J. Plasma Fusion Res. SERIES. Vol.5 (2002) 328-332

lnvestigation of Turbulence in High-Temperature Plasma byMicrowave Scattering Techniques in Modern Stellarators
SKVORTSOVA Nina N., BATANOV German M., KOLIK Leonid V., PETROV Alexander E.,
PSHENICHNIKOV Anton A., SARKSYAN Karen A., KHARCHEV Nikolay K.,

OHKUBO KUNiZOI, SHIMOZUMA TAKAShiI, IDEI HirOShil, YOSHIMURA YASUOI,KUBo Shinr, SANCHEZ Joaquin2, ESTRADA Tereza2 and VAN MILLIGEN Boudewijn2General Physics Institute, Moscow I17942, Russiafor Fusion Science, Toki 509-5292, Japant National Institute2EUnoeroM-ctEMAT, Madrid 28040, spain(Received: 12 December 2007 / Accepted: 19 July 2002)

Abstract
One of the problems of plasma turbulence is the complexity of experimental investigations offluctuations in the central region of the plasma column. The development of diagnostics that make itpossible to directly measure fluctuations of plasma parameters in the plasma core is of great importance.
A description of such diagnostics is given in this article, along with results from the first measurementsof the characteristics of fluctuations in high-temperature plasmas in three essentially different helicalsystems: L-2M (GPI, Moscow), LHD (NIFS, Toki), and TJ-II (CIEMAT, Madrid).

Keywords:
plasma turbulence, stellarator, microwave, scattering technique

1. lntroductioncolumn) has been studied in sufficient detail. Diagnostic

The study and description of the spectral andtechniques for measuring the characteristics ofprobability characteristics of random plasma processes
has long attracted the attention of investigators engaged
in the field of plasma physics. Recently, interest in thisproblem even has increased when it became clear thatmany global plasma processes (diffusion of particles,heat conductivity, equilibrium in the magnetic field,etc.), depend large on random fluctuation of a number offluctuations in the edge plasma are available in every
toroidal device (both in stellarators and tokamaks);

plasma variables [1,2]. Therefore, information on
spectral and probability behavior of fluctuations is ofprime importance for solving fundamental and appliedof the plasma column are two orders of magnitude
higher than those at the edge. Study of fluctuation
processes in this region is much more interesting, butproblems related to the creation of high-temperatureplasma in thermonuclear toroidal devices. To date, theprobability and spectral characteristics of fluctuations inmore complicated problem because adequate diagnostic
techniques are lacking. In recent times investigation of

the region of toroidal devices in which a lowtemperature plasma exists (the edge of the plasmacomplicated HIB diagnostic [2]. An original and simpler

because of this, the behavior of fluctuations at theplasma edge is studied extensively. As a rule, thedensity fluctuations in a low-temperature plasma aredescribed by the model of strong structural turbulence[3,4]. The temperature and density in the central region

plasma center fluctuations began by the very

@2OO2 by The Japan Society of Plasma

Corresponding author's e-mail: nina@fpl. gpi.ru

Science and Nuclear Fusion Research328

Skvortsova N.N. et al., lnvestigation of Turbulence in High-Temperature Plasma by Microwave Scattering Techniques

method of measuring the characteristics of density
fluctuations in high-temperature plasma was elaborated
in the General Physics Institute. This method based on
microwave scattering on fluctuations provides
information on the behavior of fluctuations in the central

received the ordinary component of the gyrotron
radiation scattered at an angle of nlZ by density
fluctuations from the central region of the plasma. Thisregion (which is indicated in Fig. I by small squares) is

the intersection region of the incident and scatteredmicrowave beams. The diameter of the scattering regionis d = 5 cm. For a wave number of gyrotron radiation fte= 15 cm-r, the Bragg condition for scattering at an angleof p/2 is satisfied for the density fluctuations dn whose
size corresponds to k""= 20 cm-l 1i." = 3-4 mm).
Fluctuations in the edge plasma were measured byplasma region.

2. Scattering Experiment in the L-2M
Stellarator
The basic parameters of the L-2M stellarator aredescribed in dotail in ref. [5]. The major radius is R =100 cm, and the mean vacuum separatrix radius is r, =Langmuir probes.

It was shown earlier, that the wavelet-coherence
coefficient between fluctuations in the central and edge
regions is high [6], which allows us to assume thatturbulence in both regions is associated with similar

11.5 cm.

The plasma was created and heated with a gyrotron
operating at a frequency of /0 = 75 GHz (Ao = 4 mm).
The plasma parameters in these experiments were thefollowing: the mean plasma density was n = (l-2) x

processes. The difference between these processes canlOrem-3, Z"(0) - 0.5-0.7 keV, zi - 0.15 keV. Density
fluctuations 5n in the plasma core were measured with ahomodyne setup extracting a scattered signal from thebe traced in analysis of their probability parameters.
Figure 2 shows histograms for the amplitudes of plasma

heating gyrotron radiation. The setup detected theradiation arisrng from scattering of the ordinary
component of high-power gyrotron radiation (8",0 ll B,
where B is the stellarator toroidal magnetic field)

regions, respectively. The fluctuation amplitude is laidas the abscissa; the number of counts is laid as theordinate. The shape of the histogram for the plasmaedge fluctuations as well as the values of the third andresulting fronr splitting of the linearly polarizedradiation at the plasma boundary. The arrangement ofthe diagnostics in the poloidal cross section of thestellarator chanrber is shown schematically in Fig. 1. A
horn antenna that was positioned in the upper port

fourth moments allow us to identify the Probability
Distribution Function (PDF) of these fluctuations as adensity fluctuations from the central and the edge

Gaussian probability distribution. The histogram for thecentral region is essentially non-Gaussian. The third andfourth moments are equal to 0.9 and 8.2, respectively.
This indicates clearly that the PDF for the plasma centercannot be classed among Gaussian distributions and,
consequently, the state of plasma fluctuations in thisReceiving antennaof scattered radiation

region is essentially nonequilibrium. The probability oft40
130o-beam

b: ml = 0.05

ii

80
709t

m2=8.2i1tl

90

Gyrotronradiation

a: m1 = 0.9

tti'i

fi0
n tm

- lr"

shot N 50847

flall

1X

m2=3.2

i t.t

60
50z

40

n,t00.o{.r04.05

0.m

0.05

0.r00.,t50.20

Amplitude, arb.un,Fig. 2 PDF of turbulent pulsations in (a) the high-temperature and (b) low-temperature regions.

Fig. 1 Scattering geometry for L-2M.
329

Skvortsova N.N. et al., lnvesttgation of Turbulence in High-Temperature Plasma by Microwave Scattering Techniques

Heating
BeamDetection
Beam'3 o.et

Io.oo

H 0.2

I

5{o.o10n10"

1o-2100

Iime lag, mks

Fig. 3 ACF of {a) fluctuation amplitudes and (b) incre-Steerlng

ments of fluctuation amplitudes in the center ofMirror

the plasma column.

SGerlng
MirrorScattered
Beamrare events for density fluctuations increases

ProblngBeamsubstantially, which is typical of PDFs with heavy tails.

It should be noted that the high-temperature plasma inthe central region is under the direct action of theFig. 4 Scattering geometry for LHD.

heating microwave beam, whereas the dominant process
for the plasma edge is the energy dissipation. It may be

ShotN220l6osuggested that the difference from the Gaussian
distribution is a direct consequence of turbulent

?00
600

J00

processes associated with plasma heating in the central

t00
t00

zregion.

200The autocorrelation functions (ACF) of thefluctuation amplitudes for the central region and the1000|.0increments of fluctuation amplitudes are also shown inO,EFig. 3. The ACF of fluctuation amplitudes has a shape
typical for the strong structural turbulence [7]. We cannotice that the ACF of increments of fluctuation
amplitudes in Fig. 3 is more peaked and contains nopulsations at its tail. This means that the temporal
sample of the increments of density fluctuation
amplitudes is homogeneous and independent. The

0.6
0.1
0.1
0.0.0 .2.0.{0.5Iag,m3ur .)correlation time for the increments is much shorter thanother characteristic times of the turbulent process understudy (the oscillation periods, the amplitude correlationtime). This time is about l-2 ps and is comparable withthe characteristic time of turbulent flux measured in theedge plasma [8].

J.6-1
.8

l0

l0

l0

l050

Frcquenoy, kH z
Fig. 5 (a) PDF, (b) ACF and (c) Fourier-spectrum forplasma density fluctuations in core plasma.

3. Scattering Experiment in the LHD
arrangement is shown in Fig. 4. One of two ECH
antennae was adapted for use as a receiving antenna. A
84 GHz gyrotron heating beam launched by the otherantenna was used as a probing beam. The scattering
volume was situated near the focuses of two launchine

The LHD parameters are described in detail in [9].
The LHD is the largest superconducting helical device
with a divertor (l = 2, m = tO, R = 3.6-3.9 m, r = 0.6 m,
B < 3 T). The fluctuations 6z in the plasma core werealso measured with a homodyne setup. The experimental
330

Skvortsova N.N . et al., lnvesttgation of Turbulence in High-Temperature Plasma by Microwave Scattering Techniques

antennae [0]. For the present geometry of the antenna

central electron temperature was I"(0) - 0.5 - 0.7 keV.

sets as shou,n in Fig. 4, the scattering angle
corresponded to the fluctuation wave number ft = 10-15_lcm'-

scattering of a probing microwave beam (wavelength 2mm, power 0.5 W), as shown in Fig. 6. Note, the 2 mm

Figure 5 shows the PDFs of amplitudes, the ACF,

scattering diagnostic was first implemented in the L-2M

and the Fourier-spectrum of plasma density fluctuations.

stellarator in the early 1990s [2]. In the present
experiments, the scattered volume was located at r = r"l
2. The measured scattered signals correspond to two
wave numbers: 3 cm-l and 6 cm-I.
The spectral, probability, wavelet-coherence andPlasma density fluctuations were measured from

For the frequency and wave number range observed inthis experimenl, we can conclude that associated density

fluctuations originate from driffdissipative or trappedelectron instabilities. The shapes of the PDF and ACF
exhibit non-Gaussian features of turbulent processes inother characteristics were determined for turbulent
plasma signals from the region r - r"12. Below we only

the central region. This, again, leads us to the conclusionthat the heating microwave beam brings on the plasma
perturbation processes and the state of plasma
fluctuations in this region is essentially nonequilibrium(as it was shov'n for the L-2M stellarator).

present the experimental data referring to a series of TJ-II experiments on the nitrogen cold pulse injection inplasma.

The 2 mm measurements were successfully used toestimate the lag time of the nitrogen appearance in the4. Scattering Experiment in the TJ-llStellarator
The parameters of the TJ-II stellarator are described

Shrttiul35

in detail in [1 1]. This is a four-period helical axis
CotdG-.

slellarator, Bo< 1.2 T. The major radius is R = 150 cm,
and the mean vacuum separatrix radius is r" 1 22 cm.
The plasma was created and heated with a gyrotron
operating at a frequency of /e = 53.2 GHz (second
harmonic, X-mode). In these experiments, the averageplasma density was r? = (0.6 - 0.7) x 10re m-3, the{tEra8,,

2.0

ildt00t0taonils

N,Ls6gEEa

2060 1@ t40

lEOltTlme, mf
Fig. 7 (a) Scattered signal, (b) RMS deviation of the scat-tered signal, and (c) Fourier-spectrum of plasma
density fluctuations (k= 6 cm-t). The cold nitrogenpulse reaches the scattering region is indicated byarrows. The spectral intensity is shown by grayshadding on the logarithmic scale.

Fig. 6 Scattering geometry for TJ-11.
331

Skvortsova N.N. et al., lnvestigation of Turbulence in High-Temperature Plasma by Microwave Scattering Techniques

middle radius of the plasma column. Figure 7 illustrates
the scattered signal, RMS, and Fourier-spectrum of theturbulent signal with the wave number 6 cm I for a shotwith nitrogen pulse injection. It is seen that the structure

Foundation for Basic Research (project no. 00-02-17507
and 0l-02-16143) and the LIME program.

of the spectrum changed noticeably when the cold[] G.M. Batanov et al.,Plasma Phys. Control. Fusion,

References
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5. Conclusion[3] N.K. Kharchev, K.A. Sarksyan and N.N. Skvortsova,
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[10] S. Kubo et al., Ann. Rep. NIFS 1999-2000, 34

Comparative measurements of density fluctuations

in high-temperature core plasmas were performed inthree essentially different devices: L-2M (GPI,Moscow), LHD (NIFS, Toki), TJ-II (CIEMAT, Madrid).

The studies of the spectral, correlation, probability
characteristics of amplitude of fluctuations in the hightemperature plasma show that the turbulent state of thisplasma can be identified as strong structural turbulence.
A characteristic feature of turbulence of this kind is thatrare events become significant and, hence, should betaken into consideration when constructing a model for(2000).

turbulent transport in high-temperature plasma. The
question of stochastic plasma structures in high-[11] I. Garsia-Cortes et a/., Nucl. Fusion 40, 1867

temperature plasma invites further investigation.

[12] G.M. Batanov et al.,Plasma Phys. Reports 19,628(2000).

This work was supported in part by the Russian(1993).

332