

100
125
Time[ms]

Fig.5

Fig. 4b400
Potential[V]5

Diamagnetism[10-4Wb]

Electron Line Density[1013 cm-2]

In GAMMA 10, after starting up the plasma with theboth sides of plasma gun, ICRF heating systems are usedin the central cell. The confinement potentials are formed
at both end mirror region of GAMMA 10 by local
electron heating. The plasma was heated from 50 ms by
ICRF heating and increased the ion temperature. In thisshot, RF1 and RF2 power were 180 and 150 kW,
respectively. The plasma confinement was improved from150 ms by electron cyclotron resonance heating. In thispaper, we focused attention on ICRF heating time from50 ms to 150 ms. Figure 4a shows the electron line
density measured by microwave interferometer and the
diamagnetism measured by diamagnetic loop in thecentral cell. The diamagnetism depends on thetemperature and density. It shows the plasma stored
energy. The electron line density and diamagnetism
became the constant value from 100 ms. Figures 4b and4c show the central potential measured by GNBP and end
plate potential, respectively. Both central and end plate
potential were kept in a steady state on the time whendiamagnetism became the constant value.
The potential fluctuation was measured by GNBP at
central cell. It is necessary that some plasma shots inwhich the heating sequence was fixed for discussing thecharacteristic of fluctuation on radial position. For
measuring the radial profile we change the measurement
point every shot by deflecting voltage in the ion source of
GNBP. Figure 5 shows the spectrum of potential
fluctuation near the central cell at 134.7 ms. The power
spectrum was averaged by using root mean square (RMS)
averaging. The analysis time interval is almost 1.5 ms.
The RMS averaging points are 3. The potential

diamagnetism,

respectively. b) Time evolution of the central
potential measured by GNBP in radial position. c)Time evolution of the end plate potential from #1
to #4.
86

Y. Miyata et al., Correlation of Low-Frequency Fluctuations Measured by the Gold Neutral Beam Probe and End Plates in GAMMA 10

fluctuation at central cell. It seems unlikely that thedrift-type fluctuation occurs in a low plasma pressurecase because the magnetic field line diverges at end cell.
These results show that the drift-type fluctuation
occurring at the central cell which has high plasmapressure propagates from the central cell to the end cell.
The measurement of end plate obtains theinformation of core plasma in radial direction
simultaneously. It is also possible to analyze thefluctuation propagation in circumferential direction if theplates are disconnected each section. The measurement ofend plate is useful fluctuation measuring technique using
the feature of linear device which has the end.

Fluctuation Level of
End Plate Potential[rel.unit]

100

Fig.7

134.7[ms]
10

1

0.1

4

0

4

1 10
2 10
3 10
Frequency[Hz]

4

4 10

4

Fluctuation spectrum of #1 end plate potential at
134.7 ms.

Frequency[Hz]#1 End Plate(Rcc ~5.5[cm])#2 End Plate(Rcc 5.5~7.8[cm])#3 End Plate(Rcc 7.8~11[cm])#4 End Plate(Rcc 11~16[cm])

4

3 10

Fig. 8a

4

2 10

4

1 10

0

0

5

10
15
Radius[cm]1000Fluctuation Level of
End Plate Potential[rel.unit]

4

4 10

#1 End Plate(Rcc ~5.5[cm])#2 End Plate(Rcc 5.5~7.8[cm])#3 End Plate(Rcc 7.8~11[cm])#4 End Plate(Rcc 11~16[cm])100

5. Conclusion

Fig. 8b

We use GNBP for the measurement of potential
fluctuation in core plasma region. The data analysis
system of end plate settled at both side of GAMMA 10
was upgraded for fluctuation measurement. The drift-type
fluctuation with the azimuthally mode number of 3 near
10 kHz was observed using GNBP at central cell androtates in same frequency in radial direction. The
fluctuation of end plate potential also has peak near 10
kHz in radial direction. It showed a strong correlation
between the potential fluctuation measured by GNBP and
the potential fluctuation of end plate. These results showthat the drift-type fluctuation occurring at central cellwhich has high plasma pressure propagates from central
cell to end cell. We found that the measurement of end
plate is useful measuring technique of core plasma.

10

1

20

0

5

10
15
Radius[cm]20

Fig.8 a) Frequency profile of this potential fluctuation
measured by end plate #1 - #4 from 136.2 to 143.8
ms. The fluctuation near 10 kHz was observed inradial direction. b) Profile of potential fluctuationlevel measured by end plate #1 - #4 from 136.2 to143.8 ms.

by end plate #1 - #4 from 136.2 to 143.8 ms. The
fluctuation near 10 kHz was observed in radial direction.
Figure 8b shows the profile of potential fluctuation levelmeasured by end plate #1 - #4 from 136.2 to 143.8 ms.
These results show that potential fluctuation of end plateis the same level in radial direction in the same way as
the potential fluctuation measured by GNBP.
Figure 9 shows the cross spectrum between thepotential fluctuation measured by GNBP and potential
fluctuation of #1 end plate at 134.7 ms. A strong
correlation was observed near 10 kHz. The drift-type
fluctuation measured at central cell correlated strongly
with the fluctuation measured at end cell. The coherence
and cross-phase between end cell and central cell were
0.7 and 0.2 at 134.7 ms, respectively. Therefore thisfluctuation at end cell appears identical to the drift-type

6. Acknowledgement

The authors would like to thank members of
GAMMA 10 group of the University of Tsukuba for theircollaboration.�This work is performed with the supportand under the auspices of the NIFS Collaboration
Research Program.�NIFS04KUGM009�This work waspartly supported by Ministry of Education, Culture,
Sports, Science and Technology, Grant-in-Aid for
Scientific Research in Priority Areas, No 16082203.

7. References[1] B. Fischer et al., Plasma Phys. Control. Fusion 31, 453(1989).
[2] H. W. Hendel et al., Phys. Rev. Lett. 18, 439 (1967).
[3] H. W. Hendel et al., Phys. Fluids. 11, 2426 (1968).
[4] W. Horton, Rev. Mod. Phys. 71, 735 (1999).
[5] E. J. POWERS., Nucl. Fusion 14, 749 (1974).
[6] Y. Miyata et al., Trans. Fusion. Tech. 55, 168 (2009).
[7] Y. Miyata et al., J. Plasma Fusion Res. 2, S1101 (2007).
[8] Y. Miyata et al., Rev. Sci. Instrum. 79, 10F308 (2008).
[9] S. Tanaka et al., Rev. Sci. Instrum. 70, 979 (1999).

Cross Spectrum[rel.unit]

1000

10
1
0.1
0.01

Fig.9

134.7[ms]

100

0

4

4

4

2 10
3 10
1 10
Frequency[Hz]

4

4 10

Cross spectrum between the potential fluctuation
measured by GNBP and potential fluctuation of #1
end plate at 134.7 ms.

87