J. Plasma Fusion Res. SERIES, Vol.5 (2002) 310-313

ICRF Heating using Folded Waveguide Antenna on LHD
TORII Yukir, KUMAZAWA Ryuhei, WATARI Tetsuo, MUTOH Takashi, SEKI Tetsuo, SAITO Kenji,YAMAMOTO Taror, TAKEUCHI Norior, SHIMPO Fujio, NOMURA Goro, MATSUSHITA Hiroyukir,
WATANABE Tsuguhiro and LHD Experimental Groups I / II
National Institute for Fusion Science, Toki 509-5292, Japan' Nagoya University, Nagoya 464-8603, Japan(Received: ll December 2001 / Accepted: l8 April 2002)

AbstractUsing a folded waveguide (FWG) antenna in the ion cyclotron range of frequency, a plasma
production and heating experiment was carried out on the large helical device in National Institute forFusion Science, which was the first experiment in the torus system. In the 4th experimental campaign in
2000-2001 this antenna produced the plasma at the average electron density up to 3xl0r8 m-3. In thiscampaign, the pure hydrogen plasma was produced mainly using the frequency of 25 MHz in themagnetic field strength of 2.6-2.8 T.
It is planned that an ion Bemstein wave heating will be carried out to heat the plasma at a higher
frequency, i.e. 37 .43 MHz (second harmonic resonance of FWG antenna). In the helium plasma produced
by electron cyclotron heating, the antenna launches the wave of the frequency o)-3(D"s" at the antenna
front. A spatial distribution of the wave energy damping was calculated using the dispersion relation ofion Bernstein wave and an analytical expression of the magnetic field strength with a rotating helicalcoordinate system. The propagating wave was absorbed near the resonance of a-2a"s".

Keywords:
ICRF heating, LHD, folded waveguide antenna, ion cyclotron wave, ion Bernstein wave

1. Introduction
In the 4th experimental campaign on the large

with IBW heating, and the density and the temperature

profile was peaked [1]. A high performance of theconfinement is expected at the IBW heating. It is

helical device (LHD), a plasma was produced using afolded waveguide (FWG) antenna. The obtained plasma
densities reached 3x1018 m-3. This becomes a target
plasma of neutral beam injection or ion cyclotron range

important for an effective IBW heating that the heating
characteristics in the LHD magnetic configuration areinvestigated beforehand. In this study IBW is launchedof frequency (ICRF) heating. This is the firstat the outside of the last closed flux surface in the low
field side. The wave propagates toward core and damps
at the second harmonic cvclotron lavers of Helium ions.

demonstration of the plasma production using an FWG

antenna in the magnetic confinement device. The
mechanism of the plasma production was investigated in
the propagation of the shear Alfven wave.
In the lower magnetic field or at the higher
frequency, the FWG antenna can launches ion Bernstein
wave (IBW). In the PBX-M, a transport barrier wasobserved in neutral beam injection discharge plasma

2. Folded Waveguide Antenna
A cutoff frequency is determined by the width of
the waveguide, i.e., /"u1o1i = c/2a, where c and a are thelight velocity and the antenna width. For ICRF wave
@2O02 by The Japan Society of Plasma

C o rr e sp o ndin g autho r' s e - mail : t o rii @ nifs. ac.j p

Science and Nuclear Fusion Research310

Torii Y. et al., ICR.F Heating using Folded Waveguide Antenna on LHD

3. Shear Alfv6n Wave Heating
In the 4th experimental campaign, the plasma

launching, an antenna width needs to be wider than 5 m.
The antenna size is made smaller by folding the antenna
many times [2] as shown Fig. 1.

production experiment by the FWG antenna was carried

An mock-up FWG antenna was tested andout [5]. Plasmas were produced and the achieved
electron density was 3x1018 m-3. This is the first

demonstrated as an application of the LHD [3]. TheFWG antenna is folded 23 times. The FWG antenna is
electrically shcrted at the front by polarization plates sothat high voltage does not appear near the plasma andthat the wave number parallel to the magnetic field, /<11 isminimized.
The FWG antenna is installed at the horizontal port

demonstration in magnetic confinement devices.

The experiment was carried out in a hydrogenplasma and the applied frequency was 25.33 MHz (TE1emode). It was confirmed that the achieved density
depended on the magnetic field strength. Figure 3 showsits dependence. The dots are the experimentally[4] of LHD. 'fhe location of the antenna, magnetic

achieved line averaged electron density. The density
increases with the magnetic field strength. A dispersion
relation of ICRF wave reflects this phenomenon [6],surfaces, and the resonance layers are shown in Fig. 2. It
has an angle with respect tothe equatorial plane so that

the RF electric field is parallel to the magnetic field at
the last closed magnetic flux surface for the purpose of
the slow wave excitation.

*t,!'
4=ra'c'(l)where al"s, a, (4H, c, and kl are a hydrogen cyclotron
frequency, an applied frequency, a hydrogen plasma frequency, a light velocity, and a wave number perpendicu-lar to the field, respectively.

=E#The propagation area of shear Alfv6n wave wascalculated at the various electron density and themagnetic field strength. In this calculation, a cold/approximation was used and the electron density profile
was assumed to be n"=r.o(l-p8). where ,?e0 and p are/0.3+0.25(n.E0.2oot

Fig. 1 A concept of the FWG antenna. The antenna isthe waveguide antenna folded many times. Theantenna width is denoted by'a'.

a0.15
FxG,oEls2c0""" cyclotronres.

0.1

oo

0.05
0 f-l

2.5

2.6 2.7 2.8

2.9

B"t (I)
Fig. 3 Dependence of achieved electron density on mag-3co."" cyclotronres.

netic field strength. The dots are experimentallyachieved line-averaged electron density. The solidline is the line-averaged electron density at which

Fig. 2 A schematic drawing of the FWG antenna in LHD.
The second and third helium cyclotron resonancelayers (f=37.43 MHz, B*=2.7 T) are also shown.

the calculated shear Alfv6n wave propagation
area is the largest.

3tl

Torii Y. et al., ICRF Heating using Folded Waveguide Antenna on LHD

4.2 Radial distribution of perpendicular wave
number of IBW

central electron density and a normalized minor radius,respectively. The dependence of the line-averaged
electron densities where the propagation region is theelectron densities qualitatively agree with the calculated
ones. It is concluded that the plasma was produced by
the shear Alfv6n wave.

The parameters of the target helium plasma are
assumed; Temperature profile is To=Too1l-p2) at theplasma core region of 0<p<0.8 and To-To* exp(-plpro*) at the peripheral region of p>0.8. Density profile
is no=noo11-ps; also at 0<p<0.9 and, no=no* exp(-plp,o*) at p>0.9. Constants of Zo*, flo*, Pro*, and p,o* are

4. Propagation and Absorption Area of lon

determined as the temperature and the density profiles atthe peripheral region are connected with ones at the corelargest on the magnetic field strength is also plotted inFig. 3 as solid line. The experimentally achieved

region continuously and smoothly. The magnetic fieldstrength is available analytically using a rotating helicalBernstein Wave
The FWG antenna also launches the ion Bernsteincoordinate system [8]. Characteristics of the analyticalmagnetic field agree well with the actual one calculatedusing Biot-Savart's law.
The wave number perpendicular to the magnetic
field, k1 was calculated numerically by solving thedispersion relation, eq. (2) using plasma parameters andwave at the higher frequency, f=37.43 MHz (TE26mode). The calculation of the IBW propagation isrequired for the efficient launching IBW.

4.1 Dispersion relation of ion Bernstein wave
The dispersion relation of the electrostatic wave isgiven by a following equation [7],the magnetic strength. The complex Newton method
was used to solve a real part and an imaginary part of-24i H

D=k1+k;+ L-lq

k1. Figure 4 shows a profile of the real and theimaginary part of the wave number. In this calculation,
following parameters were used: 1[=37.43 M}Jz, Bu*=2.7T (R"*-3.6 m), n"e-5.0x1018 m-3, and l"o=7r"0-200 eV.
Here plotted are profiles of the electron density, theVtd l=--e*p (- p") r, (1"){

r * zs"Z(21")\ = 0(2)

andk2,v?-

lro=ffi'a - la.o
Zta=klvro

electron temperature and the ratio of the appliedfrequency to the helium cyclotron frequency, da"t".
The wave number parallel to the magnetic field was
fixed at ftrr=3.0 m-r. Summation of the cyclotron
harmonics was carried out over l=0, +1, ..., +9.

(3)where v,o, aoo, I{x), and Z(x) are a thermal velocity ofspecies a, a plasma frequency, an l-th order modified
Bessel function, and a plasma dispersion function, respectively.

For the simplicity following assumptions areemployed; electrons absorb the wave energy through3 104

Landau damping. A finite Larmor radius effect of

2fi4

electron is ignored. Ions absorb it through afundamental, a second and a third harmonic cyclotron
damping. A finite Larmor radius effect of helium ion isvery small, and phase velocity parallel to the magnetic
field is much larger than the thermal velocity of ions.

1.5'oooe,{Then the above dispersion relation is simplified in thefollowing equation;(D=kt+ft;+ll\2.S*1 104F"lq

1-'t $4o-{6-{aa,.\*l.2104

0.5(D2J-3 1 043:a!," a1.''-?eL(vi\ , a'- al,+u:a2 -4a7i*f;u?#a,)=o=04AR(n)Fig. 4 A perpendicular wavenumber kr profile. The density, temperature, and magnetic field strength profiles are also shown.

(4)

312Torii Y. et al., ICRF Heating using Folded Waveguide Antenna on LHD

The wavo propagates from the FWG antenna(R=4.6 m) near the helium third harmonic cyclotron

at the higher frequency. The wave number perpendicular

to the magnetic field, k1 was calculated numerically.
The calculation was carried out with the constant ftn on
the equatorial plane. The waves propagates into theplasma core region and the energy is expected to beabsorbed by ions at the second cyclotron resonanceresonance layer, as shown in Fig. 2, into the plasmacore. As the rvave approaches the second harmonicresonance layer, the real wave number increases. The
absolute value of the imaginary one also increases
sharply just in front of the layer. This wave number is anegative value because of the characteristics of the IBWof the backward wave. The wave energy is absorbed byhelium ions. At the wave passes the second cyclotron
resonance layer, the wave number decreased sharply as
shown in Fig. 4.

layer.

References

tll B.LeBlanc et al.,Phys. Plasmas 2,741(1995).
[2) T.L. Owens, IEEE Transactions on Plasma Science,PS-14, 6, 934 (1986).

t3l R. Kumazawa et al.,Flsion Eng. Des. 26,395
5. Summary
In the LI{D, a folded waveguide antenna is(1995).

t4l R.Kumazawa et al.,J. Plasma Fusion Res. SERIES
1, 330 (1998).
t5l Y. Torji et a/., Nucl. Fusion 42,679 (2002).

installed. The antenna is a waveguide antenna folded 23

times in order to reduce the cutoff frequency to theICRF. Plasma is produced by shear Alfven wave

t6l T.H. Stix, The theory of plasma waves, (McGrawHill, New York, 1962).

launched by this antenna. The achieved electron density

is increased with the magnetic field strength. This

[7] J.P.M. Schmitt, Phys. Rev. Lett. 31, 982 (1973).
t8l T. Watanabe et al., J. Plasma Fus. Res. 73, 186(1997).

phenomenon is explainable by the shear Alfven wave
propagation.
The FWG antenna launches the ion Bernstein wave

313