J. Plasma Fusion Res. SERIES, Vol.2 (1999) 314-317

Alfv6n wave Excitation Due to Pressure Anisotropy
in the GAMMA1O Tandem Mirror
NAKAMURA Motoyuki, ICHIMURA Makoto, TANAKA satoru, KANAZAWA Seikou.
MOTEGI shinji, SAoSAKI Soshun, SAKATA Katsuaki, NAKAGAWA chikahiro,
KADOYA Kiyoomi, KAWABATA Toshiki, OHTA yuriko, HOJO Hitoshi,
MASE Atsushi, TAMANO Teruo and YATSU Kiyoshi
Plasma Research center, university of rsukuba, Tsukuba, Ibaraki 305-8577, Japan(Received: 8 December 1998 / Accepted: 20 May 1999)

Abstract
Alfvdn ion cyclotron (AIC) modes are driven by a strong temperature anisotropy in the case of thehigh power ion cyclotron range of frequency (ICRF) heating on the GAMMAI0 tandem mirror.
Parameters on which the AIC modes are observed in the GAMMAI0 are much smaller than thetheoretically predicted parameters. The axial structure of the AIC modes is measured by magnetic probes
and depends strongly on the axial pressure profile. It is suggested that the axial boundary condition isessential for the excitation of the AIC modes.

Keywords:
tandem mirror, anisotropy, AIC modes, eigen mode, boundary condition, ion distribution

1. Introduction

peaks in the frequency spectrum which indicate theexcitation of eigen modes in the axial direction. The
scattering of ions to the parallel direction due to the AIC

An ion cyclotron range of frequency (ICRF) wave
has been effectively used for plasma heating in themodes is predicted theoretically. In the mirror

GAMMA10 tandem mirror. In the central cell which is amain plasma confinement region, an ion temperaturereaches several keV and the temperature anisotropy T/211 (defined as the temperature ratio of the perpendicular
to the parallel to the magnetic field line) becomes above
10. As a result, Alfv6n ion cyclotron (AIC) modes are
spontaneously excited due to the strong anisotropy Il].
The AIC modes are one of the micro-instability and arein the branch of shear Alfv6n wave. Although there aremany theoretical works for the AIC modes, there arefew experimental studies in the laboratory plasma. The
AIC modes in the GAMMAIO tandem mirror are
observed in the parameter region above Br(71/7,,), - 9.3[2], which is much smaller than the condition for theabsolute instability of BITIT)2 - 3.52, predicted by theconfiguration, an increase of the scattering implies thedegradation of the confinement. In this paper, we study
the excitation mechanism of the AIC modes from theaxial structures of the AIC modes and the plasma
parameters.

2. Experimental Setup
GAMMAI0 is the axisymmetrized tandem mirror
which consists of five mirror cells. The central cell isthe main plasma confinement region where the vacuum
chamber has an inner diameter of 1.0 m and a length of6.0 m and the magnetic field strength in the midplane is0.41 T. The ICRF antennas for plasma heating arearranged near both ends of central cell and excite thepresent theory [3]. The AIC modes have several discrete
Corre sponding author's e-mail: nakamura@ prc.tsukuba.ac.jp314@1999 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchNakamura M. et al., Alfvln Wave Excitation Due to Pressure Anisotropy in the GAMMAI0 Tandem Minor

slow wave. The ion cyclotron resonance layers exist
near the midplane of the central cell. The slow wave
propagates to the resonance layer and transfers theenergy to ions via the cyclotron dumping. Two anchor
cells for the macroscopic stability are located on bothmodes in the GAMMAIO is observed as the eigen
modes with discrete peaks in the frequency spectrum'
Each peak has different ft11 in the initial phase' Ansides of the central cell and two plug/barrier cells for theformation of the confinement potential are located at theAIC modes depends on B1 and the temperature
anisotropy of ions and is insensitive to the energy

outermost region.

distribution of the electrons [6]. This result is consistent
with the numerical calculation including the effect of theexistence of the axial boundary condition is suggested. It
becomes clear experimentally that the amplitude of theThree diamagnetic loops are arranged on thepositions ofz =-0.3 m, z = +1.5 m ande = +1.95 mto
evaluate the axial pressure distribution. The pressure
anisotropy is estimated from the diamagnetic loop arrayelectron temperature. Figure 2 shows the time evolutionof (a) plasma parameters, (b) k11 of each peak of themodes and (c) the amplitude of the AIC modes on thetypical discharge. In Fig. 2(a), the value of theby using the axial pressure profile models [4], and MHD
equilibrium equation [5]. We measure the magnetic
fluctuations generated in the plasmas by using thediamagnetic signal near the midplane is twice as large asthat off-midplane. It means that the central plasma has
strong temperature anisotropy. In Fig. 2(b), k;1 of eachpeak approaches to nearly zero from a finite value as

magnetic probes. The magnetic probes are installed
along the magnetic field line and their positions are z =-1.12 m and z - -1.28 m to measure axial structure ofincrease of the diamagnetic signals. In Fig. 2(c), theamplitude of AIC modes becomes remarkably large
when k;1 reaches zero. Since the probes are located off-

the AIC modes. The probe signals are analyzed by using
a conventional fast Fourier transform (FFT) method andthe axial wave numbers ft11 are calculated from the phasedifference of two probes.
10

3. Experimental Results and Discussion
3.1 Characteristic of the AIC modes
Figure I shows the power spectrum of the magnetic

E?ll ^.9,E=
EDq'probe signal. The peak of 6.36 MHz in this figure is awave excited by the ICRF antennas for the plasma(gbEFovheating. The AIC modes are shown below the ion
cyclotron frequency, wherc al9"i = 0.8 - 0.9. The AIC105

AIC modes

104

o

20
Anisotropy

16>
CL

129
o

64

8.9tr

2

400tt(!

03E
o:-lfE -2\q,

{€103
lti

8(a)

=offi293;
3ddl-_ 10
lto
1-3
3.0
2.0cL<E- 1.0

10'110'25.5

5.7 5.9 6.1

6.3

ozb

6.5

Frequency(MHz)

Time(msec)

Fig. 1 Power spectrum of the magnetic fluctuations
measured by the magnetic probe. The peak of
6.36 MHz is applied ICRF for the plasma heating.
AIC modes are excited in the range of olQ"t = 0.8 -Fig. 2 Time evolution of the plasma parameter on thetypical discharge: (a) an anisotropy and theplasma pressure at the midplane and offmidplane in the central cell, (b) &, of the AIC
modes. (c) the amplitude of the AIC modes.

0.9.

315

Nakamura M. et al., Alfv6n Wave Excitation Due to Pressure Anisotropy in the GAMMAI0 Tandem Mirror

midplane at z = -l .12 m and z = -l.28 m, the variationof /<,' indicates that there are two different regions of a
propagating wave and a standing wave. The AIC modes

When the electron cyclotron resonance heating (ECRH)

in both plug/barrier cells is used for the potential
formation, the density in the central cell increases due tothe improvement of the confinement. A typicaldischarge is shown in Fig. 4. Figure 4(a) shows theare propagating from the midplane in the case of thefinite k1, and become standing waves when t1 - 0 [7]. In
the previous experiment, the AIC modes are observed as

temporal evolution of the line density, the diamagnetic
signal and the anisotropy. An initial plasma is produced

the standing wave by inner probes located near 7 = -Q.!,

m. It is considered that the boundary of two regions

and heated by ICRF waves and the potential

passes through the probe location as increase of theof the AIC modes, it is necessary to understandconfinement by ECRH is performed from 130 ms to 190ms. The density increases during ECRH pulse. Figure4(b) and 4(c) shows the temporal evolution of the phaseparameters of the boundary condition and the reflection

difference and the amplitude of the AIC modes,

mechanism.

respectively. As mentioned previously, the pressure atthe probe location increases when the anisotropy
becomes weak in the case of the same diamagnetic
signal at the central cell midplane. The boundary

plasma parameters, To clarify the excitation mechanism

3.2 Axial boundary conditions of the AIC
mod6s
To find the parameters of the boundary condition,
we have analyzed data on the following twoexperiments. One is an experiment with the different(ar10

magnetic field strength. In the case, the axial

E8.9,^qll

distribution of the plasma pressure changes due to thedifferent location of the cyclotron resonance layer. We
employ two magnetic field conditions of 0.41 T and
0.39 T. The location of ICRF resonance layer in the caseof 0.39 T exists at the location outer than in the case of0,41 T. As a result, the axial pressure distribution of0.39 T is relatively flat in the axial direction. For;=
CDq'oofr.go=Br8:331

6:,/' ' "-42010050150Time(msec)

250

analysis of the AIC modes, we adopt the experimental

conditions with the same diamagnetic signal at theF 1oo

midplane. Figure 3 shows the typical discharges of thetwo condition. Figure 3(a) shows the temporal evolution(b)

Bo=o'41T.

__rS

F rooof the diamagnetic signals in the central cell on thetypical discharges. A solid line indicates the case of0.4l
T and the dotted line 0.39 T. In both cases, thediamagnetic signal at the midplane reaches 6.0 x
10 s Wb, it means the same pressure at the central cellcooo5002468

250

eq200

6l200

Bg=0'397

tt#10Dlamagnetism(10'5W b)

t'omidplane. Figure 3(b) shows the parameter region of the0.5

3Fo: -0.5

AIC modes in B1-anisotropy space. In this figure, open
circles and closed circles mean the cases of 0.41 T and0.39 T, respectively. The B1 at the midplane is almost
equal and the anisotropy is different in consequence ofthe location of ICRF resonance layer. Figure 3(c) shows
the phase difference between two probes set at z = -1.12t'. , r Standing

0fpo-1.5=o-2-1

Wave

Bd:0.41r :o o-^t.ood\86=0.397

o?amasfietismfiro'sw%)

toz=1.2m

m and z = -1.28 m as a function of the local
diamagnetism estimated from the axial pressure

Fig. 3 Plasma parameters in the experiments with thedifferent locations of the ICRF resonance layer: (a)distribution. Although the parameter region is different,&1 in both cases closes to 0 at the same value about 4.5 xl0-5 Wb. This suggests that the boundary is determined

typical diamagnetic signals in both cases: solidline for 0.41 T and dotted line for 0.39 T, (b)parameter region of the AIC modes excitation. (c)by the pressure.
Another is an experiment with the different density.

the phase difference between two probes as afunction of the diamagnetic signals at z = -1.2 m.
316

Nakamura M. et aL, AlfvlnWave Excitation Due to Pressure Anisotropy in the GAMMAI0 Tandem MirrorE€ ato)$t8l-3-6mG€.+' 'F.co.-12roPy

e9mechanism of the wave reflection.

e9-c4. Conclusion
The AIC modes are strongly excited in theparameter region above Br(TrlTfiz - 0.3 in theCLDiamag.

4CEdensity rather than the temperature. The experimental
results shown in Fig. 4 indicate the temperature at theprobe location decreases and is essential for the15odenslty

g-: (b).{sGAMMA10 tandem mirror, which is much smaller thanthe parameters predicted by the theory. We discussed
the excitation of the AIC modes including the axial
boundary conditions. The AIC modes have two different

o0oogof]....

- 0.5o^=tt
aEo5!r-1

3.

lt&'!1..

;r'regions of the propagating wave and the standing wave.
These two regions are definitive element of AIC modes
excitation. It is suggested experimentally that the!An*r*.

-1.5

thsa.o(c)
at
rif

10

t9o.

0L_50

boundary is determined by the axial temperature
distribution and is essential for the excitation of the AIC
modes in the GAMMAI0.

,

15skr',Ei
100

Acknowledgements
The authors deeply acknowledge the GAMMAI0r 50200

group of the University of Tsukuba for their250

Tlme(msec)

collaboration and stimulating discussions.

Fig. 4 Plasma parameters in the experiment with thepotential confinement. ECRH is applied between

Referencestll

130 ms and 190 ms: (a) the line density, thediamagnetic signal and the anisotropy in thecentral cell, (b) the phase difference between two

M. Ichimura et al., Phys. Rev. Lett. 70, 2734
(1993).

t2l R. Katsumata, M. Ichimura, M. Inutake, H. Hojo,

probes and (c) the amplitude of the AIC modes'

A. Mase and T. Tamano, Phys. Plasmas 3,4489(1996).

between the standing wave and the propagating wave
regions is expected to still exist outside the probe

t3l G.R. Smith, Phys. Fluids 27, 1499 (1984).
t4l R. Katsumata, M. Inutake, M. Ichimura, N. Hino,location. However, Fig. a(b) shows the phase differenceof each mode becomes finite when ECRH is applied.
The finite k1 indicates the waves are propagating at theprobe location and the boundary moves toward themidplane. When the density increases due to theH. Onda, I. Katanuma, H. Hojo, A. Mase and S.
Miyoshi, Jpn. J. Appl. Phys. Part.l 31, 2249(reez).

[5] J.B. Taylor, Phys. Fluids 6,1529 (1963).
t6l M. Nakamura, et al., Jpn. J. Appl. Phys. Part.l 37,342 (1998).

potential confinement under the condition of the fixedheating power, it is considered the temperature
decreases relatively. The increase of the pressure at theprobe location is mainly due to the increase of thet7l A.Kumagai, et al.,Jpn. J. Appl. Phys. Part.l 36,6978 (1996).

3t7