J. Plasma Fusion Res. SERIES, Vol.5 (2002) 314-317

The Radio Frequency Gharacteristics of the Gombline
Antenna
TAKEUCHI Norio, KUMAZAWA Ryuheit, SAITO Kenji, WATARI Tetsuor, SEKI Tetsuor,TORTT YuKi. MUTOH TaKashi|. TAKASE Yuichi2 and YAMAMOTO Taro
Nagoya University, Nagoya 464-8603, Japanfor Fusion Science, Toki 509-5292, JapanI National Institute" University ofTokyo, Tolcyo 113-8656, Japan(Received: 11 December 2001 / Accepted: 18 June 2002)

Abstract
A combline antenna was designed and fabricated to improve the plasma performance of the LHD. It
has a capability to drive plasma current and to heat the plasma by ICRF heating. The LHD combline
antenna consists of ten antenna elements. The two elements of those are an input and an output antenna
element. Equations were derived to examine the RF characteristics. The currents at the Nh antenna
element and L't antenna element were formulated in a 4x4 matrix using the RF current at the RF power
supply. A traveling wave was found to be excited at the frequency range as referred to a pass-band. Thephase velocity of the traveling wave can be controlled by changing an applied frequency as one ofseveral features of the combline antenna. The width of the pass-band is a function of the value of theplasma loading resistance, the distance between antenna elements, how to feed the RF power and aconfiguration ofthe Faraday shields, etc. A T-shaped antenna strap was employed at the present designof the combline antenna. which results in a mixture of the even mode and the odd mode. However theundesirable odd mode can be eliminated by selecting the frequency.

Keywords:
ICRF heating, combline antenna, current drive, helical system, high harmonic heating

1. Introduction

frequency. In this paper, the radio frequency (RF)The combline antenna was designed and fabricated,
and will be installed into the large helical device (LHD)characteristics of the combline antenna are described.

at the sixth experimental campaign (2002). The

2. Modelingcombline antenna is expected to achieve two main
objectives; one is to drive a current to obtain MHD
stability at the high beta plasma and the other is to

Decomposed parts of the LHD combline antenna
element are shown in Fig. l; they are a back-plate,
Faraday shields (Mo) and a T-shaped antenna strap. A
schematic drawing of the comline antenna array isshown in Fig. 2. Two antenna elements on both sides of
the array are an inlet antenna element and an outlet
antenna element, into which the coaxial transmission
line from the LHD vacuum port is connected. The

conduct higher harmonic ion cyclotron rage offrequency (ICRF) heating. It has some advantages; l)use of mutual coupling of a traveling wave,2) vacuum

feed-throughs required only for end antenna straps, 3)easiness to obtain an impedance matching, 4) wide passband, 5) controllability of parallel wave number withC o rre sp ondin g autho r' s e - mai I : no ri @ nifs. ac@200.2by The Japan Society of Plasma
Science and Nuclear Fusion Researchjp
3t4

Takeuchi N. et al., The Radio Frequency Characteristics of the Combline Antennaequivalent circuit of the LHD combline antenna isshown in Fig. :j. It consists of the two end-elements andI and the capacitance, C of the antenna and thethe eight middle-elements, which are the same. Thereare two resonance frequencies referred to as an evenmode are and an odd mode aro, which is caused by thesupport of the antenna. These frequencies are calculated

mode is more preferable in the view point of theeffective RF wave penetration beyond an R-cut off
layer; therefore it is thought that the elimination of theas ae=lh[rc iltd rt,o=l/'[174419 using the inductance,issue.

inductance of the support of the antenna, 1". The evenodd mode with an applied frequency is an important

3. Galculation
At the l"t antenna element, the equations ofKirchhoff's law was applied on the left hand and theright hand of the support (see Fig. 3) taking into accountof a mutual coupling from the adjacent antenna element.
The mutual inductances of the even mode and the odd
mode are expressed as M* and M*, respectively.

It\o=(n+ iaL+1)(r., * ro.,)+2iaL"r",Fig. 1 Decomposed parts of the LHD combline antenna* (tat, + iaL") I, + iaM

element.

I"" ".2+ioM*1o.,F1',,o = {n + iaLI,-iroL.I.+iaMnI.r-ioM*Io.r.

.1,-(1)

Here, R is a resistance including an Ohmic loss of theantenna element and a plasma loading. 1".; and 1o.1 are thecurrents of even mode and of the odd mode at the i6 antenna element, and 12 is the current at the RF power supply at the I't antenna element. From above two equations, equations for the even mode and the odd mode areobtained as followsl,' Dunnyl Loud,+J'.
roLl) 1r., - r".,) - 2iaL"r.,-ti'

0 =2t.1"., + LtI.+2M""1".2RFo =2tolo.r+ (ir + zLc)1,+2f[*1o.2

Fig. 2 Schematic drawing of the comline antenna array.

(2)

whereL=iaL, e =iaC, f4""=iaM"", M*=iolM*,M

fol *-Iolr"=R+"CC L+L, /^=R+ L+zL"+4.
In the similar way, the following equations were obtained at the 2nd element, te element (3Sl*N-2), (N-l)d'-lelelement, and Nth element, respectively

A

Ion+IoNO = 2t.I".,+ zil *(l ..t + I".r)+ M ,1,

0 = 2t oI o., + zfu *(I ,.t + I,') + fr ,1,
O = 2t.I+IeN".r+ 2M *(t0 = 2t oI o.u + zfu *(IFig. 3 Equivalent circuit of the LHD combline antenna.

315".r-,".0-,+ 1".0*,+ 1..0*,(3)))(4)

Takeuchi N. et al., The Radio Frequency Characteristics of the Combline Antenna

0 =2t"1".r-, + 2M""(1.*-2+ I"N) - M
0 = 2t oI o.*-, + 2fr *(I".r-2^I ^+ I..r) + M oI o(5)u{;" =-2t"u',r, "+zfr""+4*2M""

0 = 2t"1"., + 2M

yTrN-tt-fuotolr'tev 12

N-t - L^I o""1"
0 = 2t oI o.* + zfu o.N-t + (2. + zLr) t*IoUS-zt(6)Z^

2Mui't .
arr(N-l) lvtA,bZl^Utr- -LA
Uff-zt ==wher e, frf t=i 16 M 7, frI 6=i 61 114o.

Here M7 and Ms are mutual inductances at the RF2M*

power supply and at the RF power output connected tothe dummy load, and 1a is a current at the output transmission line. Therefore the output impedance Za and thef't *2t"Ulr-') +2M""+':)-lU'lr '' =input impedance Z are expressed as follows.

ZIr=-tr(l".r+ I..r)Z6Io=-lo(r"."-r..")=--Here two recurrence formulas for both modes at the k thantenna element (see eq. (4)) were solved. The currents
at the 3'd element and the 2nd element were calculatedusing {,'-1 and Ip-2 in the following formulas.

(7)

whereI"=R+ L"+L.

u\')(t') =(;[, u9 [*)f"=R +L-+ L-.

C'C

Substituting above equations for eqs. (6), the current atthe (N-l)th antenna element is expressed using 1"iy andu,9)

1',"")=(l,E', u9(10)(*)

1o.,v'

where(i;.l) = ( rn-:: ;r-ir) (i;)(8)

u\tl=Huuff-zt-H"ruff-"tJ\t) = H U$-zt - H U'X-')",",
U'91 = H., Uff-zt - H orU{r-')uf), = H.rU$-zt - H orU#-')u\1'=F^utI;"-F"ruff-"u\'] = F (/$-zt - F"r.uff-"^where elements of the 2x2 matrix for the (N-l)th antenna element areL^tp.), . LutoZeZotyJ/N-t)---'"
11rN
vf l, vt2 -rfr;ufr)=Ftu{;t'-F.,Ufl-"

ZM*

Ufl', =a!-'B",",=Fi#.F"2= a"B!-'F"- d"2M*I.,Uff., =uf)=F^u$-zt-F"ru#-"-L,o,-l2Lr+Z^,.,=Ni#,-\L^)toa"BY'- d!-'8"
Fo- do2M*'"'=" i"--ZY' '"=The currents at the (N-2)n antenna element is obtainedby substituting eqs. (8) for eqs. (5).

(Foz=f : ; ) = ('$,'; xr'; ::,) (';.,:)

o.,=Ni#,(e)d"P!-o - a!-o B"F"- d"a"B:-o - d{-o B.
Ho2=
9o- a"

Here a" and p. are solutions of the recurrence formulaof the even mode, and ao and Bo are those of the odd
mode. a and p are parameters to characterize the for-where elements of the 2x2 matix for the (N-2)m areward and backward traveline waves.
316

Takeuchi N. et al., The Radio Frequency Characteristics of the Combline Antennao"=--Ja#4,F"=ao = --tffq

Using all above equations, 1".ry and /o.ry were expressedby 17. A formula to relate 1..r, Io.v /ey and 1o.1y, to 12 wasestablished in the following equation using a 4x4 ma-i", g = -t+#- t o * ur-f;+utrix;

o-lr,"t \l.tl-L.ry.* I

2t"002[r..ufr)

2t.

2[,I."Un)o2t"Ufr) +2[4""rJfr)

2M*zt"Uf,) +zfu*un)2fu""

I0+ 2[42t,9)".u"u\')
2t"Uf) +2[,t".uf]

4. RF Characteristics of LHD Combline/-\

I -L,L \tI -(zr +_2Lr\1, I|t--l - M,I, l'z[,t."uf]2[4""u9\\"l -M-I-(t t)I^E 2001505Antenna
The LHD combline antenna has ten elements; theo 100

i'characteristics of the combline antenna are examined inthe case of N= l0 and in an adequate case; t=9x10-8 [H],I 0-e [H],L1=L2=[.u=Lo=4.5x 1 0-8 fH], L"=M""-Moo=gx
C=50x10-r2 [F'], R=0.5 l{ll, M7=ltlto=3x10-e [H], andZr50 [Q]. A leal and an imaginary part of Z are plotted

so0t s0E100oN-0.50

50-100 L0.5

as a function of alas in Fig.4. o6 is a resonant
frequency of ttre even mode of the antenna element. The1 .5

1w/woFig. 4 A Real and imaginary part of Z as a function of o/real part of 2', rs found around 50 O at the regionab.

between 0.85<allars<l.2, which is called a pass-band. A

high RF power can be injected to the LHD plasma via
the combline E.ntenna with a relatively low RF voltage
and a traveling wave can be driven in the plasma within
this bandwidth. The bandwidth becomes wider with theincrease in R or the decrease in C. It can be alsochanged by tht: distance between elements, how to feed
the RF power. a configuration of the Faraday shields

mode, dot:odd mode

FlCALc{and so on.

I1

A resonant frequency of the even mode a"/2tt isselected at 75 MH4 however taking into account a!"'r--r---]--r---r--r--246

mutual inductance, a good condition where the evenmode dominatos over the odd mode is obtained at the alittle higher fiequency than 75 MHz. A decay of thecurrent across each antenna element is shown in Fig. 5,
where the fre<luency is employed at 76 MHz. As thevalue of the loading resistance R increases, thedifference between the adjacent antenna elements
becomes smaller and the decay length of the current

f,ntrance

810
Element numberExitFig. 5 Current across each antenna element at f = 76
MHz.

References[1] Takase Y. et al., TCM-Steady state Oparation,
Kyushu (1999).
I2l H. Ikezi and D.A. Phelps, Fusion Technology 31,
106 (1997\.

becomes shortt:r.

Acknowledgments[3] C.P. Moeller, R.W. Gould, D.A. Phelps and R.I.

The authors would like to thank the members ofICRF heating group at National Institute for Fusion
Science, for their fruitful comment and their support ofPinsker, The IAEA Technical Committee Meetingon RF Launchers for Plasma Heatins & Current
Drive (1993).

calculations.
317