Stochastic structures in the low-frequency plasma turbulence: measurement of characteristics and determination of general features
Results are presented from the experimental and statistical studies of low-frequency turbulence in a magnetized plasma. It is shown that, for all types of driving instability (drift, ion-acoustic, MHD instability), this turbulence is accompanied by the formation of stochastic structures demonstratin...
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| Zitieren: | Stochastic structures in the low-frequency plasma turbulence: measurement of characteristics and determination of general features / N.N. Skvortsova, K.A. Sarksyan, N.K. Kharchev // Вопросы атомной науки и техники. — 2000. — № 6. — С. 24-26. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-785032015-03-19T03:01:52Z Stochastic structures in the low-frequency plasma turbulence: measurement of characteristics and determination of general features Skvortsova, N.N. Sarksyan, K.A. Kharchev, N.K. Magnetic confinement Results are presented from the experimental and statistical studies of low-frequency turbulence in a magnetized plasma. It is shown that, for all types of driving instability (drift, ion-acoustic, MHD instability), this turbulence is accompanied by the formation of stochastic structures demonstrating a statistically consistent behavior and similar correlation, spectral, probability characteristics. The stochastic structures that are existing in the state of dynamic equilibrium and non-random interaction determine all common features of very different turbulent processes: ionacoustic nonlinear solitons, drift vortices, and MHD spatial structures. It follows that the structural turbulence is a non-Gaussian probability process with the long memory, i.e., a self-similar probability process. 2000 Article Stochastic structures in the low-frequency plasma turbulence: measurement of characteristics and determination of general features / N.N. Skvortsova, K.A. Sarksyan, N.K. Kharchev // Вопросы атомной науки и техники. — 2000. — № 6. — С. 24-26. — Бібліогр.: 8 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/78503 533.9 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Magnetic confinement Magnetic confinement |
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Magnetic confinement Magnetic confinement Skvortsova, N.N. Sarksyan, K.A. Kharchev, N.K. Stochastic structures in the low-frequency plasma turbulence: measurement of characteristics and determination of general features Вопросы атомной науки и техники |
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Results are presented from the experimental and statistical studies of low-frequency turbulence in a magnetized plasma. It is shown that, for all types of driving instability (drift, ion-acoustic, MHD instability), this turbulence is accompanied by the formation of stochastic structures demonstrating a statistically consistent behavior and similar correlation, spectral, probability characteristics. The stochastic structures that are existing in the state of dynamic equilibrium and non-random interaction determine all common features of very different turbulent processes: ionacoustic nonlinear solitons, drift vortices, and MHD spatial structures. It follows that the structural turbulence is a non-Gaussian probability process with the long memory, i.e., a self-similar probability process. |
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Skvortsova, N.N. Sarksyan, K.A. Kharchev, N.K. |
| author_facet |
Skvortsova, N.N. Sarksyan, K.A. Kharchev, N.K. |
| author_sort |
Skvortsova, N.N. |
| title |
Stochastic structures in the low-frequency plasma turbulence: measurement of characteristics and determination of general features |
| title_short |
Stochastic structures in the low-frequency plasma turbulence: measurement of characteristics and determination of general features |
| title_full |
Stochastic structures in the low-frequency plasma turbulence: measurement of characteristics and determination of general features |
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Stochastic structures in the low-frequency plasma turbulence: measurement of characteristics and determination of general features |
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Stochastic structures in the low-frequency plasma turbulence: measurement of characteristics and determination of general features |
| title_sort |
stochastic structures in the low-frequency plasma turbulence: measurement of characteristics and determination of general features |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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2000 |
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Magnetic confinement |
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http://dspace.nbuv.gov.ua/handle/123456789/78503 |
| citation_txt |
Stochastic structures in the low-frequency plasma turbulence: measurement of characteristics and determination of general features / N.N. Skvortsova, K.A. Sarksyan, N.K. Kharchev // Вопросы атомной науки и техники. — 2000. — № 6. — С. 24-26. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT skvortsovann stochasticstructuresinthelowfrequencyplasmaturbulencemeasurementofcharacteristicsanddeterminationofgeneralfeatures AT sarksyanka stochasticstructuresinthelowfrequencyplasmaturbulencemeasurementofcharacteristicsanddeterminationofgeneralfeatures AT kharchevnk stochasticstructuresinthelowfrequencyplasmaturbulencemeasurementofcharacteristicsanddeterminationofgeneralfeatures |
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2025-07-06T02:34:50Z |
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2025-07-06T02:34:50Z |
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1836863235620339712 |
| fulltext |
UDC 533.9
24 Problems of Atomic Science and Technology. 2000. № 6. Series: Plasma Physics (6). p. 24-26
STOCHASTIC STRUCTURES IN THE LOW-FREQUENCY PLASMA
TURBULENCE: MEASUREMENT OF CHARACTERISTICS AND
DETERMINATION OF GENERAL FEATURES
Nina N. Skvortsova, Karen A. Sarksyan, Nikolai K. Kharchev
General Physics Institute, 117942 Moscow, Russia, e-mail:nina@fpl.gpi.ru
Results are presented from the experimental and statistical studies of low-frequency turbulence in a magnetized
plasma. It is shown that, for all types of driving instability (drift, ion-acoustic, MHD instability), this turbulence is
accompanied by the formation of stochastic structures demonstrating a statistically consistent behavior and similar
correlation, spectral, probability characteristics. The stochastic structures that are existing in the state of dynamic
equilibrium and non-random interaction determine all common features of very different turbulent processes: ion-
acoustic nonlinear solitons, drift vortices, and MHD spatial structures. It follows that the structural turbulence is a
non-Gaussian probability process with the long memory, i.e., a self-similar probability process.
1. Introduction
At present, studies of a stochastic structure of low-
frequency plasma turbulence attract particular attention.
These studies are related both to a fundamental problem,
namely of creating a model of structural plasma
turbulence, and to applied problem, for example, in
connection with attempts to explain anomalous heat and
particle transport in the edge plasma in magnetic
confinement systems.
In the last few years, systematic studies of low-
frequency plasma turbulence have been carried out at
the General Physics Institute in two different
experimental devices, namely, the TAU-1 device and the
L-2M stellarator. The former is a linear system in which
plasma is created by an injected electron beam, whereas
the latter is a toroidal magnetic confinement system in
which a plasma is created and heated by a high-power
microwave beam. These two essentially different plasma
sources with individual instability features allowed us to
carry out a comparative analysis of associated turbulent
processes. It was shown experimentally that, in a
magnetized plasma, regardless of the type of turbulence
(drift or ion-acoustic turbulence) [1] or the type of
magnetic confinement system (stellarator or linear
device) [2–5], low-frequency turbulence demonstrated a
number of characteristic features.
As is known, statistical studies of fast plasma
fluctuations require adequate techniques of data
processing and experimental equipment. During the last
two decades, computerized data acquisition systems
have been commonly used in plasma experiments. These
systems capable of accumulating and processing long
arrays of experimental data from a large number of
detectors situated in various points in a plasma offer a
new means for studying the spectral, correlation, and
statistical properties of both steady and transient states
of plasma turbulence. The ability to analyze these
properties theoretically and computationally, which
confidence in the validity of the results of the analysis, is
a very important attribute of such systems. The problem
is overcome by using many supplementary methods for
statistical treatment of experimental data: all traditional
versions of multidimensional Fourier analysis, bispectral
analysis, wavelet analysis, correlation analysis,
probability methods of analysis, analysis of long-living
correlations [5,6].
2. Stochastic structures in ion-acoustic
turbulence in the TAU-1
The first experiments, where the stochastic structures
in the ion-sound plasma turbulence were observed, were
carried out in the TAU-1 device. This device was
constructed especially for studying nonlinear plasma
processes. Low-frequency turbulence is excited at
frequencies of the ion-acoustic frequency range after the
onset of current instability. The device end experiments
are described in detail in [5,6]. Here, we only list the
main parameters of a plasma: the cylindrical plasma
column is 4 cm in diameter and 100 cm in length, the
working gas is argon, the electron density is n = (0.9-2)
× 1010 cm -3, the electron temperature is Te = 5–7 eV,
and the ion temperature is Ti ≈ 0.1Te. The steady-state
operating conditions can be maintained for 3–5 h.
Fluctuations in the electron density, plasma
potential, and electron flux were measured with
Langmuir probes. Two 2-mm-spaced probes (0.1 mm in
diameter and 10 mm in length) were oriented along the
magnetic field. After amplification and filtration, the
probe signals were led to analog-to-digital converters
(ADC); for data processing, we used a local computer
net. In this experiment, we used CAMAC ADCs with a
10-kB buffer and OS-2 ADC plates with a 256-kB
buffer. The sampling frequency was 10 MHz.
In the experiment, turbulent acoustic oscillations
with a continuum frequency spectrum extending up to
the plasma frequency (near 5 MHz) were excited by the
electron current. The use of wavelet analysis allowed us
to trace the time evolution of the structures, their
emergence and disappearance in the spectrum. The
frequency wavelet spectrum was repeatedly computed.
Interpolation was used to diminish the computer time.
Figure 1 shows the time evolution of the spectrum of
plasma-potential fluctuations which is compiled from
ten spectra computed for successive intervals of 20µs.
The initial time is chosen arbitrarily. The amplitude of
spectral components (in arb. units) is shown by gray
shading; dark regions show highest amplitude and may
be attributed to quasi-harmonics. The frequency
corresponding to the wavelet duration is plotted on the
25
abscissa, and the time is plotted on the ordinate. The
spectrum of ion-acoustic fluctuations varies substantially
with time, whereas both the macroscopic plasma
parameters and the average oscillation energy remain
constant. First, a single quasi-harmonic is seen in the
spectrum; then, there two quasi-harmonics; and, finally,
a single quasi-harmonic remains in the spectrum. The
structure lifetime ranges from tens to hundreds of
characteristic ion-acoustic oscillation periods (from 10-5
to 10-4 s). Structures in the structural ion-acoustic
turbulence interact with each other; only a fraction of
them is excited spontaneously. In the experiment, we
observed the processes of the nonlinear coupling and
decay of structures and measured the characteristic time
of one cycle of the nonlinear interaction between
structures. This time is a maximum measured
characteristic time of the structural ion-acoustic
turbulence. It ranges from 0.5 to 2–3 ms which is the
maximum turbulence time.
Fig. 1. Temporal evolution of the wavelet spectrum of
potential-fluctuation amplitudes for H = 500 Oe,
p = 3 ×10-4 torr, Ib = 60 mA, and Ub = 90 V
The steady-state structural ion-acoustic turbulence exists
in the form of the dynamic equilibrium of nonlinearly
interacting solitons.
-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2
0.00
0.02
0.04
0.06
0.08
0.10
shot s9900203.0
127000 pointsKurtosis=3.8
Pr
ob
ab
ilit
y
Amplitude, arb.un.
Fig.2. Probability distribution function of ion-sound
turbulent signal. The total time window is 25.4 ms,
H = 500 Oe, p = 3 × 10-4 torr, I b =200 mA,U b = 120 V
Probability distribution function of the ion-sound
signals differs from the Gaussian (normal)
distribution.The PDF usually has a more peaked profile
and heavy wings. A histogram representing the
distribution of amplitudes of turbulent signals is
illustrated in Fig.2. Note that the fourth moment
(kurtosis) is equal to 3.8. It should be recalled that the
long-living correlation was observed for ion-acoustic
turbulent signals [5]; it determines the characteristic
“memory” time of the process. This indirectly indicates
that low-frequency plasma turbulence is as a self-similar
probability process [7] rather than a Gaussian
probability process.
The self-similarity parameter is determined by two
temporal influenced functions, describing the
appearance of stochastic structures in turbulence and
non-linear interaction between the structures.
3. Stochastic turbulent structures in the edge
plasma of the L-2M stellarator
The experiments considered in this Section were
carried out in the edge plasma of the L-2M stellarator.
The L-2M stellarator is a toroidal magnetic system for
plasma confinement [8,9]. The radius of the torus is R =
100 cm; the plasma cross section is elliptical, its mean
radius (the mean radius of the magnetic sparatrix) is < rs
>= 1l.5 cm and can be reduced by inserting a limiter. A
helium plasma is produced and heated by a microwave
beam (the wavelength is 4 mm and the power is up to
200 kW). The discharge duration is about 10 ms.
Edge fluctuations were measured with Langmuir
probes which can be inserted into the plasma (Fig. 3) to
the radius r = (0.8 - 0.9) rs, where the density is n(r) =
(1-2) x 1012 cm-3, the electron temperature is close to
Te(r)=30 - 40 eV. The relative level of the density
fluctuations is (δn/n)out = 0.2 - 0.25 in the outer regions
and (δn/n)in=0.1 in the inner regions of the plasma.
Fig.3. Arrangement of the probe devices: a) top view of
the toroidal chamber, b) poloidal section A-A;
1 – vertical probe, 2 – outer horizontal probe, 3 – inner
horizontal probe; distances between probes l12 ~ 20 cm,
l13 ~ 15 cm, l23 ~ 35 cm
Each probe device consisted of several (two or three)
individual cylindrical probes separated from each other
by distances l = 7-4 mm in the radial and poloidal
directions. The distance between the probe devices in
the poloidal direction was equal to tens of centimeters.
Probe signals were digitized at 1 MHz using a 10-bit
digitizer. The probes detected fluctuations in the plasma
density δn (specifically, the ion saturation current Is, so
δIs ~ δn) and floating potential δφ.
26
Wavelet coherences in the poloidal (4 mm) and in
the radial (7 mm) directions were investigated for
density and potential fluctuations. Figure 4 demonstrates
a high level of the wavelet coherence in these directions
for density fluctuations, which is evidence of structure
existence. One can notice that the shape of the frequency
resolved radial and poloidal coherence of fluctuations is
asymmetric, i.e. the structures have different scales in
these directions. It should be noted that the presented
wavelet coherence spectra were computed for signals
measured by probes radially separated by 7 mm with
zero delay time. With increasing the delay time between
signals to ∆t = 3 µs, the coherence coefficient decreases
remarkably. From the time delay in the maximum of the
cross-coherence and the dispersion relation (phase
versus frequency), we estimated the propagation
velocity of the radially correlated fluctuations, which
value turned out to be close to 4⋅104 m/s. It is suggested
that mode coupling effects responsible for a high radial
correlation of fluctuations in the high frequency range
/4/.
Fig. 4. Radial and poloidal coherence of fluctuations
These measurements showed a high degree of
correlation of fluctuations at large distances in the
poloidal direction, with a correlation length as large as
lcor = 20 cm. The radial correlation length reached 7 mm.
The highly correlated fluctuations are localized
predominantly in the outer region of the plasma column.
According to theoretical predictions, such fluctuations
may be attributed to magnetohydrodynamic (MHD)
resistive ballooning instability. The arising stochastic
structures determine the spatial (poloidal and radial)
correlation length of MHD turbulence in the edge
plasma of the L-2M stellarator.
4. Conclusions
It has been shown in the experiments in the TAU-1
device that the structures exist in ion-acoustic turbulence
of current-carrying magnetized plasma. Structures in this
low-frequency turbulence are spatially correlated. We
suggest that these structures are nonlinear ion-acoustic
solitons in nature. Nonlinear soliton structures interact
with each other. Only fraction of them is excited
spontaneously. In the experiment, we observed the
processes of the nonlinear coupling and decay of
structures and measured the time of one cycle of
nonlinear interaction between structures (the maximum
characteristic time of the process). The steady-state
structural ion-acoustic turbulence exists in the form of
the dynamic equilibrium of nonlinearly interacting
structures. This turbulence is a self-similar probability
process rather than Gaussian probability process.
Experiments on studying turbulence in the edge plasma
on the L-2M stellarator confirm that low-frequency
plasma turbulence with resistive-interchange MHD
modes appears in the form of radial-poloidal structures.
It should be noted, that in this case too, the structural
low-frequency turbulence in the edge plasma exists also
in the form of dynamic equilibrium nonlinearly
interacting plasma structures and cannot be described as
a Gaussian process. Two types of turbulent structures
are observed: nonlinear MHD structures near the
separatrix surface and drift vortex structures in deeper
plasma layers. MHD structures govern the dynamic
behavior and non-Gaussian probability characteristics of
turbulent flux in the boundary plasma region.
Therefore, the turbulence under study can be called
the structural plasma turbulence. The stochastic
structures that are existing in the state of dynamic
equilibrium and non-random interaction determine all
common features of turbulence caused by essentially
different (drift, ion-acoustic, MHD) instabilities. This
leads us to the conclusion that, in general case, the non-
Gaussian probability process with the long memory
determines the characteristic features of plasma
turbulence over a wide range of its state – from weak to
strong turbulence.
This work was supported in part by the Russian
Foundation for Basic Research, projects no.98-02-
16345 and no.00-02-16345.
References
1. Batanov, G.M., Sarksian, K.A., Sapozhnikov A.V.,et
al., Proc. IV Int. Conf. on Nonlinear and Turbulent
Processes in Physics, Kiev (1989) vol. 1, 231.
2. N.N. Skvortsova, G.M. Batanov, O.I. Fedianin,
N.K. Kharchev et al. J.Plasma Fusion Research
SERIES (Japan), Vol.1 (1998) 298.
3. C.Hidalgo, B.Ph. van Milligen, M.A. Pedrosa, E.
Sanchez, et al. J.Plasma Fusion Research SERIES,
Vol.1 (1998) 94.
4. G.M. Batanov, O.I. Fedianin, N.K. Kharchev,
Yu.V. Khol'nov, et al. Plasma Physics and Control
Nuclear Fusion, 40 (1998), 1241
5. K.A. Sarksyan, N. N. Skvortsova, N. K. Kharchev
and B. Ph. van Milligen, Plasma Physics Reports,
(1999)Vol. 25, No. 4, 312.
6. A.N. Kolmogorov, Reports of Academy of Science
(1941), v. XXX, 299.
7. N. N. Skvortsova, N.K. Kharchev, K.A. Sarksyan,
JETP LETTERS (1999) v.70(3), p.201.
8. G.M. Batanov, A.E. Petrov, K.A. Sarksyan, N. N.
Skvortsova et al.JETP LETTERS (1998), Vol 67, 662.
D.K. Akulina, G.M. Batanov, A.E. Petrov, L.V. Kolik,
K.A. Sarksyan, et al. JETP LETTERS (1999), Vol. 69,
407.
Nina N. Skvortsova, Karen A. Sarksyan, Nikolai K. Kharchev
General Physics Institute, 117942 Moscow, Russia, e-mail:nina@fpl.gpi.ru
Results are presented from the experimental and statistical studies of low-frequency turbulence in a magnetized plasma. It is shown that, for all types of driving instability (drift, ion-acoustic, MHD instability), this turbulence is accompanied by the
1
1. Introduction
2. Stochastic structures in ion-acoustic turbulence in the TAU-1
3. Stochastic turbulent structures in the edge plasma of the L-2M stellarator
4. Conclusions
References
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