Proceedings of ITC/ISHW2007

Demonstration of Plasma Current Control by Using
High Power Millimeter-Waves
Takashi NOTAKE1), Takashi SHIMOZUMA2), Shin KUBO2), Hiroshi IDEI3), Katsumi IDA2), Mikirou
YOSHINUMA2), Takashi KOBUCHI4), Kiyomasa WATANABE2), Shigeru INAGAKI3), Tokihiko
TOKUZAWA2), Yasuo YOSHIMURA2), Hiroe IGAMI2), Tetsuo SEKI2), Kazunobu NAGASAKI5),
Hitoshi TANAKA5), Teruo SAITO1) and Yoshinori TATEMATSU1)
1)

Research Center for Development of Far-Infrared Region, University of Fukui, Fukui 910-8507, Japan2)
3)

National Institute for Fusion Science, Toki, 509-5292, Japan

Research Institute for Applied Mechanics, Kyushu University, Fukuoka, 816-8580, Japan4)
5)Faculty of engineering, Tohoku University, Sendai, 980-8579, Japan

Graduate school of Energy Science, Kyoto University, Kyoto, 606-8501, Japan

Active current drive is one of promising tools to improve plasma quality even in the helical devices through thecontrol of the rotational transform or magnetic shear profiles and suppression of some magnetohydrodynamics
activities. The current drive by electron cyclotron waves is the most suitable actuator for these purposes in terms ofcontrollability of driven current with high density. Optimum conditions for efficient electron cyclotron current drive(ECCD) in large helical device (LHD) are explored using 3-dimensional ray-tracing code which can treat electron
cyclotron waves with large parallel refractive index. In the experiment, inversion of plasma currents corresponding
to injected ECCD modes is first demonstrated and the result can be elucidated by the Fisch-Boozer theory.
Displacements of rotational transform are also verified by use of the motional stark effect polarimetry.
Keywords: electron cyclotron resonance heating, electron cyclotron current drive, plasma current control,
magnetic shear control, rotational transform control, gyrotron.

1. Introduction
The current drive to form the poloidal magnetic field isvital in the Tokamak devices. There is no necessity todrive plasma current externally in the helical devices
because the magnetic fields to confine plasmas can beyielded by only external coils. However, the plasma
currents driven by plasma pressure gradients or powerfulneutral beam injection change the magnetic field structuresuch as rotational transform and magnetic shear. Plasma
performances will degrade according to these changes.
Therefore, the study of controlling the plasma current issignificant even in the helical devices.
Electron cyclotron current drive (ECCD) is the mostprospective tool to control plasma current profile because
the power transitions from electron cyclotron waves toresonant electrons are take placed very locally which leadto locality of plasma current with high density [1-2].
Besides, we can select the location of driven plasma
current almost arbitrarily by adjusting some parameterssuch as magnetic field strength, wave-frequency, parallel
refractive index and so on.
This paper consists of following sections. The section
2 describes inspection for effective ECCD in LHD
author’s e-mail: notake@fir.fukui-u.ac.jp

configurations. The section 3 is devoted to explanation ofexperimental results. The plasma current control by
ECCD is firstly demonstrated and shift of rotationaltransformation is observed. Finally, our research issummarized in the section 4.

2. Scrutiny for ECCD in LHD
In an inward shifted configuration of large helicaldevice (LHD), improvements of not only neoclassicaltransport but also anomalous one are observedexperimentally. According to a linear MHD theory, on theone hand, it is predicted that some MHD instabilities
affect plasma confinement in such inward shifted
configurations due to the magnetic-hill structure. As oneof the reasons for present fine confinement capability inthe configuration, some non-linear effects are pointed out.
They may prevent MHD activities from growing further.
However in order to extend an operation parameter rangeof LHD, MHD activities should be suppressed by somekind of ways because they must cause severe degradation
to plasma confinement in high b plasmas. ECCD has
possibility that it can improve MHD properties only by
local current control without degradations both ofProceedings of ITC/ISHW2007

k!2N2+l2Ò 2à!2?

c+k! 4N 4+2! 2N 2l2Ò 2+l 4Ò 4kk! 2N 2l2Ò 2+l4Ò 4à! 2l 2Ò 2k

ò

ó2! 2N kvkc à ! 2N 2+l 2Ò 2
k=1

Where N||,l,Ω,ω, v⊥, v|| and c mean parallel refractive
index, harmonic number of cyclotron resonance, electron
cyclotron frequency, wave frequency, perpendicular
thermal velocity, parallel thermal velocity and lightvelocity, respectively. For N||<1, this equation describes anellipse, and resonant interaction is only possible for
lÒ=! > (1 à N 2) 0:5
kwhich excludes anomalous cyclotron resonance. On theother hands, for N||>1, it represents a hyperbolic curve inthe velocity space. As for an example, the calculated
resonant curves in the momentum space under the certain
parameters are shown in Fig.1. In the case of large N||
injection, the resonant curves move toward high parallel
velocity regions in velocity space due to strong up-shiftof cyclotron resonance frequency. And the resonancebegins to arise even in the lower magnetic field side than
3 Tesla corresponding to fundamental resonancecondition of usual ECRH for 84GHz-waves. Thesefindings indicate that electron cyclotron waves with large
N|| tend to interact with electrons having higher parallel
velocity component. Therefore, injecting electron
cyclotron waves with large N|| must be effective in termsof collisionality to achieve high ECCD efficiency
The effect of electron trapping is another critical issue.
Trapped electrons reduce the ECCD efficiency or may

reverse the direction of the driven current since thediffusions in velocity space involved with electron
cyclotron damping is mainly to perpendicular directions[6]. Especially, LHD has not only toroidicity but alsohelicity and the fraction of them strongly depends onmagnetic configurations. In order to avoid such trouble,
depositing the wave power at magnetic ripple top region
is ideal. Fig.2 shows contour plots of magnetic ripples forthe two magnetic configurations of LHD. Upper column
corresponds to the case of magnetic axis is set at 3.5m
which is one of the inward shifted configurations. Thisconfiguration has fine confinement performance andsuitable for effective ECRH. On the other hand, lower
column shows magnetic ripples when the magnetic axis
set at 3.75m which is standard magnetic configuration ofLHD. This configuration may be more suitable from theviewpoint of the ECCD efficiency because it hardly has
magnetic ripple near the magnetic axis. So, theimprovement of the efficiency degradation due to trappedelectrons can be expected. However, only 84GHz
gyrotoron is available in this configuration by the limit ofachievable magnetic field strength. As shown in the Fig.2,
magnetic ripples are more enhanced in the peripheral
regions. Unfortunately, it is not compatible that to injectelectron cyclotron waves with large N|| component and todeposit it near the magnetic axis where magnetic ripples
are weak since strong Doppler up-shift is induced. To
inspect more rigorously, we have to solve theFokker-Planck equation under the 3-dimensional LHD
configuration.
To try higher power ECCD experiments, the survey ofoptimum condition under the inward shifted configurationis considered in this paper.

3.1

3 Te=5keV
N||=0.5

Vperp/Vthneoclassical and anomalous transports even in the inward
shifted configurations.
To improve plasma confinement capability by ECCD
in LHD, two schemes can be conceivable. One of them is
ECCD to co-direction (Co-ECCD) which raises rotationaltransform and result in exclusion of low-order rationalsurfaces at plasma core region where magnetic shear isvery weak. The other is ECCD to counter-direction(Ctr-ECCD) which can enhance negative magnetic shear
locally. Therefore, driving plasma current to arbitrary
directions is desirable as current drive actuator.
The mechanism of ECCD is based on asymmetricmodification of electron resistivity in the momentum
space formed by selective electron cyclotron resonance.
Electron cyclotron waves are absorbed by electrons thathave velocity component satisfying the following
condition taking Doppler up-shift and relativistic
down-shift into consideration [3-5].
!2N2+l2Ò 2 ð v ñ 23.0
2.9
2.8

22.7

1-3-2-10

Vpara/Vth123Fig.1. Resonance curves in the velocity space. Here,electron temperature, parallel refractive index,
harmonic number and wave frequency are set to5keV, 0.5, 1 and 84GHz respectively. Numerics on
the lines indicate magnetic field strength.

Proceedings of ITC/ISHW2007
propagation angles satisfying following condition,
Njcosòj > j1 à lÒ=!j; vt=c;
the relativistic down shift of the cyclotron frequency can beneglected because Doppler effect become dominant.
Where θand vt mean propagation angle with respect tomagnetic field lines and electron thermal velocity,respectively. So, we can use absorption coefficientsobtained from the non-relativistic dielectric tensor for a hot
Maxwellian plasma [8]. In this frame, power absorption
line is decided using the conventional Fried-Conte function
described byFig.2. The profiles of magnetic field strength normalized
by the maximum value on the each flux surfaces.
Zero of toroidal and poloidal angles correspond tovertically elongated cross section and inside ofequatorial plane respectively.

Fig.3. The ECCD configuration by using 2O-port antenna.
Two gyrotrons whose frequencies are 84 and168GHz are connected to the port.

To investigate optimum incident angle for ECCD, a
ray-tracing calculation is carried out. Ray-tracing is asophisticated technique, providing quite a little insights on
wave-propagation and absorption in dispersant fusion
plasmas. Its condition of validity called WKBapproximation is the following.
~j ü k2
jrk

Electron cyclotron waves in the wavelength range ofmillimeters are sufficiently adequate for existing fusionresearch machines. Ray-tracing code had developed for
ECRH in the 3-dimensional magnetic field structure ofLHD, but by that code quasi-perpendicularly propagatingwaves with respect to magnetic field lines in weakly
relativistic thermal plasma can only be treated [7].
Therefore existing ray-tracing code is extended in order todeal with obliquely propagating waves. Under theZ(ð) = ip

R p2ið
2 exp(à ð2) à1 exp(à t2=2)dt

which can be calculated numerically. Here, an argument ðis defined as follows.
pð ñ c(! à !c)=( 2 vt!Ncosò)The 2O-port antenna installed the horizontally elongatedcross section of LHD is suitable for ECCD because it canswing the beam to toroidal directions widely. From thisport, we aim a beam at magnetic axis of neighbor verticallyelongated cross sections as shown in Fig.3. According to
the Fisch-Boozer theory, plasma currents by ECCD aresupposed to be driven to clockwise/counterclockwise
directions corresponding to the beam injection tocounterclockwise/clockwise directions respectively.
Fig.4 shows parameter changes along the central ray
obtained from multi ray-tracing calculation applied to84GHz beam from 2O-port antenna [9]. Here, the magnetic
axis of 3.5m and average magnetic field strength of 2.829T
is employed and beam is aimed at magnetic axis ofvertically elongated cross section. In this configuration,
on-axis ECCD will be possible because the power ofelectron cyclotron waves almost absorbed within ther=0.2.

1
normalized beam power

0.50w
1- wcenormalized abs. coef.

N||-0.5
2.8

33.2

3.4

3.6

3.8

Path-length from antenna [m]Fig.4. Ray-tracing result for the fundamental O–mode
ECCD obliquely injected from 2O-port antenna.

Proceedings of ITC/ISHW2007

3. Experimental results and discussion

1

Ip-Ip(t=0.25s) [kA]

In LHD, ECCD is tried using 2O port antenna at themagnetic configuration of Rax=3.5m. Magnetic fieldstrength, injection angle and wave polarization [7-8] are
optimized based on oblique ray-tracing code as
mentioned above. Target plasma is sustained by only
ECRH to omit NBCD effects and ECCD is superposed tothe target plasma from 0.25s to 0.75s. Fig. 5 shows
comparison of temporal evolutions of total plasma
currents measured with Rogowski coil. Bootstrap current
is contained in the total plasma currents, but that
contribution is weak judging by balanced ECCD
discharge. For Co- and Ctr-ECCD discharges, directionsof driven plasma current are consistent with linear theory.
Therefore authentic plasma current control by ECCD isdemonstrated successfully. However, absolute values ofplasma currents are still very low because of highelectron temperature which leads to huge L/R timecompared with ECCD duration. So some extent of thedriven current may be cancelled by the induced backelectromotive force. However, certain shifts ofpolarization angle which reflect changes of rotationaltransform are observed by the motional Stark effectpolarimetry [10] as shown in the Fig.6. This result very
encourages us to control magnetic field structure and thenimprove confinement capability of LHD plasma.
However, further experiments are needed with higher
power and longer pulse duration time to impact
drastically the plasma performance through themodification of plasma current profile and magnetic fieldstructures.

Co-ECCD

0Balanced Injection-1

Ctr-ECCD-2-3
0.2

ECH(600kW)&ECCD(400kW)
0.3

ECH(320kW)
0.4
0.5

0.60.7

Time [s]Fig.5.

Temporal evolution of the total plasma currents.
Plasma currents are normalized by the values atthe ECCD is injected (t=0.25s.)

) 0.4
g.
e 0.2d(g. 0na.l -0.2
opΔ-0.4)
g. 0.4e 0.2d(g. 0na.lo -0.2pt=1.5(s)
after
300ms

ECHCtr ECCD
Co ECCDafter
t=1.8(s)600msΔ-0.4
3.8

3.9

4R(m)

4.1

4.2

Fig.6. Change of polarization angle during ECCD
diagnosed by MSE polarimetry measurement.

4. Summary
With a view to control of plasma current and magnetic
field structure in LHD, the application of ECCD is
considered in detail and actually tested. The inversion of
directions of plasma currents is clearly observed. So
plasma current control by ECCD is successfully
demonstrated for the first time in LHD because thisinversion is consistent with conceptual prospect. ECCD
will be expected as an indispensable tool in order toimprove plasma performance.

Acknowledgment
I would like to express my gratitude to the manycolleagues, especially, Dr. Takahiro Suzuki of JAEA andProf. Testuo Watari of NIFS who gave me valuablecomments. This work was supported by the NIFS under
the grant code numbers NIFS06ULRR501,502 and 503.

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