Proceedings of ITC/ISHW2007

Excitation of Stable Alfvén Eigenmodes by Application of Alternating Magnetic
Field Perturbations in the Compact Helical System

T. Itoa, K. Toia,b, G. Matsunagac, M. Isobeb, K. Nagaokab, and CHS Groupb
aDepartment of Energy Engineering and Science, Nagoya University,Furo-cho, Chikusa-ku, Nagoya City, Aichi 464-8601, Japanbc

National Institute for Fusion Science,322-6 Oroshi-cho, Toki 509-5292, Japan

Japan Atomic Energy Agency, 801-1 Mukouyama, Naka, Ibaraki 311-0193, Japan
ito.takafumi@lhd.nifs.ac.jp

In the Compact Helical System (CHS), alternating magnetic perturbations were applied to NBI
heated plasmas by using two electrodes inserted near the plasma edge by 180 degree away toroidally, toexcite stable Alfven eigenmodes and measure the damping rate. The frequency dependence of thetransfer function defined by the ratio of a magnetic probe signal for an electrode current signal shows thepresence of a few resonant peaks which would be related to stable Alfvén eigenmodes(AEs) excited.
Each observed resonance frequency fo agrees well with the frequency of each corresponding toroidicity
induced Alfvén eigenmode of which gap is located in peripheral plasma region, where fast ion drive ofAEs would be sufficiently small. The derived damping rates γ are very large, i.e., γ/(2πf0)～10%.

1. Introduction
In a D-T fusion plasma, one of the mostdangerous MHD modes driven by energetic particle
is the toroidicity-induced Alfvén eigenmodes(TAEs)[1]. In this situation, the first wall and various
plasma facing components may be seriously damaged
by energetic alpha particles lost by TAEs. It is
important to assess the stability of energetic-ion
driven MHD modes such as TAEs experimentally andcompare the theoretical predictions. The stabilityof TAE is determined by competition between thelinear growth rate and various damping rates. The
linear growth rate will be expressed as[2],⎞ ⎛ υ ⎞⎤γ 9 ⎡ ⎛ ω*α≈ ⎢ βα ⎜− 1/ 2 ⎟ F ⎜ A ⎟ ⎥ω0 4 ⎣ ⎝ ω0⎠ ⎝ υα ⎠ ⎦(1)

Here, the quantities ω∗α, βα, vΑ, F and vα arerespectively the diamagnetic drift frequency of anenergetic ion, the toroidal beta value of energetic ions,
Alfven velocity, the fraction of resonant energetic

particles with shear Alfven wave and energetic ion
velocity. On the other hand, there are several
important damping mechanisms: Landau damping by
bulk electron and beam ions, continuum damping,radiative damping and so on.
However, thetheoretical prediction of these damping rates would
include large uncertainty depending on theoreticalmodels because of lack of precise information of
eigenfunction of TAE, shear Alfven spectrum and soon.
Accordingly, it is necessary to establish themost reliable theoretical model of the damping rates
in a future burning plasma through comparison
betweenvarioustheoreticalresults
andexperimentally measured ones.
A powerful method to measure thedamping rate was developed in the JET tokamak[3]and then has been applied to the Alcator C-Mod
tokamak[4]. This method is based on a response
analysis of a plasma for applied magnetic
perturbations generated by a set of loop antennas
arranged in the toroidal direction of a torus. In thismethod, the frequency of applied fields is swept tosearch resonance points related to TAE frequencies.
Excitation of stable TAEs by application of magnetic
perturbations was also attempted in the Compact

Proceedings of ITC/ISHW2007

Helical System (CHS) where a couple of electrodes
inserted into the plasma boundary were adopted togenerate magnetic perturbations purely perpendicular
to the toroidal magnetic field line [5].
This
experiment was carried out in low temperatureplasmas produced at the toroidal field less than 0.1T
by using 2.45 GHz electron cyclotron waves, where
no energetic ions were present.
Recently, thismethod was also applied to a plasma heated byneutral beam injection(NBI). This paper describes
the experimental results.

2. Experimental setup
Alternating voltage of about 75V wasapplied to a couple of electrodes inserted into aplasma edge region to produce alternating magnetic
perturbations.
The detailed structure andarrangement are shown in ref. 5.
The driving
frequency fext was swept up to 500 kHz to include
the expected TAE frequency[6]. The maximum
current of each antenna is ~5A, and the maximum
amplitude of the perturbation field is estimated to be~5x10-6T at the magnetic axis position of 0.921m.
These electrodes are placed by 180 degrees away inthe toroidal direction to specify the toroidal mode
numbers of applied perturbation fields. In thisexperiment, the polarity of two electrode currents
were adjusted to be the same. This is called “even”
mode operation. The so-called “general” mode

operation was also tried by energizing only a single
electrode. The dominant toroidal mode numbers ofapplied perturbation field are n=0, ±2, ±4, ... ( n=0,±1, ±2, ...) for “even” (“general”) mode operation byusing double (single) electrode.
The electrodecurrent and the applied voltage are monitored at thevacuum feedthrough. The magnitude of applied
voltage to an antenna and a time-dependent sweeping
pattern of fext are created by a function generator
controlled with PC in the control room of CHS. The
sweeping pattern of signal is amplified by ahigh-speed bipolar power supply. Typically, thefrequency was swept from 1kHz to 300kHz in 100
ms. The response of a plasma for applied magnetic
perturbations was obtained with the magnetic probesarranged in poloidal and toroidal directions. The
toroidal array of magnetic probes consists of the fiveprobes and is used to determine the toroidal mode
number of the response. The poloidal mode number
was determined by a poloidal array with 12 probes.

3. Experimental results
A typical discharge waveform of an NBI
heated plasma in this experiment is shown in Fig.1.
In this shot, the line-averaged electron density rises
from 1.0x1019 m-3 to 4.6x1019 m-3 by gas puffing, asshown in Fig.1(b). The toroidal current and thevolume-averaged toroidal beta value reach about 3kA
and 0.25%, respectively,
as shown in Figs.1(c) andFig.1. A typical discharge of the AE excitation experiment by using the double electrode(#236280). Timeevolution of the power of external heat sources(a), line-averaged electron density(b), net toroidal current(c),volume averaged beta(d), the spectrogam of a magnetic probe signal(e). The absolute value of the transfer
function (f), its real part(g) and imaginary part(h) as a function the driving frequency fext .

Proceedings of ITC/ISHW2007(a)damping rate γ/(2π fo) were evaluated by fitting of thetransfer function with that of a general viscousdamping system . The transfer function of such
system is expressed as [7]:G (ω ) =B(ω )
A(ω )

*⎧⎫
RrRr= ∑⎨+⎬i (ω − Ω r ) + γ r ⎭r =1 ⎩ i (ω + Ω r ) + γ r

(2)

N(b)

Fig.2(a). The n=2 shear Alfvén spectra calculated fortwo dimensional approximation of the actual CHS
magnetic configuration (a). The dashed and thedot-dashed horizontal lines indicate the observed
resonance frequencies of fo=158kHz and 259kHz,
respectively. (b) The power spectra of magnetic
fluctuations in the time windows of t=0.071s to t=0.075 s and t=0.105s to t=0.109s. The modes in thelower frequency range less than 100 kHz are theenergetic ion driven TAE and EPM.
The broad
spectral peaks of these modes are caused by rapid
frequency sweeping.

(d). In Fig.1(e), the spectrogram of a magnetic
probe signal is shown. In this figure, strong MHD
activities driven by energetic ions are observed
together with a weak perturbation signal induced bythe electrode current. In this shot, two electrodes
were driven with the same polarity, that is, “even”
mode operation.
Figure 1(f), 1(g) and 1(h) showrespectively the absolute value. the real part andimaginary part of the transfer function as a functionof the driving frequency fext, of which transfer
function was derived from the ratio of the magnetic
probe signal for the electrode current. Two resonancepeaks have been observed in the transfer function.
The resonance frequency fo and the normalized

Here, Ωr, γr, Rr, and Rr* are respectively the angulareigenfrequency, damping rate, residue and its
conjugate term at r-th resonance. The output signal
B(ω) corresponds to the magnetic probe signal andthe input signal A(ω) corresponds to the electrodecurrent.
The part of G(ω) less than 120 kHz will beaffected by the energetic ion driven instabilities.
Accordingly, the fitting was carried out over thefrequency range from 120 kHz to 300 kHz on theassumption that four resonances exist.
The lowest
peak corresponds to the peak of energetic ion driven
TAE, which should be ignored. Moreover, thehighest resonance much larger than 300 kHz was alsoobtained by this fitting, but was also ignored becauseof a virtual resonance. The second and third
resonance frequencies fo2 and fo3 derived from thefitting are 158kHz and 259kHz, respectively. The
corresponding damping rates are γ/(2πfo2)=6% andγ/(2πfo3)=12.5%, respectively. These damping rates
are considerably larger than those obtained in JETexperiments.
The toroidal and poloidal mode numbers
for these resonant components were attempted todetermine using the magnetic probe arrays.
However, the mode numbers for these resonant
fluctuations induced by the applied perturbations
were not derived because of irregular phase relations
among magnetic probes.
The reason is notclarified yet, but may be due to the presence ofbi-directional perturbations along the toroidal line offorce.
Here, the lowest and non-zero toroidal
mode was assumed to be n=2 for these oscillations
excited by the applied magnetic perturbations. An
n=2 shear Alfven spectra calculated with two
dimensional approximation of the CHS configurationis shown in Fig.2(a), where a hydrogen plasma withfully ionized carbon impurity was taken into accountto be the effective charge of Zeff=3. The frequenciesof excited resonant magnetic perturbations agree wellwith the gap frequencies in the plasma peripheral
region.
That is, the mode of f=158kHz willcorrespond to the n=2 TAE due to m=3 and m=4
coupling, and that of f=258 kHz the n=2 TAE due tom=2 and m=3 coupling. In this shot, two types ofenergetic ion driven modes were observed in theProceedings of ITC/ISHW2007

lower frequency range less than 100 kHz, as seenfrom Fig.1(f) and Fig.2(b). In contrast to the excitedmodes by applied field perturbations, the mode
numbers of them were clearly determined to be
m~5/n=2 for the mode of f=65 kHz and m~3/n=1 forthe mode of f=30 kHz. The former agrees very wellwith the n=2 TAE due to m=5 and m=6 coupling.
The latter mode with n=1 is thought to be energetic
particle mode (EPM) because the frequency is well
below the expected minimum gap frequency. From
this comparison, the above-mentioned resonantmodes driven by electrodes are thought to be stable
TAE near the plasma peripheral region where the fastion drive will be too small to destabilize. So far, it
is not clear whether or not the TAE resides moreinterior region was excited by applied magneticperturbations. More larger magnetic perturbations
will be necessary for the excitation of stable TAEs inmore interior region.

4. Summary
An active diagnostic method for measuring
the damping rate of Alfven eigenmodes by using
external magnetic perturbations induced by a coupleof electrodes has been developed in CHS. Thesingle or double electrode inserted into a plasma edge
was successfully applied to NBI heated plasmas.
Several resonant responses are clearly observed atboth of the single and double electrode operations.
Some resonant peaks observed in the transfer
function agree well with those of the low n TAEs ofwhich gap locate near the plasma edge. The
identification of the toroidal mode number of theexcited stable TAEs is difficult in most of cases,
which may be caused by simultaneous excitation ofbi-directional waves and/or several modes having
different toroidal mode number. Measured damping
rates of excited TAEs are fairly large in the range ofabout 10% for the eigen-angularfrequency.
Excitation of stable AEs by application of magnetic
perturbations is being tried in the Large Helical
Device (LHD).

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[3] A. Fasoli et al (1995) Phys. Rev. Lett. 75 645.
[4] J. A. Snipes et al (2004) Plasma Phys. Control.
Fusion 46 611.
[5] G. Matsunaga et al (2005) Phys. Rev. Lett. 94
225005.
[6] G. Matsunaga et al (2001) Rev. Sci. Instrum. 72
402[7] A. Nagamatsu (1993) Introduction to ModalAnalysis, Corona publishing CO., LTD(in Japanese)