J. Plasma Fusion Res. SERIES, Vol.5 (2002) 390-394

Non-Linear Phenomena of Energetic-lon-Driven
MHD Instabilities in LHD
YAMAMOTO Satoshir, TOI Kazuo, OHDACHI Satoshi, NAKAJIMA Noriyoshi, SAKAKIBARA Satoru,
OSAKABE Masaki, YAMADA Hiroshi, MASUZAKI Takashi, WATANABE Kiyomasa,
NARUSHIMA Yoshiro, TAKEIRI Yasuhiko, NARIHARA Kazumichi, YAMADA Ichihiro,
KAWAHATA Kazuo, TANAKA Kenji, TOKUZAWA Tokihiko, MORITA Shigeru,
GOTO Motoshi, OHYABU Nobuyoshi, and LHD Experimental Groups I / IINational Institute for Fusion Science, Toki 509-5292, Japant Dep. of Energy Eng. and Science, Nagoya University, Nagoya 464-01, Japan(Received: 7 January 2002

/ Accepted:2 October 2002)

Abstract
Energetic ion driven MHD modes were observed in NBI heated plasmas of LHD. The observed
modes are classified into three kinds of modes, depending on the frequency range, degree of amplitude
modulation (continuous or bursting) and temporal evolution of the mode frequency with or without rapid
frequency chirping. It is important and of interest to study these phenomena related to non-linear waveparticle interactions. We have investigated the excitation conditions of continuous and bursting TAEs.
Continuous TAEs are only observed just above the threshold. When drastic TAE bursts are excited, about
15 Vo of the beam power is lost by each burst. This suggests that the bursting TAEs induce energetic ion
transport before the thermalization. Two kinds of frequency chirping were observed in NBI heatedplasma. One is rapid frequency chirping, of which chirping time scale is much shorter than acharacteristic time of the change of the plasma equilibrium, and the other is slow frequency chirping.

Keywords:
energetic ion, TAE, non-linear, MHD instability, transport of energetic ion

1. Introduction

instabilities may be qualitatively explained by "predator-MHD instabilities destabilized by the energetic ionsare being studied in many magnetic confinement
devices, because they might considerably degrade theconfinement of a-particles and damage the wall in afusion reactor. Furthermore, the studies of energetic ion
driven MHD instabilities are important and of interest to
clarify the mechanism of non-linear wave-particle
interactions. Non-linear phenomena related to theseMHD instabilities such as bursting behavior, saturationof mode amplitude, frequency chirping and spectrum
splitting were observed in many devices [-5]. The

prey relationship" model in certain experimental
conditions [1]. When the instability ("predator") isdestabilized by the energetic ion population ("prey"),energetic ions would be expelled from the plasma
confinement region and/or the energetic ion density
profile would be redistributed. Then, the instability isstabilized because the energetic ion population and thespatial gradient are not large enough to destabilize them.

This cycle is repeated, as far as energetic ions arecontinually supplied. However, the frequency chirpingand spectrum splitting cannot be explained by thebursting behavior and saturation of these MHD@2OO2by The Japan Society of Plasma
Science and Nuclear Fusion ResearchCorresponding author's e-mail: syama@ nifs.ac.jp390

Yamamoto S. et aI., Non-Linear Phenomena of Energetic-Ion-Driven MHD Instabilities in LHD

simple predator-prey model. Much more complex andsophisticated theories or numerical simulations arefew continuous modes are also observed without
bursting nature although NBI is continued. Therequired [6].

transition from bursting to continuous mode is shown in
Fig. l, where hydrogen beam of energy ENer = 155 keV
is tangentially injected into a hydrogen plasma in theconfiguration of R"* - 3.6 m at B, = 1.5 T. The frequencyof the lower frequency modes with m - 2/n = I agree
well with the TAE gap frequency /rAE (dotted line in
Fig. 1) that is formed by m = 2 and m = 3 mode
coupling for n = 1 mode. The mode amplitude and thedegree of the frequency chirping gradually decrease intime when the energetic ion beta <B67> gradually

In NBI heated plasmas of LHD, various energetic
ion driven MHD instabilities were observed 14,71. The
following three kinds of MHD modes, toroidicity
induced Alfvtin eigenmodes (TAEs), global Alfv6n
eigenmodes (GAEs) with toroidal mode number n = O
and resonant TAE (R-TAEs) or energetic particle modes(EPMs) are identified in the recent experimental studies.

TAEs reside in the TAE frequency gap which is formedby the coupling of cylindrical Alfvdn spectra withdifferent poloi<lal mode number m and m + I induced bydecreases because of the decrease in electron

finite toroidicity. When the mode frequency istemperature and increase in electron density. That is, theappreciably less than the TAE gap and intersects theshear Alfv6n continua, TAE would suffer from strong
damping due to the continuum damping. In thissituation, TAEs will be stabilized. However, when theenergetic ion drive of the mode is large enough toovercome varjous damping mechanisms, R-TAEs orEPMs would tre unstable [8,9]. R-TAE is a beam-likemode of which frequency is mainly determined by thewave-particle resonance condition and is usually lessmagnetic fluctuation amplitude of TAE decreases from
bslB.-3x10-7 (burst r = 0.8 s) to lxl0-7 (continuous I =1.2 s) and saturates. Recently, theoretical [10] andnumerical simulation [11] studies point out a possibility

that wave trapping of resonant particles would play akey role in controlling the above mentioned non-linear
behavior. If the growth time of the wave is comparable
to or shorter than slowing down time of energetic ion t",
the burst mode will take place. On the other hand, if thethan the TAE gap frequency.

growth time of the wave is longer than slowing down

2. Experimental Setup
LHD is a heliotron type device with / = 2 fieldpolarity and the toroidal field period of M = 10. In thestudies of energetic ion driven MHD instabilities, thetoroidal magnetic fields strength and magnetic axis

t86'26, Bt=1.49(T'), far=3.6(m), Hz, Prvrr-3.7 MW, Es1-155 keV70Soo

5position are respectively varied in the range ofB,= Q.J -Hso

2.9 T and Ru* = 3.5 - 4.05 m. The energetic ions areproduced by the tangential NBI up to 6 MW with the9F40

beam energy up to 160 keV hydrogen. The velocity of
injected ions can easily become super-Alfv6nic velocityFeven in relatively low density at lower magnetic field B,

45 tb^^
E1a< 1.5 T. The primary fluctuation diagnostics for thesestudies are two types of toroidal and helical array ofFxmagnetic probes, of which frequency response is up to600 kHz. The toroidal array of six magnetic probes isused to determine the toroidal mode number (n), and thehelical array of twelve probes is used to determine the5'B
00'':^:l 04a 'xJ<poloidal mode number (m) using the toroidal mode

\number obtained from the toroidal array.

Many observed modes have a character of periodic
burst with an interval of l-20 msec. Furthermore, thefrequency of some modes is rapidly chirped up and/ordown (increased and/or decreased). On the contrary, at'\a100.8 0.9

3. Amplitude Modulation

>z

201.0

Time (sec)

1.1ilE
1.2

Fig. 1 The transition from bursting to continuous mode
at t-1 s is clearly seen. Time evolution of magnetic fluctuation spectrum. magnetic fluctuation
amplitude and some plasma parameters.

391

Yamamoto S. et aI., Non-Linear Phenomena of Energetic-Ion-Driven MHD Instabilities in LHD

with m - 2ln = 1 are observed, is shown in Fig. 2. The
continuous TAEs are destabilized in the condition of0.4<v,o11/ v a<l and <fto1p < 2 Vo . This indicates that thecontinuous TAEs may be excited via sidebandexcitation. When the <&r> ir greater than 0.2 7o, theTAEs become busting. Note that no TAE is detected in
the range of <Frrp < 0.05 7o. The continuous TAEs
seem to be excited just above a certain threshold. TheTAEs with m - 3/n = 2 are always bursting and theexcitation threshold seems to be systematically higher
than that of TAE with m - 2ln = l. lf m - 2ln = | T AEs

time of energetic ions, the continuous mode will takeplace. In our case, however, t, is thought to be much
longer than the mode growth time. The observed
phenomenon might be explained by introduction of theeffective collision frequency v"i1 that is discussed in ref.

lr2l.
We have investigated the excitation conditions,changing the relevant parameters <fio1p and v611lvs,
where <B5a> and v611/vs are the volume averagedenergetic ion beta and the ratio of energetic ion velocity
to Alfv6n velocity. The <B,o1p is estimated on theassumption of the classical slowing down of energeticions. The parameter space that the continuous TAEs

are located in the core region. They may have apossibility of core-localization for minimization ofcontinuum damping [3].
The fluctuation amplitude is rapidly increased withthe increase in <0o,,>. The relative amplitude ofcontinuous TAE is typically bslBr- 10-8-10-7, and burst
TAE is bslB, -10-7-10-6 at the probe position. When themagnetic shear become low due to the plasma current in
the co.-direction and the higher plasma beta at the lower,B,, the drastic TAE bursts can be excited. These modestl

consist of TAEs with m - 3/n = 2 and - l/l modes.
These modes may affect the fast ion transport because
the some plasma parameters are simultaneously
modulated by TAE bursts, as shown in Fig. 3. In thisshot, the calculated <h,,> is increased up to 3 7o andthe
amplitude of TAEs reaches up to bslB,-8x10-6. The
transient decrease in the plasma stored energy (dWldt)
suggests that about 15 Vo of the beam power is lost byeach burst. Besides, the signals of EllB neutral particle
analyzer suggest that the transport of passing beam
particles to the plasma edge is enhanced by these TAE
bursts [14]. From these results, we can speculate thatthese TAEs enhance radial transport of energetic ion
before the thermalization. These TAEs gap are locatedin the plasma edge region (p > 0.5). As mentioned
above, it is usually hard to destabilize the TAEs in low
beta plasma because frequency intersects with the shear
Alfv6n continua in the edge region. However, the good

012
v611

lva

Fig.2 Excitation conditions of TAEs with m-2ln=1 andm-3ln=2.

250

E 200E rsoq*o loo

Fr 50-0, 400

alignment of the frequency gaps from the plasma core
towards the edge can be realized by the decrease in themagnetic shear under low B, and higher beta.

50*€F-ooo103ofr-ro

Fls
3ot-ts 1.23

4. Frequency Ghirping

1.35

Two kinds of frequency chirping in TAEs and RTAEs were observed in NBI heated plasma. The timescales of frequency chirping are respectively muchsmaller than that of plasma equilibrium evolution and1..15Time(sec)Fig. 3 Time evolution of magnetic fluctuation spectrum,

time derivative of the stored energy of the bulk

comparable to it.
The former is observed with burstine behaviors andplasma, and filtered magnetic fluctuation amplitude.
392

Yamamoto S. et al., Non-Linear Phenomena of Enersetic-Ion-Driven MHD Instabilities in LHD

80*25892,8r=O.75"1,Ro= 3.6 m,He,Pmr- 35 M%r*r- 160kev

to change the energetic ion slowing down time t., which

is proportional to 7"3t2, ECH with PEcs - 0.6 MW wasinjected a low density plasma. The electron temperature
increases from 2 keV to 3 keV and density slightly
decreases during the ECH injection. The frequencies ofobserved TAEs and R-TAEs are chirped up during
ECH. This phenomenon may be related to the changesof r, and z" profile.

SooFI
5bao(l)620
L-5. Conclusion
Various types of MHD instabilities destabilized byenergetic ions are observed in NBl-heated plasmas onLHD. Clear non-linear effects in TAEs and R-TAEs areobserved as bursting amplitude modulation and rapidly
frequency chirping. Observed modes often exhibit a0.6

Time (s)1oo FEGeOrFrl
f+i

TLE (m-2ln=1')

Eft

Ftl

AF,

,

character of periodic burst. However so-called

5so h//

continuous TAEs without busty nature were sometimes
observed on the condition that <\atp is in just above acertain threshold.
When the magnetic shear becomes low due to the6zoF,= tr-"
iooF

plasma current in the co.-direction and the higher
plasma beta at lower 8,, the TAEs exhibit a very strong
bursting character and rapid frequency chirping. Thetransient decrease in the plasma stored energy (dWldt)
suggests that about 15 Vo of the beam power is lost byeach burst. These TAEs induce energetic ion transport-t 50t

0.78Time (sec)Fig. 4 Time evolution of magnetic fluctuation amplitudeand frequency tor m - zln = 1 R-TAEs (a) and m-each burst are repeated every 1-30 ms. The R-TAEs

before the thermalization.
Two kinds of frequency chirping were observed in
NBI heated plasma. One is rapid frequency chirping, ofwhich chirping time scale is much shorter than thecharactestic time of the plasma equilibrium evolution,with rapid frequency chirping down were typicallyobserved in the conditions of B, < I T and <p'o1p > | Vo,
as shown in Fig.4 (a). Hydrogen beam ofenergy ENer =and the other is slow frequency chirping variation.
Further experimental investigations are required toclarify the correlation between the nonlinear behavior

140 keV is tangentially injected into a Helium plasma inthe configuration of Ru* = 3.6 m at Br= O.75 T. The
amplitude of these R-TAEs reaches tp to bslB. -10-5 andby one order of magnitude lager than that of TAE evenin the similar plasma conditions. The TAE and R-TAE
with rapid frequency chirping upward or downward
were sometimes observed with burst duration of 20 - 30
ms, as shown figure 4 (b). In this case, the amplitude ofthese R-TAEs and TAEs are bslB. - 10-6 and bslB, -and energetic ion transport.

2ln = 1 TAEs (b). These modes exhibit rapid frequency chirping.

Acknowledgements
This work was supported in part by a Grant-in-Aidfor Scientific Research from Japan Society for thePromotion of Science.

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