J. Plasma Fusion Res. SERIES, Vol. 9 (2010)

Investigation of turbulence by microwave imaging
reﬂectometry in the TPE-RX reversed ﬁeld pinch
Zhongbing SHI, Yoshio NAGAYAMA1) , Soichiro YAMAGUCHI2) , Tomokazu YOSHINAGA1) ,Daisuke KUWAHARA3) , Yoichi HIRANO4) , Haruhisa KOGUCHI4) , Satoru KIYAMA4) , Hajime
SAKAKITA4) and Kiyoyuki YAMBE4)
The Graduate University for Advanced Studies, Toki 509-5292, Japan
Southwestern Institute of Physics, Chengdu, 610041, China
1)National Institute for Fusion Science, Toki 509-5292, Japan
2)
Kansai University, Suita 564-8680, Japan3)
Department of Energy Science, Tokyo Institute of Technology, Tokyo 152-8550, Japan
4)
Advanced Industrial Science and Technology, Tsukuba 305-8568, Japan
October
2009 2 February 2010)(Received: 20 November
2009 15,/ Accepted:
The two-dimensional density turbulence around the ﬁeld reversal surface has been studied by using
microwave imaging reﬂectometry (MIR) in TPE-RX reversed ﬁeld pinch (RFP). In the standard plasma,
the turbulence is intermittent and is dominated by the broad wavenumber spectrum. The turbulence
are signiﬁcantly suppressed when the magnetic relaxation is reduced by using pulsed poloidal current
drive (PPCD). In the PPCD plasma, the ﬂuctuation is dominated by the low n mode (n < 10). Theintermittency is not observed and the PPCD plasma has high conﬁnement as the soft-X-ray (SXR)
intensity is signiﬁcantly increased.
Keywords: turbulence, microwave imaging reﬂectometry, reversed ﬁeld pinch
the turbulence is also the main cause for energy andparticle transport [7]. The second type of plasma
is the pulsed poloidal current drive (PPCD) plasma
formed by modifying the inductive current drive to
reduce the tearing instability [8]. This technique has
been demonstrated in several RFP devices. The magnetic turbulence is decreased, and the reduction of theheat and particle transport has been observed in several RFP devices during PPCD [9, 10]. The conﬁnement time has been improved by order of magnitude[8, 10]. Therefore, comparison between the PPCD andwithout PPCD plasmas is a good example to study the
RFP turbulence.
This paper presents the two-dimensional (2D)
density ﬂuctuation around the ﬁeld reversal surface(ρ ∼ 0.8) in TPE-RX RFP. The turbulence in thestandard and the PPCD plasmas are compared. Signiﬁcant results are as follows: The standard plasma
has high turbulence and the ﬂuctuation of microwave
imaging reﬂectometry (MIR) signal is intermittent.
The broad spectrum agrees with the multi-helicity(MH) state in the standard plasma. PPCD suppresses
the turbulence. The ﬂuctuation in PPCD is dominated by the low n mode, while the high n mode issuppressed.

1. Introduction
Turbulence is interested by many physicists as itenhances the transport and degrades the overall conﬁnement in the toroidal devices [1]. In the reversedﬁeld pinch (RFP), the plasma has the characteristic ofstrong ﬂuctuation [1]. The MHD turbulence is known
to drive the dynamo, which plays an important role tosustain the plasma conﬁguration in the standard RFP
plasmas [2]. The electrostatic turbulence plays an important role in the edge transport [3]. MHD theory
suggests that the core RFP dynamo corresponds to them = 1 (low n) tearing mode whose resonant surface islocated in the inside region [4]. The edge RFP dynamo
corresponds to the m = 0 tearing mode whose resonant surface is around the ﬁeld reversal surface. The
strong turbulence is expected due to the resonances ofm = 0 mode, densely packed high n (m = 1) modes
and high electrostatic turbulence around the reversal
surface [1, 3]. Therefore, the ﬂuctuation in the inside region may highly relate to the sustainment of the
RFP conﬁguration. So far the edge turbulence of RFP
plasma has been reported by electrostatic probes andoptical gas-puﬀ imaging (ρ = 0.96 ∼ 1.0) [5], while theturbulence in the inside region has not been researched
due to the inaccessible condition of the probes.
There are two types of operation in the RFP device [6]. The ﬁrst is the standard RFP formed bysteady toroidal induction. Standard plasmas are selforganized via a magnetic relaxation (dynamo) process
involving MHD tearing. Previous works showed that

2. Experiments
TPE-RX is a large RFP device with major radius
R =1.72 m and minor radius a =0.45 m [11]. It ischaracterized by a multilayered shell system in a conductive all-metallic vacuum vessel which provides rela-author’s e-mail: shizb@swip.ac.cn

54©2010 by The Japan Society of Plasma
Science and Nuclear Fusion Research

Z. Shi et al., Investigation of Turbulence by Microwave Imaging Reflectometry in the TPE-RX Reversed Field Pinch

tively high Ip /N values ( 10−19 Am; N = πa2 < ne >,the number of electron per unit toroidal length, derived using the line-averaged electron density < ne >).
The all-metal ﬁrst wall also provides MHD mode stabilization and the fast equilibrium control in a shorttime scale less than millisecond. A six-pulsed PPCD
operation has been developed to improve the energy
conﬁnement time. The total duration of PPCD isabout 18 ms. About ten-fold improvement in conﬁnement has been observed [12]. The operations of thestandard and the PPCD plasmas have been reported
in Ref. [6].
The plasma density is measured by a double-chord
CO2/HeNe laser interferometer in TPE-RX, whose
impact parameters, normalized by minor radius a, are
0 and 0.69. The density proﬁle is estimated by ﬁtting
the experimental data with the following relation [14].




ne (r, t) = ne (0, t)(1 − r4 )(1 + C(t)r4 )



(1)

where, ne (0, t) is the core density, C(t) is the proﬁlefactor, r is normalized by minor radius a. The proﬁlefactor C > 1 represents the hollow density and C < 1
represents the peaked density proﬁle. Both ne (0, t)
and C(t) are determined by the two measured chordvalues. In TPE-RX, the ﬂat and hollow density proﬁle is often observed in the PPCD and the standard
plasmas.
A MIR system has been developed to investigate
the turbulence around the reversal surface in TPERX. MIR is expected to be a powerful tool to measure
the images of the density ﬂuctuation [15, 16]. In the
MIR signal A exp(iφ), the phase φ corresponds to thedisplacement of the cutoﬀ surface in the radial direction. However, the phase φ is often distorted due tothe fringe jumps. The fringe jumps might be removedby numerical algorithm sometimes [13]. The amplitude A corresponds to the reﬂection power which isscattered by the perpendicular wave on the cutoﬀ surface [17]. The amplitude signal is used to study the
turbulence on the cutoﬀ surface in this work.
The detail of the MIR system has been reported
in the previous papers [14, 18]. The image of the cutoﬀ surface is made on the detector surface by the optical system. A 4 × 4 planar Yagi-Uda antenna array is used. The spatial resolution is 3.7 cm bothin toroidal and poloidal directions, so the highest detectable toroidal (n) and poloidal (m) modenumbers
are 292 and 76, respectively. A Gunn oscillator generating the microwave with frequency of 20 GHz isused. The microwave illuminates in the O-mode, so
the cutoﬀ density is necut = 0.5 × 1019 m−3 . The
experiments with MIR have been performed with theplasma current of 200-300 kA and electron density of(0.5 − 1) × 1019 cm−3 . The normalized cutoﬀ radius
r/a mainly locates in the region from 0.7 to 0.9 dueto the ﬂat or hollow density proﬁle, which is often ob-












 





 







 
 
 




Fig. 1 The plasma parameters, magnetic and MIR signalsof the standard (F = −0.5) and PPCD plasmas.
(a) plasma current Ip , (b) reversal parameter F ,(c) soft-X-ray (SXR) intensity, (d) cutoﬀ radius of
MIR,(e) poloidal magnetic ﬂuctuation, (f) and (g)MIR signal.

served in TPE-RX. This region is near the reversed
ﬁeld surface.

3. Turbulence in standard and PPCD
plasmasExperiments with MIR have been performed in
the standard and PPCD plasmas in TPE-RX. In
the standard plasma, the reversal parameter F =Bt (a)/ < Bt > is used to identify the strength of the
ﬂuctuation as the edge reversal toroidal ﬁeld Bt (a)is mainly sustained by the turbulence [7]. Here <>denotes average over the whole volume. The deeper
F corresponds to the stronger ﬂuctuation in the standard plasma. The magnetic ﬂuctuation becomes more
coherent in the deep F plasmas [4]. In the PPCD
plasma, the edge toroidal ﬁeld Bt (a) is mainly driven
by the external ﬁeld, so the F is not an indicative
parameter in the PPCD plasmas.
Figure 1 shows the plasma current (Ip ), the reversal parameter (F ), soft X-ray (SXR), the normalized cutoﬀ radius (rcut ), the poloidal magnetic ﬂuctuation and the MIR signal in the standard (# 53441,
F ≈ −0.5) and PPCD (# 53362) plasmas. The rapid
increase of the SXR intensity and the rapid decreaseof the F are observed after turn on the PPCD (t ≥ 18ms). The SXR intensity of the PPCD plasma is about
100 times higher than that in the standard plasma.

55

Z. Shi et al., Investigation of Turbulence by Microwave Imaging Reflectometry in the TPE-RX Reversed Field Pinch


1


Coherence



0.8






PPCD

0.6

Stand
0.4
1/e

0.2



0







V



0

5

10

15

toroidal distance (cm)Fig. 2 Probability distribution function of the standard(asterisk, F = −0.5) and PPCD (square) plasmas.
X-aixs represents the normalized deviation of amplitude of MIR from the average value.

Fig. 3 The toroidal coherence length of the standard(square, F = −0.5) and PPCD (dot) plasmas.

coherent structures or intermittency of ambient turbulence. The PDF of PPCD plasma is similar to theGaussian distribution, and the ﬂuctuating quantities
are limited at the low (A− < A >)/σ values (no Gaussian tail). This suggests that the ﬂuctuation in PPCD
plasma has been suppressed. In the standard plasma,a strong negative non-Gaussian tail is observed. It corresponds to the negative intermittent bursts of MIR
signal (see Fig.1). The non-Gaussian tail is increased
as the reversal parameter F is increased in the negative direction. This suggests that the intermittency is
increased as the magnetic ﬂuctuation is enhanced in
the standard plasma.
The coherence length identiﬁes the size of the ﬂuctuation. The toroidal coherence length is deﬁned as
the coherence is decreased to 1/e. Figure 3 shows
the toroidal coherence length of the standard (square)and PPCD (dot) plasmas. The coherence is obtainedby averaging the toroidal coherence at f = 10 ∼ 100
kHz. The coherence is decreased as the distance isincreased. The coherence length is longer than thedetector size. The coherence of PPCD plasma ishigher than that of standard plasma. This corresponds to a longer wavelength of the ﬂuctuation in
the PPCD plasma. Therefore, the ﬂuctuations in the
PPCD plasma have the characteristics of large-scale
structures. The ﬂuctuations in the standard plasma
have the characteristic of small-scale structures. The
toroidal correlation length of the PPCD and standard
plasmas at the cutoﬀ surface (rcut ≈ 0.8) can be estimated from the tendency of the coherence. The estimated correlation length may be larger than 40 cm
in the PPCD plasma, while it is about 15 ∼ 20 cm inthe standard plasma. The estimated toroidal correlation length at rcut ≈ 0.8 is similar to the results at
r/a = 1.0 measured by GPI in TPE-RX [5].
Figure 4 shows the mode spectra of the magnetic
ﬂuctuations (m = 0 and m = 1 modes) as a functionof the toroidal modes n in the standard and the PPCDThis indicates good conﬁnement with PPCD operation. In the standard plasma, F is constant during
the ﬂattop of the plasma. Both the standard and the
PPCD plasmas have similar cutoﬀ radius rcut ≈ 0.8
during the ﬂattop of the plasma current. The ﬂuctuation amplitude of MIR signal is very small if there
is no cutoﬀ surface in plasma. The standard and the
PPCD plasmas have similar ﬂuctuation level. However, their ﬂuctuation structures are diﬀerent. In thestandard plasma, the ﬂuctuation in the amplitude signal is intermittent which bursts mainly in the negative
direction. While in the PPCD plasma the ﬂuctuationin the amplitude signal is symmetric.
The poloidal magnetic ﬂuctuation is measured by
the complex edge probe (CEP) which is sensitive tothe fast magnetic ﬂuctuations [19]. The magnetic ﬂuctuation is suppressed during PPCD, while in the standard plasma (F = −0.5, deep F ) the magnetic ﬂuctuation amplitude is high. It should be noted that themagnetic ﬂuctuation before PPCD is low because ofshallow F (F = −0.15). Actually, the deep F plasma
in the standard RFP has a higher SXR intensity than
the shallow F plasma. The SXR intensity of shallow
F (t = 10 − 18 ms at the right hand side) is much lessthan that with PPCD. The high magnetic ﬂuctuation
at t = 24 ∼ 25 ms may be caused by the time interval
between two PPCD pulses. This can be eliminatedby optimization of the operation [20]. After switch oﬀ
the PPCD operation, the strong magnetic ﬂuctuation
is observed at t = 34 ∼ 35 ms.
Figure 2 shows the probability distribution function (PDF) of the MIR amplitude signals in the standard (F = −0.5) and PPCD plasmas. Here, the x-axis
represents the normalized amplitude: (A− < A >)/σ.
< A > and σ denote the average value and the standard deviation of the amplitude of MIR signal, respectively. The solid line denotes the Gaussian distribution. A non-Gaussian PDF represents the presence of56

Z. Shi et al., Investigation of Turbulence by Microwave Imaging Reflectometry in the TPE-RX Reversed Field Pinch






   

to the power spectrum as there are unique values ofcross-correlation points. As a result, the location ofpeak mode becomes clear, especially when the imaged
region is smaller than the wave measured. The detailsof the MEM method have been discussed in [21, 22]. In
the PPCD plasma, the ﬂuctuation power is localized
in the low m and n ranges, and the spectrum is dominated by a pinpoint (m = 1±1, n = −7±5). The mode
spectrum of the standard plasma distributes in a wide
mode range, especially expands in the toroidal direction. The mode range is (m = 0 ± 6, n = −70 ∼ 20).
The magnetic ﬁeld is mainly poloidal near rcut ≈ 0.8.
Since the modenumber spectrum has the propagation
direction of the modes, the modes mainly propagate
in the electron drift direction. The expansion into
the high n range suggests presence of many turbulent
structures. The analysis of MIR signal is consistent
with the multi-helicity state shown in Fig. 4 (a).

  















         
          
 

Fig. 4 m = 0 and m = 1 mode spectra of the standard(F = −0.5) and PPCD plasmas. The n and m
are the toroidal and poloidal modenumbers, respectively.

(a) standard (F=-0.5)

10

k
0

e

-10
-20
-100

2 0 0 9 . 7 . 1 9 .8 .9 . 5 4 S u n d ay _ D:\RS I\M E M _ L HD\Ou tp u t\sk en t\5 3 4 4 7 _ 2 _ 3 0 _ 3 5 ms.d at--M E M . emf(b) PPCD

20
poloidal modes, mpoloidal modes, m

20

-50
0
50
toroidal modes, n

10

2

0

4. Summary and discussion

-10
-20
100
-100

2 0 0 9 .7 . 1 9 . 8 . 1 8 . 2 3 S u n d ay _ D:\RS I\M EM _ L HD\Ou tp u t\sk en t\5 3 3 3 0 _ 2 _ 2 8 _ 3 3 ms.d at--M EM . emf

-50
0
50
toroidal modes, nIn summary, the turbulence around the ﬁeld reversal surface has been studied by comparing the ﬂuctuations of the standard and the PPCD plasmas. The
turbulence in the standard plasma has the features ofintermittency. The broad spectrum agrees with themulti-helicity state in the standard plasma. The turbulence are signiﬁcantly suppressed when the magnetic relaxation is reduced by the PPCD operation.
In PPCD, the ﬂuctuation is dominated by the low nmode (n < 10), while the high n mode is suppressed.
The intermittency is not observed and the conﬁnement
is improved.
In this work, the low n mode is measured near thereversal surface by MIR in the PPCD plasma. However, the resonant surface of the low n mode locatesin the core region from the MHD theory [1]. Previous
measurements showed that the low n mode has thedominant ﬂuctuation amplitude [4]. The measured
low n mode near the ﬁeld reversal surface may be asa result of strong ﬂuctuation in the core region.
The features of the turbulence in the standard
and the PPCD plasmas are signiﬁcantly diﬀerent. The
turbulence and the tearing modes are correlated. Thisobservation supports that suppression of the tearing
modes leads to the reduction of the turbulence. Nevertheless, the relation among the turbulence, the tearing modes and magnetic relaxation remains unclear.
Further theoretical and experimental works will beneeded.

0100

Fig. 5 The 2D mode spectra of the standard (F = −0.5)
and the PPCD plasmas. The n and m are thetoroidal and poloidal modenumbers, respectively.

plasmas. The magnetic ﬂuctuations are obtained by
an extensive magnetic measurement system (MMS)[19]. In the PPCD plasma, the amplitude of the m = 1
mode is higher than that of the m = 0 mode. This
may relate to the suppression of the m = 0 mode.
The ﬂuctuation in the PPCD plasma is dominated by
the localized m = 1 mode. The low n modes (n <10) have the high ﬂuctuation energy, while the high nmodes have very small power. This suggests that thehigh n modes (or small-scale ﬂuctuations) have been
suppressed. The longer coherence shown in Fig. 3
may contribute to the coherence of the low n mode.
In the standard plasma, the power spectra isstronger than that of PPCD plasma. This is as aresult of strong magnetic ﬂuctuation. The power ofthe m = 0 modes is higher than the m = 1 modes
especially for the low n modes. It suggests the globalfeatures of the ﬂuctuations (m = 0 modes) in the standard plasma. The high n modes are observed in thestandard plasma. The wide distribution of m = 0 and
m = 1 modes suggests that the standard plasma is richof turbulent structures (multi-helicity (MH) state).
Figure 5 shows the 2D modenumber spectra of thestandard and the PPCD plasmas by using the MIR
amplitude signals. The modenumber spectra are analyzed by the 2D maximum entropy method (MEM)[21, 22]. This method allows us to ﬁt as many peaks

5. Acknowledgment
This work is carried out as one of the NINS Imaging Science Project (Grant No. NIFS08KEIN0021).
This work is also supported by NIFS (Grant
No. NIFS08ULPP525), and SOKENDAI (Grant

57

Z. Shi et al., Investigation of Turbulence by Microwave Imaging Reflectometry in the TPE-RX Reversed Field Pinch

No. NIFS08GLPP003). A part of this study was ﬁnancially supported by the Budget for Nuclear Researchof the Ministry of Education, Culture, Sports, Scienceand Technology of Japan, based on the screening andcounseling of the Atomic Energy Commission.
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