J. Plasma Fusion Res. SERIES, vol.5 (2002) 94-99

Plasma Gonfinement in an RF-driven Tandem Mirror with aStrong Temperature Anisotropy
ICHIMURA Makoto, CHO Teruji, HIGAKI Hiroyuki, HIRATA Mafumi, HOJO Hitoshi, ISHII Kameo,
ITAKURA Akiyosi, KATANUMA Isao, KAWAMORI Eiji, KOHAGURA Jyunko, NAKASHIMA Yousuke,
OKAMOTO Yuji, SAITO Teruo, TATEMATSU Yoshinori, YATSU Kiyoshi and YOSHIKAWA Masashi
Plasma Research Center, University of Tsukuba, Tsukuba, Ibaraki 305-8577, Japan(Received: 12 December 2001 / Accepted: 2 August 2002)

Abstract
In the GAMMA l0 tandem mirror, the axial transport by the excitation of the Alfv6n ion cyclotron(AIC) mode due to strong temperature anisotropy is discussed. The AIC modes are spontaneously excitedin the high beta plasmas with a strong temperature anisotropy. The amplitude of the modes can becontrolled by changing the cyclotron resonance conditions. The increase of the line density andanisotropy are affected by the excitation of the AIC modes. A resonant interaction between electrons andthe AIC modes are observed in the end-loss energy analyzer. Pitch angle scattering ofhigh energy ionstrapped magnetically in the central cell and the enhancement of the end loss of high energy ions are also
observed experimentally.

Keywords:
tandem mirror, ICRF, ECH, axisymmetrization, temperature anisotropy, AIC mode, axial transport,
radial transport, high energy ion, pitch angle scattering

1. lntroduction
The high density plasma production anddirection [3].

confinement with electrostatic potentials are the major

central cell is another important issue. The hot ion mode
has been appeared and the ion temperature has reachedat 10 keV when the strong ICRF heating is applied in
the central cell [4]. In such a mode of operation, theThe realization of the high beta plasmas in theimportant issues in the present tandem mirror
experiments [1,2]. In the GAMMA l0 tandem mirror,
the ion cyclotron range offrequency (ICRF) heating andplasmas with a strong temperature anisotropy are
confined magnetically. In the high beta plasmas with thestrong anisotropy, the Alfv6n ion cyclotron (AIC) modes

the electron cyclotron resonance heating (ECH) are used

for the plasma production and heating, and for the
potential formation, respectively. The GAMMA 10 has
MHD anchors with the minimum-B field configurationand is arranged to be effectively axisymmetrized
configuration. The axisymmetrization of the heating
system is the most important subject on the mirror
experiments in relation to the radial particle transport.
The improvement of ICRF antenna systems has been
performed because the antenna configuration in thecentral cell affects the plasma profile in the azimuthal

are excited spontaneously. The plasma confinement will

be affected from the externally applied RF waves andalso spontaneously excited waves in the plasma.

Occasionally, the saturation of the density and the
diamagnetism is observed when the power of ICRF isincreased. The magnetic mirror configuration iscommon in the toroidal devices and also in the space@20O2 by The Japan Society of Plasma

Corresponding author's e -mail: ichimura@ prc.tsukuba.ac.jp
94

Science and Nuclear Fusion ResearchIchinrura M. et al., Plasma Confinement in an RF-driven Tandem Minor with a Strong Temperature Anisotropy

plasmas. In this manuscript, the experimental

diamagnetic loops arrayed in the axial direction in thecentral cell. Electrostatic and magnetic probes are set inboth axial and azimuthal directions for measuring theobservations in relation to the particle transport in theaxial direction are described.
In the next chapter, the experimental setup isbriefly indicated, and characteristics of the AIC modes
and the possibility of the control of the AIC modes are

density and magnetic fluctuations, respectively. To
measure the behavior of high energy ions, twodiagnostics with semiconductor detectors are installedon the east end (east end High Energy-ion Detector:
eeHED) for the end-loss ions and at the midplane of thecentral cell (central cell HED: ccHED) for themagnetically trapped ions. The structure of eeHED andthe sensitivity of the semiconductor detector for protons

described in Chap. 3. In Chap. 4, the effects of AIC
modes on the particle transport are indicated and thesummary is in Chap. 5.

2. Experimental setup
In the GAMMA 10 tandem mirror, three ICRF

are described in ref. 8. The ccHED is inserted
perpendicularly to the magnetic field line and ispositioned just outside of the limiter radius. By rotating
the ccHED against the normal axis to the magnetic field
line, a pitch angle distribution ofhigh energy ions in thecentral cell can be measured [9]. High energy ionssources (RFl, RF2 and RF3) are used in the central cellfor the initial plasma production and heating. The initialplasma is produced by using short-pulse plasma guns (lmsec) and applying an ICRF pulse (RFl) with hydrogengas puffings. frast Alfv6n waves excited by RFI in thecentral cell propagate to the anchor cells which areneighboring on both sides ofthe central cell. These fast
Alfv6n waves are converted to slow waves in thewhich are produced by a fundamental cyclotron heating
are mainly trapped in the magnetic mirror field of thecentral cell. The minimum energy of the detection isroughly estimated to be around 10 keV.

transition region between the central and anchor cells[5,6] and heat ions in the anchor cell. The magnetic fieldstrength in the anchor cell is adjusted so that thefundamental cyclotron resonance layer exists at the
midplane for keeping MHD stabilization. The antennas
for RFI are so-called Nagoya Type III antennas andinstalled at both east and west ends of the central cell,
To avoid the strong interference between east and west
antennas, the frequency of the west RFI antenna (10.3
MHz) is slightly higher than the frequency of the east
antenna (9.9 MHz). For the ion heating (RF2), theconventional double half-turn antennas, DHT, are placed
inside of the RFI antennas. Slow Alfv6n waves excitedby RF2 (6.36 MHz) propagate to the midplane of thecentral cell and heat ions because the fundamental ion
cyclotron res()nance layer exist near the midplane.
Recently, an ICRF system (RF3) for launching highharmonic fast waves has been constructed. RF3 with afrequency of 6ll MHz is successfully used for the higher
density plasma production [7]. Typical input powers of
RFl and RF2 are around 200 kW and that of RF3 isbelow 100 kW. The magnetic field profile in the central
and anchor cells, locations of ICRF antennas and thefrequencies of RFl, RF2 and RF3 normalized by the
local ion cyckltron frequency are indicated in Fig. 1.
The strength ol'the magnetic field at the midplane of thecentral cell is 0.4 T and the mirror ratio is 5 in thestandard mode of operation. A limiter with a diameter of

(a)

^3
t

Central Cell

West Anchor GellE

anchor
midplane-RF2-o2 DHT{east)(west) -RF3

c

E
!i

;1

Type-lll

E
ltI

o0

y' Allenna

0246
Lcentalcellmidplans

Z-axis(m)

(b)

.-3
,-O

iz
1

%

Z-axis (m)Fig. 1 (a) Magnetic field profile and location of ICRF antennas, (b) Frequencies of RF1, RF2 and RF3 normalized by the local ion cyclotron frequency.

0.36 m is set near the midplane.
The temperature anisotropy is evaluated from three95

Ichimura M. et al., Plasma Confinement in an RF-driven Tandem Mirror with a Strong Temperature Anisotropy

3. Experimental results
3.1 Excitation of AIG modes in plasmas with a, (a)strong temperature anisotropy
In the case of a strong ICRF heating with the input-ll

midplane;=power of RF2 up to 250 kW, plasmas with the ion
temperature of more than l0 keV have been achieved.
Because the cyclotron resonance layer exits near the

EI
trel

midplane of the central cell, the temperature anisotropy,

.g

CDa!v

'---,-,/ off-midplaneEvo

A=TtlTl, which is defined as a ratio between
temperatures in the perpendicular, 71, and parallel, T11,
directions to the magnetic field line, becomes more than

15

(b)
f

10. The Alfv6n ion cyclotron (AIC) modes are
spontaneously excited in such high beta, fl plasmas with

>10

<

o

!t

.Es
C

==CL

o

CL

the strong temperature anisotropy. In GAMMA 10,
magnetic fluctuations due to the AIC modes have been
observed experimentally in the parameter range of
PA2>0.3. The discrepancy from the theoreticalprediction of BA2>3.54 [0] has been explained by thepressure distribution in the axial direction Il]. As
indicated in Fig. 2(a), signals of diamagnetic loops
located at the midplane and at z=1.5 m from the

0

E

,f'

0

9

50

100

Time (msec)
Fig. 2 (a) Signals of diamagnetic loops located at the
midplane and off-midplane, (b) Temporal evolu-

midplane increase with time and the differences between
both signals indicate the anisotropy as shown in Fig.
2(b). When the diamagnetism at the midplane reaches athreshold value, the AIC modes appear. In Fig. 2(b), thetotal amplitude of the magnetic fluctuations which aredetected by a magnetic probe in the AIC frequency
range is plotted. The anisotropy becomes more than 10.
Figure 3 shows a frequency spectrum of the magnetic
probe signal. The peak of 6.36 MHz which corresponds
to the ion cyclotron frequency near the midplane of thecentral cell is externally applied frequency for theplasma heating. Just below the 6.36 MHz peak, several
discrete peaks are observed. These peaks indicate thetion of estimated anisotropy and amplitude of the
AIC modes.

104

RF2 for heating

Atc modes

f
d

.^1
'tu

excitation of axial eigenmodes which are determined by
the plasma pressure profile in the axial direction. The
number of the peaks and the amplitude of each peak

\l

\

rc-2

7

Frequency [MHz]depend on the plasma parameters. By changing themagnetic field strength under the fixed frequency, thelocation of the resonance layer is varied resulting in theFig. 3 Frequency spectrum of the magnetic probe.

change of the anisotropy. Figure 4(a) shows theresonance layer is located in the off-midplane.

anisotropy as a function of the diamagnetism for typicaltwo cases of the magnetic field strength. In the low
magnetic field case, the strength of the magnetic field is
reduced to 977o of the standard operation. Figure 4(b)shows the amplitude of the AIC modes as a function of

3.2 Effects of AIC modes on the particle

transport
The drive force of the AIC modes is the anisotropic
energy distribution of ions. Then, the behavior of theplasma in the central cell is affected from the excitationof the modes. Figure 5 shows temporal evolution of theline density, the diamagnetism and the amplitude of AIC

the anisotropy. On both cases the value of the
diamagnetism is fixed to be same as indicated in the
figure. The amplitude of the AIC modes becomes small
clearly in the low magnetic field case, that is, the96Ichimura M. et al., PlasmaConfinement in an RF-driven Tandem Mirror with a Strong Temperature Anisotropy(x 10'5 wb)( x1013 cm-2 )610standard case

\

*10

o

L

@@-

o

.9

tr
5

,{

02550
Time (msec)
Fig. 5 Temporal evolution of line density, diamagnetismand amplitude of the AIC modes.

48
Diamagnetism(l0'5 Wb)(b)passing particles due to the acceleration in the4

perpendicular direction contributes to the increase in the

Diamag.=$.5110'5 Wb

density. When the diamagnetism reaches at the thresholdvalue and the AIC modes appear, the increasing rate of

?

oS

ttoo

the density becomes small or sometimes zero. lt

standard case >trsuggests the number of particles trapped magnetically inthe central cell stops to increase and the axial transportof the bulk ions into the loss region is enhanced. Theoooanisotropy also becomes stronger with thediamagnetism. When the AIC modes appear, thelow field case

t,
=
=CL

\

anisotropy saturates even if the diamagnetism still
increases.

E

The resonant interaction between electrons and the0

AIC modes has been also observed in the experiments.
By using a multigrid type energy analyzer installed on

051015the end, electrons escaping from the confinement region

Anisotropy

are detected. In Fig. 6, the temporal evolution of the
diamagnetism, the amplitude of the AIC modes and thesignal of the end-loss electron flux are indicated. The
amplitude of AIC modes is plotted as in Fig. 5. The
stepwise increase in the end-loss electron flux with theappearance of the AIC modes are clearly observed . In
GAMMA 10, the power from ICRF sources is absorbed
directly by ions. The electrons are heated mainly due tothe drag from such hot ions. The enhancement of theelectron flux in Fig. 6 can not be explained by theincrease of the electron drag power and the existence ofFig. a (a) Anisotropy as a function of diamagnetism inboth standard and low field cases, (b) Amplitudeof the AIC modes as a function of the anisotropy

under the fixed diamagnetism conditions.

modes. The arnplitude of AIC modes is plotted as a
trace from the top of figure to the bottom in an arbitrary
unit. In a start-up period, the density increases and thetemperature also increases as indicated in the figure. The
start-up of the GAMMA 10 plasma depends strongly on
the anchor formation for the MHD stabilizatton ll2l.
After build-up of the anchor plasma, the central cell
plasmas start l-o increase and are heated by applying
RF2 pulse. In addition to the plasma production with thethe additional electron Landau damping of the AIC
modes has been suggested [13]. By analyzing energy
distributions of electrons on both just before and after
AIC modes excitation, the clear increase of the electron

gas puffing near the RFI antennas, the trapping oftemperature is observed.
9'7

Ichimura M. et al., Plasma Confinement in an RF-driven Tandem Mirror with a Strong Temperature Anisotropy(a)l xto's wo;

60

x

:

AIG modes

=
ci

lr.

c
o
L

e

g(, 1.5

CEHED

=?n

uJ

0
o
o

o

Ittr

.9
(t,

IE

tr

I

IJJ 0

25

25

0

Time (msec)(b)Fig. 6 Temporal evolution of diamagnetism, end-loss
electron flux and amplitude of the AIC modes.

50

Time (msec)

The resonant interaction between bulk ions and the

AIC modes has been discussed in ref. 14. The effects of
the AIC modes on the particle transport have been

Pitch Angle 75"

observed clearly in the behavior of the high energy ions.

Figure 7 shows the signals of high energy ion detectors
on both perpendicular (ccHED) and parallel (eeHED)

directions. In Fig. 7(a), the temporal evolution of bothsignals and the amplitude of the AIC modes areindicated. The amplitude of AIC modes is plotted as inFig. 5. The signal of the ccHED increases with anincrease in the diamagnetism until 5Omsec due to theheating. The AIC modes appear at 3Omsec and the0255075

amplitude also increase. When the amplitude of the AIC
modes becomes strong, the ccHED signal begins todecrease though the diamagnetism is still increasing.
While, the eeHED signal increases clearly with theTime (msec)

Fig. 7 (a) Temporal evolution of signals of ccHED and
eeHED and amplitude of the AIC modes, (b) signals of ccHED on pitch angles of 90, 75 and 60 degrees.

increase of the amplitude of the AIC modes as shown in

Fig. 7(a). It is seen the behaviors of magneticallytrapped ions and escaping ions are out of phase. Figure7(b) shows the signals on the pitch angles of 90, 75 and
60 degrees. The signals on the smaller pitch angles (75and 60 degrees) are smaller than the signals on the large
pitch angle. It indicates that the axial pressurelarger pitch angle scattering due to spontaneously
excited waves are unknown. It is suggested that the AIC
modes excitation restricts the increase in the plasma
parameters on future tandem mirror experiments.

distribution of the ions in the central cell becomesstrongly anisotropic. The signals of the small pitch
angles tend to increase slightly though the signals of the

4. Summary

large pitch angles decrease with an increase of the AIC
modes. The behavior of ions with the small pitch angle
is the same as that in the end region. These behaviors on

In the GAMMA 10 tandem mirror, the Alfv6n ion
cyclotron (AIC) modes are studied in relation to theparticle transport in the axial direction. The AIC modes

the various pitch angles suggest the enhancement of thepitch angle scattering of ions in the velocity space. The

are shown to be controlled by changing the resonanceconditions of the ion cyclotron heating. A resonantinteraction between electrons and the AIC modes isobserved and the electron Landau damping is strongly

axial transport of the high energy ions due to the AIC
modes is clearly observed. The mechanism of such a98

Ichinrura M. et al., Plasma Confinement in an RF-driven Tandem Mirror with a Strong Temperature Anisotropy

suggested. Pitch angle scattering of high energy ionstrapped magnetically in the central cell and theenhancement of the end loss high energy ions are also
observed clearly when the AIC modes are excited

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99