J. Plasma Fusion Res. SERIES, Vol. 8 (2009)

On the Observation of ETG-Scale Turbulence on HT-7 tokamak*
Tao Zhang ,Yadong Li, Shiyao Lin, Xiang Gao, Junyu ZhaoˈQiang Xu
Institute of Plasma Physics, Chinese Academy of Sciences, P.O.BOX 1126, Hefei,
Anhui 230031, People’s Republic of China(Received: 28 August 2008 / Accepted: 10 October 2008)

ETG-scale turbulence can be measured by CO2 collective scattering system on HT-7 tokamak. In ohmic plasma,electron density fluctuation was measured from 16 cm-1 to 38 cm-1. These turbulence show low frequency features.
At n =1.5×1019 m-3 (where n is the line average density), the k-spectrum satisfy a power law S(k)�k -4. Inorder to have an idea about the turbulence evolution in one discharge, analyses are done for shot #100878 at two
time slices in the current and density flat-top phase. It is found that at t =500 ms, an evident low frequency feature(f ~ 80 kHz) appears in the frequency spectrum of k=20 cm-1 fluctuation by contrast with that of t=300 ms. The
difference can be attributed to the steeper electron temperature profile at t=500 ms. PDF analysis is conducted on
the scattering signal. The result shows that the signal is random within the experimental precision.
Keywords: CO2 collective scattering, small scale turbulence, HT-7 tokamak

different scales. Kolmogorov law [19] show that in 3D
fluid turbulence the kinetic energy at the scale 1/k ( �E(k)dk=1/2<v2>) cascades as a power law E(k) ~ k-5/3 inthe inertial range. The situation is different for 2D
turbulence because the existence of two conserved
quantities, energy and enstrophy (integrated square ofvorticity) make dual cascade take place. It can beassumed that at a given initial time energy is injected at ascale kf. The nonlinear interaction will transfer energy tolarger scales k<kf, which is called inverse energy cascade,usually leading to the formation of large structure. Thecascade process will result in a power law energy
distribution E(k) ~ k-5/3 at k<kf. On the other hand thedirect enstrophy cascade will transfer fluctuation energy
to smaller scales k>kf until dissipation scale, leading toenergy distribution E(k) ~ k-3 at k>kf. Due to strong
magnetic field in tokamak, the turbulence is generallyexpected to follow the two dimensional picture.
In order to better understand the turbulence andanomalous transport, fluctuation measurements over arange in wavenumbers have been undertaken in a varietyof fusion research devices. These efforts include broadwave number fluctuation measurement in DIII-D [10],far-infrared (FIR) scattering and Doppler backscattering inTore Supra [11, 12], microwave scattering in NSTX [13]and enhanced upper-hybrid resonance backscattering inFT-2 [14]. On HT-7 tokamak, CO2 collective scatteringsystem has been employed to measure density fluctuation
over a broad wave number from medium k to high k

1. Introduction

It is believed that drift-wave turbulence is responsible
for anomalous transport [1] in magnetic fusion device.
Usually, the turbulence driven transport is mainly
attributed to long wavelength modes at k��s ~ 0.2, such as
ITG (ion temperature gradient) mode. Here, k� is theperpendicular wave number and �s=Cs/�ci, where
Cs=(Te/mi)1/2 is the ion sound speed and �ci the ion
Larmor frequency.
In advanced tokamak configurations with a reversed
magnetic shear, an improved confinement with theinternal transport barrier (ITB) has been found [2-4].
From transport data analyses [5, 6], it has been shown thatthe ion thermal diffusivity reduces to the neoclassicallevel in the ITB region. This can be attributed to the E×Bflow shear suppression for micro-instabilities, especiallyfor the ITG mode. However, the electron thermal
diffusivity is often still anomaly. Recent gyrokinetic
simulations have shown that smaller scale mode (e.g ETGwith k��s >1) may be responsible for the electron thermaltransport, at least partly [7-9]. Experiment results on
TFTR [24] showed that the short scale turbulence may be
responsible for the electron heat transport. So themeasurement of the small scale turbulence is necessary
and important.
Furthermore, as tokamak plasma turbulence is amultiple scale system, analyzing fluctuations on a wide
range of scales can characterize the nonlinear interaction
dynamics and the energy transfer process between
author’s e-mail: zhangt@ipp.ac.c115©2009 by The Japan Society of Plasma
Science and Nuclear Fusion Research

T. Zhang et al., On the Observation of ETG-Scale Turbulence on HT-7 Tokamak[15].The diagnostics has been applied in different
operational regime to understand the turbulence andtransport on HT-7 tokamak. In the paper, we focus onsome results in ohmic discharge.

[18] has shown that the spatial resolution can be improved

2. Experimental Setup
The HT-7 superconducting tokamak [16] is amedium size fusion research device. It has a major radiusof R = 1.22 m, minor radius of a = 0.27 m in the circularcross-section. There are two layers of thick copper shells,
and between them are located 24 superconducting coils
which can create and maintain a toroidal magnetic field(BT) of up to 2.5 T. The HT-7 tokamak with the limiter
configuration is normally operated under the basic
parameters: IP = 100 ~ 250 kA, the toroidal magnetic field
BT = 2 T, the central line-averaged plasma density n e =(1 ~ 6) ×1019 m-3, central electron temperature Te = 0.5 ~3.0 keV and central ion temperature Ti = 0.2 ~ 1.5 keV.
electron density were feedback controlled during
discharges.
Density fluctuation has been measured by a CO2collective scattering system on HT-7 tokamak. The
diagnostic is based on coherent forward collective
Thomson scattering [17]. This scattering process shouldobey the energy and momentum conservation, i.e. ��= �s- �i and k = ks - ki, where (�i, ki) are frequency and wave
vector for injected CO2 laser respectively, (�s, ks) for
scattering light and (�, k) for the density fluctuation wave.
Generally, the momentum conservation can be written as
Bragg relation, k=2kisin(�/2), where � is the scattering
angle. The diagnostics is homodyne detection currently.
The signal received on the detector ik(t) is proportional to
the spatial Fourier transform of density fluctuations
� at thescale corresponding to the scattering wave-vector k , i.e.
BFig. 1

Schematic diagram of CO2 collective scatteringsystem on Hefei tokamak-7 (HT-7).BS1, BS2 andBS3 are beam splitters; LO1, LO2 and LO3 are‘local oscillator’ beams; L1~ L7 are lenses; M1,M2 and M3 are mirrors and is adjustable; D1, D2and D3 are detectors.

for forward scattering by use of the assumption that thefluctuation wave number should be nearly perpendicularwith the magnetic field, k·B�0.
In order to measure a wide range of wave number
turbulence in the same condition, a series of identicaldischarges were conducted. The discharge gas wasdeuterium for ohmic heating. The parameters were as
follows: toroidal magnetic field, BT = 1.84 T; plasma
current, IP = 140 kA; central line average density, n =1.5×1019 m-3; central electron temperature, Te, about 0.8
keV. The measured turbulence ranged from k=16 cm-1 to
36 cm-1, the normalized wave number k�s = 2 ~ 6. In theexperiment, the scattering always take place in thepoloidal plane. According to the idea in [18] and a simple
calculation, the main contribution to scattering signal
comes from the confinement zone (� = 0.3 ~ 0.6, where �
is normalized minor radius) of the tokamak.

�� � � �ik (t ) � � n~ ( r , t )u ( r� ) e ik � r d rUsually, three independent channels with different
scattering angles are used simultaneously to monitor
density fluctuation as shown in Fig. 1. The radiation
source is a continuous-wave CO2 laser with an output
power of 12 W at wavelength � = 10.6 �m. Three beam
splitters (BS1, BS2 and BS3 in Fig. 1) are used to
produce three ‘local oscillator’ beams (LO1, LO2 andLO3 in Fig. 1) and a main probe beam. A movable mirror
M1 is adopted to adjust the angle between the main andLO beams. Since the chordis central, the observed
�fluctuation wave-vector k is in the poloidal direction,i.e. k�. Currently, the system can measure density
fluctuation with wave number k� ranging from 10 cm-1 to40 cm-1. The wave number resolution Ƹk is about 2 cm-1.
Because the scattering angle � is typically less than 1�,the measurement is non-local. The work on Tore Supra

3. Experimental results and discussions
Shown in Fig.2 (a) is the k (wave number) – f(frequency) spectrum of the turbulence. A typicalfrequency spectrum (k=24 cm-1) is shown in Fig.2 (b).
The lower frequencies (f <20 kHz) include noise of thedetector and the effects of acoustic vibrations on theoptical system have been filtered from the signal. Thepeak frequency is about 120 kHz. In the frequency range
from f = 120 kHz to 1000 kHz, the turbulence energy
satisfies a power law S(f) ĝ f -1.2 , while for f >1000 kHz
the energy fall off faster with frequency in a power law

116

T. Zhang et al., On the Observation of ETG-Scale Turbulence on HT-7 TokamakS(f) ĝ f -4.2. The spectrum which follows power law
remarkably well in a large range of frequencies implies
self-similarity. These results show low frequency
turbulences (compared to the ion cyclotron frequency fci,
which is about 14 MHz in the experiment.).
The k-spectrum shown in Fig.2 (c) indicates thedensity fluctuation energy S(k) = |��n/n |2 has a power law

attributed to the intermittency [19]. In our experiment, thePDF of fluctuation at all wavenumbers from k=16 cm-1 to
k=36 cm-1 can be Gaussian distribution. Shown in Fig.3(a) are the common logarithm of PDF (log10(PDF)) for
normalized signals of k=16 cm-1 and k=36 cm-1
fluctuation. The two plots can be fitted by quadratic
function well. In order to better understand the result,some statistic quantities usually are used for comparison,such as skewness and flatness, i.e, third and fourth ordernormalized moment. They are defined byS �Fig.2 Characteristics of fluctuation in ohmic plasma (a) k-f
spectrum (b) frequency spectrum of k =24 cm-1 turbulence (c)X 3X

23 / 2,F �

4XX22The first quantity skewness S measures the asymmetry of
the PDF, and the second quantity flatness F measure thetail’s weight with respect to the core of the PDF. For
Gaussian distribution, they are 0 and 3 respectively. The
two quantities are calculated for all the measured
fluctuations in our experiment. The results are shown in
Fig.3 (b) and Fig.3 (c) respectively. Within experiment
precision the values of skewness are zero and those offlatness are three for fluctuations at all the analyzing
scales, which are consistent with the values fromGaussian distribution. These results suggest that thesignal is random at all analyzing scales.

the k-spectrum.

distribution in k space, S(k) ~ k-4. The k-spectrum of drift
wave turbulence can be deduced from Hasegawa-Mima
equation [20, 21]. The unidirectional energy spectrum
W(K)=(1+K2)|��|2 satisfies W(K)~ K-4 in high K range asshown in [21] which is in accordance with the
Kraichnan’s inertial range spectrum, where K is thenormalized wavenumber K=k�s and ���is the normalized
fluctuating potential. It should be noted that in ourexperiment the measured physic quantity is density
fluctuation. If electron satisfy Boltzmann distribution, i.e.
�n/n~��� (adiabatic electron), then |��n/n |2 ~ K-4/(1+K2).
Due to in our experiment, K>1 leads to |��n/n |2 ~ K-6 ~ k-6.
This is not consistent with our experiment result with
S(k)= |��n/n |2 ~k-4.The experiment results on Tore Supra[23, 11ˈ18] indicate S(k) ~ k-3.5±0.5. Our result can also becompared with them. And these results can be comparedwith recent gyro-kinetic simulation [22].
One of the main hypotheses in the KolmogorovKraichnan theory is the randomness of the fluctuation.
The random character will lead to the Gaussian
distributions of events. Therefore, comparing theprobability distribution function (PDF) of the fluctuation
to Gaussian distribution can measure how random thesignal is. The deviation from Gaussian distribution can beFig. 3(a) log10(PDF) for normalized scattering signal of k=16
cm-1 and k=36 cm-1 fluctuation, fitted by quadratic
function(b)Theskewness

factors

arezerofor

fluctuation of all analyzing scales, (c)The flatness factor
are nearly three for all the fluctuation.

In order to have an idea about the turbulence
evolution in one discharge, analyses are done for shot117

T. Zhang et al., On the Observation of ETG-Scale Turbulence on HT-7 Tokamak

signal suggests the signal random character. The analysisof the shot#100878 show that the appearance of a low
frequency turbulence feature in spectrum at t=500 ms
compared with that at t=300 ms can be attributed to thesteeper temperature profile at t= 500ms.

#100878 at two time slices (t=300 ~ 320ms and t=500ms~520 ms) in the current and density flat-top phase. Thedischarge parameter is showed in Fig.4 (a). It is foundthat at t =500 ms, an evident low frequency feature (f ~ 80kHz) appears in the frequency spectrum of k=20 cm-1
fluctuation by contrast with that at t=300 ms as shown inFig.4 (b). And the fluctuation amplitude increases about* Work supported by the National Nature Science
Foundation of China under Grant Nos 10475078,10675127, 10675126, 10675124 and 10605028 and partly
supported by JSPS-CAS Core-University Program on
Plasma and Nuclear Fusion.
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On HT-7 tokamak, small scale turbulence can bemeasured by use of the CO2 collective scattering
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