J. Plasma
J.
Plasma Fusion
Fusion Res.
Res. SERIES,SERIES,Vol.
Vol.6 6(2004)(2004)410–412
000–000

Frequency Broadening ofHigh Harmonic Fast Wave in Plasmas
TANIGUCHI Tomokazu, TAKASE Yuichi, EJIRI Akira, SHIRAIWA Syun’ichi,
NAGASHIMA Yoshihiko, KASAHARA Hiroshi, YAMADA Takuma, ARAMASU Masaru,
OHARA Shinya and YAMAGISHI Kenichi
University of Tokyo, Tokyo 113-8656, Japan(Received: 9 December 2003 / Accepted: 1 April 2004)

Abstract
The high harmonic fast wave (HHFW) is a promising candidate for driving noninductive current in plasmas withhigh dielectric constant, such as in a spherical tokamak. A broadening of the HHFW frequency spectrum has been
observed in the TST-2 spherical tokamak [1]. If the broadening were caused by scattering of the HHFW by density
fluctuations, the wave number could be altered and wave absorption could be affected. The time evolution of theHHFW spectrum was calculated and the experimentally measured spectrum was reproduced well under someconditions. The power deposition profile was calculated to become broader and shifted outward as a result of scattering,which may explain the deterioration of current drive efficiency observed in some experiments.
Keywords:
high harmonic fast wave, heating, spherical tokamak, scattering, density fluctuation

1. Introduction

observed [1]. A similar broadening has also been observed in
LH heating experiments [9,10]. A frequency broadening canarise from scattering by density fluctuations [11-13] or byparametric instability [9]. The density fluctuation has large
amplitudes near the plasma edge. Waves propagating into theplasma could be scattered in the edge region by these low
frequency fluctuations (e.g., drift waves). Experimental results
are described in Sec. 2. The calculation model is described inSec. 3. The calculated results are compared with theexperimentally measured spectrum in Sec. 4. Conclusions aregiven in Sec. 5.

Attractive features of the spherical tokamak (ST) include
improved stability at high beta and high natural elongation[2]. Recent experiments performed on START [3], NSTX [4]and MAST [5] have demonstrated simultaneous achievementof good confinement and high beta [6]. For an ST reactor
elimination of the Ohmic solenoid is necessary, and therefore
non-inductive current drive by waves [7] or neutral beams
injection is required. The HHFW, which is an electromagnetic
wave in the frequency range of several times the ion cyclotron
frequency, has good accessibility to the high density coreplasma, and is therefore a promising candidate for driving
current in plasmas with high dielectric constant.
The lower hybrid (LH) waves requires high wave
numbers to satisfy accessibility, but in such a case the wave
damps at in the plasma edge region before it can propagate
into the core. The electron cyclotron waves cannot propagate
in overdense plasmas (i.e., high dielectric constant plasmas),in which

2. Experiment
TST-2 is a spherical tokamak at the University of Tokyo,
with major radius R = 0.38 m, minor radius a = 0.25 m, andaspect ratio A = 1.5. Typical values of the toroidal magnetic
field and the plasma current are Bt = 0.2 T and Ip = 0.1 MA[1].
A 21 MHz sinusoidal wave is amplified to 32 W and isinjected into the plasma. The incident wave is detected by asingle-turn magnetic probe at the antenna. The scattered wave
measured by a probe separated from the antenna by 60
degrees in the toroidal direction on the outward equatorial
plane is discussed in this paper. The detected signal isamplified, mixed with a local oscillator at 21.1 MHz amplified
again and digitized at 1 MHz. The frequency spectrum is

Π e2Ω e2 >> 1, where Πe is the electron plasma frequency

and Ωe is the electron cyclotron frequency. The HHFW canpenetrate into the core, and because it is strongly damped inhigh beta plasmas, it may be possible to control the current
density profile [8] in order to improve stability andconfinement.
In an earlier HHFW experiment using a combline
antenna, a broadening of the frequency spectrum was

Corresponding author’s e-mail: taniguti@plasma.phys.s.u-tokyo.ac.jp1410©2004 by The Japan Society of Plasma
Science and Nuclear Fusion ResearchTaniguchi T. et al., Frequency Broadening of High Harmonic Fast Wave in Plasmas

The frequency spectrum measured at the antenna without
plasma (unscattered spectrum) is shown in Fig. 2. The
frequency spectrum measured by the probe 60 degrees awayfrom the antenna toroidally with plasma (scattered spectrum)is shown in Fig. 3. The smooth spectrum (exponentially decaywidth, fexp decay ≈ 4 kHZ) becomes noisier ( fexp decay ≈ 9 kHZ)
and broader after being scattered in the plasma. A typicalfrequency width (FWHM) of the scattered spectrum is around30 kHz. The fact that the scattered spectrum decays
exponentially suggests that this broadening is caused byscattering by density fluctuations, whose spectrum decays
exponentially. In an experiment with additional gas puff, acorrelation between the frequency width and the plasma
density measured by an interferometer was found. This effectis discussed in Sec. 4.

obtained by Fourier transform.
In this paper, the frequency broadening of the HHFW isassumed to be caused by scattering by plasma density
fluctuations, primarily at the edge. The fluctuation level wasmeasured using the double probe technique. The frequency
spectrum of the ion saturation current decays exponentially,
with a characteristic frequency width of around 20 kHz(Fig. 1). The fluctuation level was around 30 % at the edge.
We assume that the ion saturation current fluctuation is caused
primarily by the density fluctuation.

Iis Spectra [dB]-20

3. Calculation model
Scattering of the LH wave was formulated before, but
the electrostatic approximation was used. This approximation
cannot be used for HHFW. We start with a cold plasma modelwith density fluctuations. The validity of using the cold
plasma model was verified. In this HHFW experiment, the-40-600Fig. 1

50100f[kHz]k ⊥v T , edifference is of order O(be), where be =
Ωe150

↔ →

↔ →
↔
ωω ′ ↔
δnD (k ,ω)E k→,ω = Σ c 2 a ′ – 1 E k ′, ω ′N→δ k, δω, where k ,ωare wave number and angular frequency of an incident→→→
wave, k ′, ω′ are those of a scattered wave, δ k = | k ′ – k |,→↔
↔
δω = |ω′ – ω | , a k→, ω is the dielectric tensor, D (k , ω) =→→↔

k × k × 1+0Signal[dB]≈ 10–6.
→→

Spectra of ion saturation current measured at the edgeof plasmas.

2δnω 2 ↔→= δ n exp – δ k – δωk fluct ω fluct
Nc 2 a k ,ω , N δ k , δω→is the normalized density fluctuation, vt is the thermalvelocity, c is the speed of light, and summention is taken over→
all wave numbers k and angular frequencies ω. Based on thefact that the frequency broadening is small compared to the∂wave frequency itself, we expand ω → ω →k + i —to obtain∂t-10-20-30→↔

00.1
0.2|f-21.1| [MHz]→↔
∂ E k,ω
↔
= – Σ ωω2 ′e k · a ′– 1 · e k ′ E k ′, ω ′ δ nie k · ∂ D ·e k,N δ k,δω∂t∂ωc→0.3→→→→→→

where ê k→ is the unit vector in the direction of electric field.
↔
Note ê k→· D · ê k→ = 0. We consider three wave coupling,
consisting of the incident HHFW, the low frequency density
fluctuation, and the scattered HHFW. For the wave energy⎯density u, we define C →k ,ω = √ u k→,ω ∝ exp(–iω t) and sinceFig. 2 Unscattered frequency spectrum (measured).

Signal[dB]2-10u →k ,ω =-20i∂ C k ,ω=Σσ∂t→-30E c2 ↔ →D k , ω , we have the following relation,
8π ω 2→→→→ →, whered k ′ d ω ′V k,k ′, ω ,ω ′ δ nN δ k , δωV(k ,k ′,ω,ω′) = –→↔

↔

2 e ·M ·e
20.9
Fig. 320.95

2121.05
f[MHz]

21.1↔

M≡

Measured (solid line) and calculated (dotted line)
frequency spectra.

↔

ω ′e · a ′ – 1 · e ′↔

e′· M ′ · e′,↔ →∂ c 2 D(k,ω ) , σ represents the mode of the wave.
∂ω 2ω

Then following time evolution of the wave energy density
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Taniguchi T. et al., Frequency Broadening of High Harmonic Fast Wave in Plasmas∂ u k ,ω=∂tfrequency, and the magnetic shear (the safety factor q varies
from 8 at the edge to 4 at r / a = 0.5), causes a change in k||.
Since the HHFW damps mainly by electron Landau Damping
under the condition discussed in this paper, a broader profile
is natural consequence of scattering. The outward shift iscaused by scattering in the outer region, where the density
fluctuation has a large amplitude. In the simulation, a large
variation was observed in k⊥ and therefore in k||. As thefluctuation level becomes higher, the waves suffer more
scattering in the outer region and an additional peak in theabsorption profile appears at an outer radius.

→u →k ,ω can be derived in the form of Pauli equation,

Σσ→→ →

dk ′ dω ′ V k , k ′, ω , ω ′δnN δ k , δω→2u σ – u k, ω→→k ′ω ′.

The wave can be converted to another mode with a certain
probability. In this paper, we do not consider mode
conversion, since there exist no other mode waves in the range
fincident ± 3 ffluct .

4. Results of calculation

Absorped Power[%/rho]

The frequency spectrum calculated by the model
described in Sec. 3 is compared with the measured spectrum
in Fig. 3. Scattering was treated by the Monte-Carlo method.
The wave is excited at the plasma edge and propagates in.
Scattering and damping within each time interval ∆t arecalculated, till the wave is detected by a probe located 60
degrees away toroidally. The density fluctuation level wastaken to be the value measured by a double probe. The
frequency spectrum matches the experimentally measured
spectrum the best when the typical wave number of thedensity fluctuation is 2000 m–1. The simulation results
indicate a correlation between the spectrum width and thecore plasma density, as observed in a gas-puff experiment.
Exponential decay width of 6.5 kHz (5 kHz in theexperiment) at n20 = 0.1 [m–3] increases 10.5 kHz (40 kHz inexperiments) at n 20 = 0.3 [m–3]. At higher densities, theHHFW rays are shifted outward, where the density fluctuation
is more intense. They then suffer heavier scattering, resulting
in a broader spectrum. Also density fluctuation level will play
an important role, which is not measured simultaniously.
The calculated damping profile (absorption profile) isshown in Fig. 4. The profile is broader and is shifted outward.
The wave number vector is scattered mainly in the direction
perpendicular to the magnetic filed with a small change of

5. Conclusions
A broadening of the HHFW frequency spectrum wasmeasured. The spectrum width was typically about 30 kHz(FWHM). A model without the electrostatic approximation
was formulated. The time evolution of the frequency spectrum
was studied by a Monte-Carlo simulation and was comparedwith experimental data. The experimentally measured
spectrum was reproduced well when the typical wave numberof the density fluctuation of 2000 m–1 was used. In a gas-puff
experiment, a correlation between the plasma density and thescattered spectrum width was observed. The simulation results
indicate that at higher densities, the HHFW with lower Alfvén
velocity suffers heavier scattering at the edge, resulting in abroader spectrum. The damping profile was calculated tobroaden a little with weak scattering, and an additional peakin the absorption profile appears at an outer radius with strong
scattering. A density profile with a lower edge density isfavorable to minimize the effects of scattering. Thismechanism may also be used as a diagnostic to obtain
information about the density fluctuation.

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864
2
000.2

0.4

0.6

0.8

1r/aFig. 4

Calculated absorption profiles with (solid line) andwithout (dotted line) scattering.

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