J. Plasma Fusion Res. SERIES. Vol.5 (2002) 50-56

lmpact of Energetic lon Driven Global Modes on Toroidal
Plasma Gonfinements
TOI Kazuo, YAMAMOTO Satoshir, TAKECHI Manabu2. NAKAJIMA Noriyoshi.
ISOBE Mitsutaka, TAKAGI Shojit, MATSUNAGA Gol, OHDACHI Satoshi,
SAKAKIBARA Satoru, OSAKABE Masaki, SASAO Mamiko, KOTANI Jyunichi',
CHS and LHD Experimental Groups
National Institute for Fusion Science, Toki 509-5292, Japan
IDep. Energy Eng. and Science, Nagoya Univ. Nagoya, Japan
2Japan Atomic Energy Research Institute, Ibaraki, Japan(Received: 12 December 2001 / Accepted: 23 August 2002)

Abstract
Excitation of energetic-ion-driven Alfv6n eigenmodes (AEs) and their impact on energetic ion
confinement are widely and intensively studied in helical devices such as CHS and LHD as well as major
tokamaks. The excitation of AEs sensitively depends on the parameter space defined by the averaged
beam beta <ft11> and the velocity ratio V6nlV6 (V611 : injected beam ion velocity, Va: Alfv6n velocity). In
LHD, these two relevant parameters are widely scanned without suffering from current disruptions. So
far, toroidicity induced AE (TAE), global AE (GAE) and energetic particle mode (EPM) or resonant
TAE (R-TAE) were identified during tangential neutral beam injection (NBI) in CHS and LHD.
Moreover, a new coherent mode with the frequency by about 8 times higher than the TAE frequency wasobserved in NBI heated plasmas of LHD at low magnetic field (<0.6T). This mode may be induced byhelical field components of the confinement field. Nonlinear phenomena of bursting amplitude
modulation and fast frequency chirping are clearly seen for TAEs and EPMs in CHS and LHD. EPMs in
CHS and bursting TAEs in LHD enhance radial transport of energetic ions in certain plasma conditions.

Keywords:
Alfv6n eigenmode, TAE, HAE, EPM, energetic ion, toroidal plasma, heliotron/torsatron, alpha particle

1. Introduction

this reason, the interaction between energetic ions andAlfv6n waves are intensively being studied by using
NBI, ICRF heating and alpha particles in not only major
tokamaks but also helical devices. Toroidicity induced

In a D-T burning plasma, alpha particles generated
by fusion reactions would excite Alfv6n eigenmodes(AEs) and other energetic-ion-driven global modes, andthen might be expelled outside the plasma confinement

Alfv6n eigenmodes (TAEs), global AEs (GAEs) andenergetic particle modes (EPMs) or resonant TAEs (R-region by these global modes. The alpha-particle-driven
modes and their effects on alpha particle confinement
attract much attention from a point of view of a D-Tburning plasma in ITER []. It is particularly importantto accurately predict the linear growth and damping
rates of AEs and establish the stabilization methods. For
C o rre spondin g autho r' s e -mail : t oi @ nifs. ac

TAEs) are commonly observed in these experiments intokamaks and helical devices.
The energetic ion drive of TAE or the linear growthrate (y) is approximately expressed as [2]:@20O2 by The Japan Society of Plasmajp

Science and Nuclear Fusion Research

50

ToiK. et al., Impact of Energetic Ion Driven Global Modes on Toroidal Plasma Confinements,of I (r) o = fr < lJ or> I a;n I a"- O.Sl F (VA I vbt)

where al*611 and ato are respectively the energetic ion diamagnetic drift angular frequency and mode angular frequency, and F is related to the fraction of ions that resonate with the Alfv6n wave. The velocities Va and V61 are
the Alfv6n velocity and energetic ion velocity, respec-g
Ao

t' 0.,

tively. Parameter space typically scanned for AE-studies
in various toroidal devices is schematically shown in
Fig. 1. The parameter space in large tokamaks covers
the region predicted in ITER [1]. It should be noted thatvery wide range of these parameters is scanned in LHD
plasmas because they do not suffer from any current disruptions. These parameters are further widely scanned ina spherical tokrmak NSTX because of very low toroidal

0.01

00.s11.52?.63
v*ffu

field [3].
In this paper, we summarize experimental results

Fig. 1 Parameter space scanned for Alfv6n eigenmodestudies in various toroidal devices.

on energetic-ion-driven AEs obtained in CHS and LHD,

comparing with those from several major tokamaks andW7-AS shearless stellarator.
that the gap width is approximately proportional to the

2. Alfv6n eigenmodes in a toroidal plasma
We now summarize Alfv6n eigenmodes in a

amplitude of the relevant Fourier component e{'u andthe mode frequency. Therefore, the width of HAE canusually be much wider than TAE gap for helical devices
with large N such as LHD (N=10). Moreover, the reso-

toroidal plasma which has the following magnetic field
expressed by the Boozer coordinate (V, 0, Q).:nance condition between enersetic ions and AEs is ex-

B lBo= t +2 e['(V)cos(1t? - vNQ)

pressed as,

where Bo is the averaged field strength, efl is the ampli-

t/ tt,t -| +21(vNq* _ ttl

tude of each Fourier component and N is the field period(N=8 for CHS and N=10 for LHD). When two following

Accordingly, the resonance condition for HAE in LHD
is similar to that for TAE.

cylindrical Allvdn branches intersect with each other,various spectral gaps are produced, that is,

3. Excitation of Alfv6n Eigenmodes by

a = k t^'v A- - krr.*r,n * uN Ve .

energetic ions

The numbers m and n are the poloidal and toroidal mode

Various aspects related to AE- excitation are being
investigated in major tokamaks. Here, we only point out
two interesting observations: "core localized TAE" and"Alfv6n cascade" that are closely related to AEs in CHS
and LHD. As mentioned in Section 2, characteristics of
AEs sensitively depend on the rotational transform (1/q-) profile. As seen in Fig. 2, a heliotron/torsatron typedevice such as CHS and LHD has a reversed shear
configuration (dqldr<O ) over the whole minor radius in

numbers, respectively. From this equation, a general expression of the gap frequency is derived as follows:,V! , ,
Jfp."=lNt,a*-ull.' 'a rl 4ttRq*-

where 4* and R are the safety factor at the gap position

and the major radius, respectively. The quantity yAl(4pRq*) corresponds to the TAE gap frequency. The gap
location is determined by the radial position of q=q*,

the low plasma beta. In CHS or LHD, the TAE gap
frquency tends to increase toward the plasma edge due
to a character of the increasing function of the rotationaltransform for the minor radius. Because of this situation.
core localized type of TAE may be more likely in CHS
or LHD because it would not be suppressed by strongwhere* 2m+lt
q*=2n+vN'
The TAE corresponds to the case of 1t=1, v=0, and EAE
to 1t-2, reo. The Alfv€n eigenmode induced by helicalcomponent cos(2&N0) corresponds to the case of 1t-2,
y=l which is termed as HAE [4,5]. It should be noted

continuum damping near the edge.

5l

ToiK. et al., Impact of Energetic Ion Driven Global Modes on Toroidal Plasma Confinements<Arr>=0.01-3Vo and V6xlVa=Q.l-)-2, and for EPMs
<Arr>=0.08-3 7o and V6n/ V 6=0. 1- 1.5, respectively I I 2].
Nonlinear phenomena of bursting amplitude modulationand fast frequency chirping are typically seen in TAEs
and EPMs observed in CHS and LHD [8]. These
nonlinear phenomena seem to closely link to enhanced
transport of energetic ions. This will be discussed in the

Heliotron/Torsatron"-- Shearless Stellarator---- Standard Tokamak----' Reversed Shear Tokamak

g 1.2
E

0

btr 0.9t!

following Section 4.

E
0.6
tr

It should be noted that a new coherent mode withthe frequency by about 8 times higher than TAE gap(E

frequency was observed in NBI heated LHD plasmas at
low magnetic field (<0.6T). A typical example of themode is shown in Fig. 5. This mode may be induced by

o

E 0.3
u
0

0.2 0.4

0.6 0.8

helical field components of the confinement field. So

far, the high frequency mode is detected in the1<P/<a>

parameter region of < ftn>-0.8-2%o and V6nl V 6- 1.6-2.2.

In shearless stellarator W7-AS, low n global Alfv6n

Fig. 2 Radial profiles of the rotational transform schematically drawn for tokamaks and helical devices.

eigenmodes GAEs are most likely and dangerous modes
because the magnetic shear is almost vanishing and thenthe frequency is much lower than that of TAE [13]. In
CHS and LHD, n=0 GAE was sometimes excited, but

The core localized TAE in a tokamak plasma wasfor the first time identified in TFTR by measuring the

n=l GAE was rarely observed in CHS[l4].

internal structure with refrectometer [6]. In a helicalplasma, the presence of core localized type TAEs was
first revealed in CHS by the direct measurement of the

4. Effects of energetic ion driven Alfv6n
eigenmodes on energetic ion transport
TAEs and EPMs sometimes enhance radial

internal structure with a soft X-ray (SX-) detector arrayand heavy ion beam probe [7-9]. An example of LHD
shown in Fig. 3 also suggests a core localized type TAE.
In CHS, both TAE and EPM with m-2ln=1 are often
observed in the inward-shifted plasmas, together withlow frequency (LF) mode (<5kHz). In the plasma, theradial profiles of SX-fluctuations and their phase for
n=l TAE, m-2/n=l EPM and m-2/n=l low frequency(LF) mode are measured by the SX array, as shown in
Fig. 4. The n=l TAE is localized near the plasma centerand m-2ln=l EPM is well inside the q-2 rationaltransport of energetic ions in tokamak plasmas. The loss
sensitively depends on the amplitude of radial magnetic
fluctuations. The clear correlation was observed in DIIID t151. The loss in JT-60U is mostly enhanced whenAEs have a character of bursting amplitude modulationand fast frequency chirping [16].

Particle orbit trajectory in CHS or LHD is very
different from that in a tokamak plasma where has only
two kinds ofparticle orbit: passing and trapped (banana)
orbits. That is, four classes of particle orbit are present
because of helical ripple as well as toroidicity. To avoid
trapped ion loss, neutral beams are injected almost
tangentially in CHS and LHD. Slowing down process isdominant in CHS and LHD because the beam energy issurface, while m-2ln=l LF mode has a peak near the
q=2 surface exhibiting the character of interchange
mode.

Recent new observation of AEs in reversed shear
plasmas of JET is so called Alfv6n cascade that mainly

much higher than the electron temperature.
In CHS, energetic ion loss flux and the pitch angle
was measured by using a scintillator-based lost-ion
probe [17]. According to orbit calculation of energetic

upward frequency sweep takes place and the time
evolution of the frequency clearly reflects that of theminimum q value, q-r, [0]. This phenomenon may be
employed as a diagnostic tool for measurement of 4.inin a reversed shear plasma. Note that TAE exhibiting

ions, these ions are lost in poloidally and toroidally
localized zone on the vacuum vessel wall. Therefore. thelost ion probe was placed near such narrow zone inside
the vacuum vessel. Figure 6 shows time evolution ofrelatively slow frequency chirp-up and down similar toAlfv6n cascade in JET was also observed in LHD,
although the underlying physics is not yet clarified [11].

lost ion flux and m-3ln=2 EPM observed in the socalled outward-shifted confisuration of CHS. The

TAEs in LHD are excited in the condition of52

ToiK. et al., Impact of Energetic Ion Driven Global Modes on Toroidal Plasma Confinements#24467, B1=1.3 T1 Ro=t.$ m, He

(a)

250

Mirnov coil#54

200

ri i.rrqriitr

N

I

5 150
o
c

I roo

ri

C'

o
ll

o\|}l',

Irae -,

50-J

1i| .",...r**"*,*r*,",u,,408

petrct

;200

.<t-l

=-o
'E4

33

tV
| (ctr.)i-'rX#l+.

NBI 2(co.)\

\

rL2

o2
4at

2 Fg.

"'"*':YP

F'8

t

?oF
tsE

i o.s

0.1 ?E
0.0

0.5

1.0

1.5

2.O

2.5

0.01 -goTime (sec)

(b)
150

h
o
o

E

z
o
@

+ 100

+ 100

it

it

.)
tr
f

(,

o

c

r

fi50

I

ts

r0

+
N

o
f

rs50

E

Fig. 3 (a) Time evolution of the frequency of magnetic fluctuations and plasma parameters (Wr: stored energy, NBI: NBI
power, n,: line averaged density, 7"(0): electron temperature at the plasma center, Vo,,lVo: ratio of injected beam
velocity to the Alfv6n velocity. (pil)"ru""i"i beam beta value based on classical slowing down) in the LHD inwardshifted configuration of F.,=9.0 m at the toroidal field &=1.3 T. The solid and broken curves in the top frame indicate the calculated frequencies tor m=2+3ltE1 TAE gap and m=3+4/n=2 one, respectively. (b) The shear Alfv6n
spectra for n=1 mode in two dimensional and three dimensional cases. ln the latter case, the toroidal mode coupling among N;1 mode family is taken into account. The horizontal line indicates the observed frequency.
53

ToiK. et al., Impact of Energetic Ion Driven Global Modes on Toroidal Plasma Confinements
Iree---ln* lqfs 1 *t{Hs---e- 0<f<S0kffi{*4-i*Sm$}{ff3.$-64.5ms}
1.--.q* 9*sfq1 l nkH? {Sd-S6ffr$}

. 10{

o

,i lo-t#t3,t*4:Br-'lJr

o.

10-12

50

0

100

150

200

250

Frequency (kHz)Fig. 5 Power spectrum of magnetic probe signal obtained in LHD. The peak around f-200 kHz corre-

sponds to the high frequency mode. The frequency related to m-2+3/rr1 TAE gap is about 25
kHz.

a#69908
Rax=99.5 cm, Bt=0.88 T
x = 40-50

210-5
110-5
0
-1 '10-5-2 1o-5200
150--',L,{*L
80

85

90

100

=
d

50

95 100 105 110
Time{ms}

30

jro
0

Step tunctlon

like

.

6f, - (bu_rr.)5

H- r0

rl,

0

Fig.4 Radial profiles of SX-fluctuation amplitude andphase for TAE, EPM and LF mode with m-2ln=1
in CHS. The locations of the phase jump for re-

-10
'-0

5 1(16 I tos 1.5 1(I5 21(r5bn-..' (nspective modes are respectively near the plasma
center for TAE, slightly outside but inside the q=2
surface for EPM, and close to 62 surface.

Fig. 6 Time evolution of magnetic fluctuations ol r*3/

n=2 EPM and energetic ion loss flux measured
with a scintillator probe. The lower figure shows

the transient increment of the energetic ion loss
flux as a function of the EMP amplitude.

increment of loss flux df1 due to EPM magnetic
fluctuations be.-. is also shown as a function of theplasmas of CHS interrupts the TAE activity, of which
phenomenon can be interpreted by the reduction of themagnetic fluctuation amplitude. The functional relation
is expressed asbeam pressure and its radial gradient caused byenhanced transport of beam ions around the peak
position of TAE. The decrease in the energetic ion

df,*(br^,)',
where s=5. When s=l and s=2 respectively correspondto resonant convection loss and diffusive transport ofpressure dlue to m-2ln=l EPM is also inferred from thetransient decrease of the Shafranov shift correlated witheach EMP burst, of which Shafranov shift was derived
from the peak position of soft X-ray emission [19]. In
LHD, bursting TAE transiently depresses the bulk stored

energetic ions [18]. The case of s>2 means the case of
the destruction of magnetic surface. In CHS, this large
value of s may link to the presence of loss cone.

Rapid growth of m-2ln=l EPM in inward-shifted54Toi K. et a1.. Impact of Energetic lon Driven Global Modes on Toroidal Plasma Confinements

ffi

0.ooo2o.ooo1

Eo

G 200
J

;

-o'

1s0

to
Y

'{+" o.ooo2-o.oo01

3 roo
trso

-o,oo02

*il

400

So
els

p{.o

t,iil*,

4.2

e

t'As

!--0 04

I--S.tl'' '' P=-0.35-''''''''''''
P=-$'4t

c

t'2s

-oa

'o.ooo4

-

'5
c0

-10

Y=0
e _15

-o.ooo23d> -600
=e 10
e1 0
g

F

o

x o,t
E

(A

Fig. 7 Time evolution of the frequency of magnetic fluctuations, time derivative of the stored energy andfiltered nragnetic fluctuation amplitudes. The fluctuations in the range of 25kHz to 150 kHz corre-

0

2
?
J

1.5

>
j

spond to the bursting TAE.

E

ct

energy Wp (Fig. 7). The reduction rate (-dWo/dt)
colresponds to about l57o of NBI power input. Thissuggests at least -157o loss of energetic ion pressure[2]. Moreover, we show a clear example of CHS in
Fig. 8 where nt-2ln=l EPM having the amplitude of

1

0.5

tr

oL
80

100 ..

120.

ilme{mg,

140

Fig. 8 Time evolution of magnetic fluctuations of m-2/
n=1 EPM, soft X-ray emissions, and line averaged
electron density. the stored plasma energy andplasma net current. The quiescent phase is in thetime window from 104 ms to 132 ms. The upper-l-2 G at the nragnetic probe position degrades the bulk
confinement considerably (-10-207o reduction in Wp).
In this particular shot, the stored energy and electron
density recover by about 20Vo when m-2ln=l EPM istrace in the top frame shows magnetic fluctuations of m-2ln=I EPM, and the lower one to low

occasionally stabilized. Note that this stabilization of
EPM is not caused by the elimination of 4=2 srnface
because LF interchange mode is again destabilized at
higher plasma current -15 ms before the turn- off of
NBI. Moreover, weak TAEs are excited by energetic

frequency nE2l11 interchange modes. Note thatboth fluctuation amplitudes stay the lowest levelfrom 110 ms to 130 ms, but are not shown in thisfigure.

ions in this EPM suppression phase. The cause of the
suppression of EPM is not yet clarified.
In W7-AS [20], GAEs and bursting AEs sometimes
enhance energetic ion loss as similar to the loss due toTAEs in tokamaks and LHD.

theories is still preliminary. In helical devices such as

LHD, very wide parameter range is being exploredwithout suffering from current disruptions. These
researches contribute to improved understanding of
Alfv6n eigenmode in toroidal plasmas, as well as thephysics design of a fusion reactor based on helical

5. Summary
Energetic ion driven Alfvdn eigenmodes areintensively being studied in three helical devices LHD,
CHS and W7-AS as well as in major tokamaks. A lot of
more general information about Alfv6n eigenmodes
excited by energetic ions was obtained, that is, TAEs,
EAEs, EPMs and GAE were identified as are predicted
by MHD theories including energetic ions. However,configurations.
Future studies of AEs in CHS and LHD are aiming

at experimentally obtaining complete sets of shear
Alfv6n spectra through Alfv6n spectroscopy, andclarifying physics related to interaction between Alfv6n
waves and energetic ions.

quantitative comparison between experiments and55

ToiK. et aI., Impact of Energetic lon Driven Global Modes on Toroidal Plasma Confinements

t10l H.L. Berk et al., Phys. Rev. Lett. 87, 185002-l

Acknowledgements(2001).

This work was supported in part by a Grant-in-Aid
for Scientific Research from Japan Society for the[11] S. Yamamoto et al., J. Plasma Fusion Res. SERIES
3, 117 (2000).
[2] S. Yamamoto et al., Proc. of 7h IAEA TCM on en-

Promotion of Science.

ergetic particles in magnetic cinfinement devices,
Goteborg, 8-11 Oct. 2001.
ll3l A. Weller et al.,Phys. Rev. Lett. 72,1220 (1994).

References[1] ITER Physics basis, Nucl. Fusion 39,2137 (1999).
t2l Y.M. Li et al., Phys. Fluids 30, 1466 (1987).

t3l E.D. Fredrickson et al., Phys. Rev. Lett. 87,[14] M. Takechi e/ al., NIFS Annual Report Apr.1999Mar. 2000, p268.
[15] H.H. Duong e/ ol., Nucl. Fusion 33,749 (1993).

14s00r-l (2001).

t4l N.Nakajima et al.,Phys. Fluids 84, lll5 (1992)[5] Ya.I. Kolesnichenko et al., Phys. Plasmas 8, 491

tl6l K. Shinohara et al.,Proc. of 1Sth IAEA Fusion Energy Conf., Sorrento, Italy,4-10 Oct., 2000, paper
No. IAEA-CN -7 7 tEXP2l05.
[17] T. Kondo et al.,NtcL Fusion 40, 1575 (2000).

(2001).

t6l R. Nazikian et al.,Phys. Plasmas 5,1703 (1998).
t7l M. Takechi et al.,Phys. Rev. Leu. 83,312 (1999).
t8l K. Toi et al., Nucl. Fusion 40, 1349 (2000).

ll8l W.W. Heidbrink et al., Phys. Fluids B 5, 2176
(1993).

t9l K. Toi et al., Proc. of 7h IAEA TCM on energetic
particles in magnetic cinfinement devices,[8] S. Takagi et al., Rev. Sci. Instrum. 72,721(2001).
[19] A. Weller et al.,Phys. Plasmas 8,931 (2001).

Goteborg, 8-11 Oct. 2001.

56