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applied
sciences
Review
Review of Advanced Implementation of Doppler Backscattering
Method in Globus-M
Alexander Yashin *, Victor Bulanin, Alexander Petrov and Anna Ponomarenko
Advanced Plasma Research Laboratory, Peter the Great St. Petersburg Polytechnic University,
195251 St. Petersburg, Russia; V.Bulanin@spbstu.ru (V.B.); a.petrov@spbstu.ru (A.P.);
ponomar_am@spbstu.ru (A.P.)
* Correspondence: a.yashin@spbstu.ru
Abstract: Doppler backscattering (DBS) is a microwave diagnostics method typically used to study
the plasma rotation velocity. Apart from conventional techniques, more advanced forms of DBS
implementation were suggested on Globus-M. More specifically the study of a variety of oscillating
processes was performed using DBS. In this review we present a detailed description of all of the
methods and techniques employed in Globus-M alongside results obtained using DBS in all the years
up until the shutdown of the tokamak. These include research similar to that done on other devices
into the properties of such phenomena like geodesic acoustic modes or limit cycle oscillations, along
with innovative works regarding the detection and investigation of Alfven eigenmodes and filaments
that were the first of their kind and that provided important and novel results. Apart from that, the
specific aspects of DBS application on a spherical tokamak are discussed. An in-depth look into the
gradual change and improvement of the DBS diagnostics on Globus-M is also presented in this paper.
Keywords: Doppler backscattering; spherical tokamak; microwave diagnostics; geodesic acoustic
Citation: Yashin, A.; Bulanin, V.; modes; limit cycle oscillations; Alfven eigenmodes; filaments; edge localized modes; quasi coher-
Petrov, A.; Ponomarenko, A. Review ent fluctuations
of Advanced Implementation of
Doppler Backscattering Method in
Globus-M. Appl. Sci. 2021, 11, 8975.
https://doi.org/10.3390/ 1. Introduction
app11198975
Doppler backscattering (DBS) is a microwave diagnostics method applied on many
magnetic confinement fusion devices typically with the aim to study the plasma rotation
Academic Editor: Gregory Slepyan
velocity [1–9]. Since the L-H transition was shown to be caused by the suppression of
turbulent plasma perturbations by the shear of the plasma drift velocity in the radial
Received: 30 July 2021
electric field (E × B velocity) [10], DBS was successfully applied to study this transition. In
Accepted: 21 September 2021
the tokamak ASDEX Upgrade, data for the analysis of L-H transitions with low density
Published: 26 September 2021
were obtained using this method [11]. A comparison of neoclassical calculations for the
radial electric field and DBS data was made, which showed a good agreement between
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
the two methods for different modes of operation of the tokamak. The TCV tokamak
published maps and institutional affil-
used a heterodyne V-band Doppler backscattering diagnostic system [12]. The first results
iations.
show that the perpendicular rotational velocities obtained with DBS are consistent with
the estimates of the poloidal rotation obtained from the charge exchange recombination
spectroscopy diagnostics. A radial profile of perpendicular velocity was successfully
obtained on the LHD tokamak using a Doppler reflectometer system [13]. The radial
electric field was extracted from measurements of perpendicular velocity. In the work [14]
Copyright: © 2021 by the authors.
the rotation characteristics of the plasma in the tokamak HL-2A before and after supersonic
Licensee MDPI, Basel, Switzerland.
molecular beam injection were also analyzed. It was shown that an SMBI pulse can reduce
This article is an open access article
distributed under the terms and
the Doppler shift frequency, which corresponds to the flattening of the electric field. In a
conditions of the Creative Commons
series of experiments on the EAST tokamak using two separate DBS systems, one for the
Attribution (CC BY) license (https:// Q-band (33–50 GHz) and the other for the V-band (50–75 GHz), Doppler shifted signals
creativecommons.org/licenses/by/ were obtained and radial profiles of perpendicular velocities were computed for the L- and
4.0/). H-mode [15]. In the Globus-M2 tokamak, the first results of the Doppler backscattering
Appl. Sci. 2021, 11, 8975. https://doi.org/10.3390/app11198975 https://www.mdpi.com/journal/applsci
Appl. Sci. 2021, 11, 8975 2 of 19
diagnostics during a discharge with the L-H transition show that the transition process
is linked to the deformation of the poloidal rotation velocity profile [16]. This diagnostic
made it possible to conduct studies in the hotter and more central plasma regions, which is
a useful addition to the velocity and field data obtained by other methods.
Apart from these conventional techniques more advanced forms of DBS implementa-
tion were suggested. More specifically the study of a variety of oscillating processes was
performed using DBS. For example, for the investigation of the high-frequency branch of
zonal flows—the geodesic acoustic mode—the DBS diagnostics were used on JET [17,18],
ASDEX Upgrade [19], HL-2A [20], EAST [21], DIII-D [22], TUMAN-3M [23], and other
devices [24]. Doppler backscattering has also proved useful for the study of limit cycle
oscillations whose typical frequency is significantly lower than that of the geodesic acoustic
mode frequency. Such research was carried out in the ASDEX Upgrade tokamak [25],
DIII-D [26,27], and HL-2A [28,29].
In this review we aim to present a detailed description of all the methods and tech-
niques employed in Globus-M in regard to DBS diagnostics used to study all the various
phenomena that occur in plasma during a discharge. A multitude of results that had been
obtained using DBS in the last 10 years up until the moments of the tokamak’s ultimate
shutdown in 2017 are revisited and described. These include the investigation of such
phenomena like geodesic acoustic modes or limit cycle oscillations using similar research
practices that had been previously adopted on other devices. Apart from that, innovative
works are reexamined regarding Alfven eigenmodes and filaments that were the first of
their kind and had provided important and novel results for the plasma physics com-
munity. Furthermore, the specific aspects of DBS application on a spherical tokamak are
discussed and highlighted. An in-depth look into the gradual change and improvement
of the DBS systems on Globus-M from a one-frequency homodyne detection system to
several multi-frequency systems can also be found in this review.
2. Doppler Backscattering on Globus-M
2.1. DBS Systems
Doppler backscattering (DBS), also known as Doppler reflectometry, is a type of Thom-
son’s collective microwave scattering. The method is based on recording the backscattered
microwave radiation with an oblique incidence of the microwave beam. Scattering mainly
occurs near the cutoff of the microwave beam on plasma fluctuations with a selected wave
vector k⊥ , which satisfies the Bragg condition for backscattering—k⊥ = 2 ki . Here ki is the
wave vector of the incident wave in the cutoff region and it is oriented in the direction of
the electron or ion diamagnetic drift. When scattering fluctuations move in the diamagnetic
direction with a certain velocity V⊥ , a Doppler frequency shift of backscattered radiation
appears—∆ωD = k⊥ V⊥ . The Doppler frequency shift ∆ωD needed for the calculation of
the perpendicular velocity V⊥ can be obtained as the position of the ‘center of gravity’
of the complex signal I(t) + iQ(t) spectral density, or the derivative of the phase of the
complex signal [30]. The sign and magnitude of the shift allow us to determine the sign
and magnitude of the velocity of fluctuations in the diamagnetic direction V⊥ .
The first implementation of DBS on a spherical tokamak was carried out on Globus-
M [31]. There are specific requirements for DBS application in a spherical tokamak that
is characterized by a significant pitch angle (more than 20◦ ) at the low magnetic field
side. To satisfy the Bragg condition, the antenna has to be tilted not only poloidally but
also toroidally. To evaluate the required antenna tilt angles, ray tracing of the incident
beam was performed for the actual three-dimensional (3D) geometry of the Globus-M flux
surfaces [32]. To determine the investigated area of each DBS channel, experimental electron
density profiles obtained by Thomson diagnostics and magnetic surface reconstruction
data obtained using the EFIT code were used. An example of the performed ray tracing is
presented in Figure 1. The locations of the ports available for the installation of the DBS
systems are also indicated. The first Globus-M DBS system was based on a monostatic
antenna scheme, which allowed one to probe the plasma by O-mode microwaves in the
density profiles obtained by Thomson diagnostics and magnetic surface reconstruction
data obtained using the EFIT code were used. An example of the performed ray tracing is
Appl. Sci. 2021, 11, 8975 presented in Figure 1. The locations of the ports available for the installation of the3DBS of 19
systems are also indicated. The first Globus-M DBS system was based on a monostatic
antenna scheme, which allowed one to probe the plasma by O-mode microwaves in the
frequency band 18–26 GHz (system #1 in Table 1). It was possible to change the incident
band shot
frequency from 18–26toGHz
shot.(system
The tilt #1 in Table
angles 1).incident
of the It was possible to change
beam were chosenthe
as incident
7° in the
frequency
poloidal from
and shot
3° in theto shot. The
toroidal tilt angles
direction. Theof the incident
relevant beam were
wavelength of thechosen as 7◦plasma
scattering in the
poloidal and 3 ◦ in the toroidal direction. The relevant wavelength of the scattering plasma
fluctuations was in the range of 1.1–1.8 cm. The cutoff position was in the vicinity of the
fluctuations
separatrix at was
highin the range
q-values. Theofradial
1.1–1.8 cm. The cutoff
resolution positionwas
of the method wasestimated
in the vicinity
to be of the
about
separatrix at high q-values. The radial resolution of the method was estimated
0.5 cm. Dual homodyne detection was employed to receive the backscattered radiation to be about
0.5 cm. Dual homodyne detection was employed to receive the backscattered radiation [1].
[1].
- − 0.6
- − 0.4
separatrix
- − 0.2
port #1
Z, m
-
− 0.0 port #2
port #3
− 0.2
− 0.4
− 0.6
0.0 0.2 0.4 0.6
R, m
Figure 1. Ray tracing for the geometry of the Globus-M tokamak.
Table 1. DBS systems on Globus-M.
Table 1. Globus-M.
DBS
DBS Systems
Systems #1
#1 #2
#2 #3
#3
Number
Number of systems
of systems 11 22 11
Number of
Number of 11 11 4
frequencies 4
frequencies
Frequency values,
Frequency values, 18–26 27–38 20,
GHz 18–26 27–38 20, 29, 39,48
29, 39, 48
GHz
Waveguide
Waveguide WR-42
WR-42 WR-28
WR-28 WR-42, WR-28
WR-42, WR-28
Wave propagation O-mode O-mode O-mode
Wave propagation O-mode O-mode O-mode
Poloidal tilt angles,◦ o 6–9 6–9 6–9
Poloidal tilt angles, 6–9 6–9 6–9
Toroidal tilt angles, o 2–5 2–5 2–5
Toroidalbeam
tilt angles, ◦ 2–5−45 2–5 −45 2–5
Probing angle, o −30, 45, −30, −30
Probing beam angle, ◦
Position −30, #2,3
port −45 45, −30,
port −45
#1,2,3 −30#2
port
Cut-off radii R, m
Position ~0.55–0.58
port #2,3 ~0.53–0.58
port #1,2,3 ~0.51–0.59
port #2
Cut-off radii R, m ~0.55–0.58 ~0.53–0.58 geodesic acoustic
~0.51–0.59
geodesic acoustic modes, limit cycle
geodesic acoustic
geodesic acoustic
Field of study modes, filaments,
geodesic acoustic oscillations, filaments,
modes, limit cycle
Field of study
modes,
geodesicfilaments
acoustic
modes,eigenmodes
filaments, oscillations, filaments,
modes, filaments Alfven Alfven eigenmodes,
Alfven eigenmodes Alfven eigenmodes,
turbulence
turbulence
The DBS system #1 was used successfully to study peripheral transport processes as
well as to obtain measurements near the separatrix. Due to the usefulness of the diagnostics,
the physics research program on the Globus-M tokamak required the expansion of the
measured region into the area of the formation of the pedestal. Accordingly, an additionalAppl. Sci. 2021, 11, 8975 4 of 19
DBS system was developed so as to probe and record the scattered signal at larger radii
(system #2 in Table 1). The microwave circuit of system #2 was similar to the one in
system #1 with the exception of a higher frequency probing range of 27–38 GHz. The same
antenna that was used for system #1 to probe the plasma was employed on system #2.
The antenna was connected to this DBS system using the WR-28 to WR-42 waveguide
transition. Because only one port (port #2) located in the equatorial plane was initially
allocated for the DBS diagnostic, only one of the two available systems could be applied
during a discharge.
Subsequently, two additional ports (ports #1 and #3) were made available for the
development of Globus-M DBS diagnostic that were located at the same toroidal angle,
but several centimeters, respectively, above and below the equatorial plane. Additional
antenna systems were installed in these ports, and one more DBS system similar to system
#2 was acquired. The simultaneous use of several DBS systems, spread out in a poloidal
direction, made it possible to develop poloidal correlation Doppler reflectometry and to
determine the poloidal scale of the developing plasma instabilities.
However, the use of systems #1 and #2 made it difficult to construct radial profiles
of the plasma processes under investigation by means of changing the probing frequency
from discharge to discharge. This method required precise repetition of plasma discharge
parameters. The fluctuation of these very parameters made it difficult to accurately interpret
the acquired results. Therefore, a DBS scheme with four fixed probing frequencies was
developed. The 4-channel DBS system in Globus-M comprised two × two-channel DBS
microwave schemes with different probing frequencies [33]. Two pairs of fixed frequencies
were chosen—20, 29 GHz and 39, 48 GHz. Each frequency channel included a microwave
circuit with dual homodyne detection. Two steerable antennas were used to probe the
plasma by O-mode microwaves. Each of the antennas was used both as an incident and
a receiving one, and were connected to a waveguide that allows only a certain range of
wavelengths to pass through. One antenna was used for frequencies of 20 and 29 GHz,
whereas the second one was used for the 39 and 48 GHz frequencies. The detection region
covered a considerable radial interval of normalized small radii ρ = 0.6–1 for a typical
Globus-M discharge.
2.2. Data Analysis
Table 2 provides the methods of analysis of DBS data that allowed one to inves-
tigate and determine the characteristics of plasma processes such as geodesic acoustic
modes, limit cycle oscillations, quasi-coherent fluctuations, Alfven eigenmodes, turbulence,
and filaments.
Table 2. Methods applied to DBS signals to study various phenomena.
Method Notes Field of Study
geodesic acoustic modes, limit cycle
connects the time domain and the oscillations, quasi-coherent
Spectral analysis
frequency domain fluctuations, Alfven eigenmodes,
turbulences, filaments
provides information on how
strongly two signals are geodesic acoustic modes,
Coherence analysis
correlated across a frequency quasi-coherent fluctuations
range
Correlation information on radial correlation geodesic acoustic modes, limit cycle
analysis properties of turbulence oscillations, filaments
geodesic acoustic modes, limit cycle
frequencies at which nonlinear
Bicoherent analysis oscillations, quasi-coherent
interaction is most effective
fluctuationsAppl. Sci. 2021, 11, 8975 5 of 19
Spectral analysis allows for the process of breaking down of any signal into its com-
ponents at various frequencies, which is an important characteristic when it comes to
turbulences and a large variety of instabilities. The Fourier transform (fast Fourier trans-
form) provides this connection between the time domain and the frequency domain. There
are various kinds of spectral analysis of the DBS signals available. They were applied
to calculate the signal spectrum that describes the distribution of power into frequency
components that the signal comprises. The fast Fourier transform is calculated in a window
of a certain length that is chosen depending on the phenomenon being investigated. The
window is then shifted by a time frame and the process continues. It was also possible to
smooth these data so as to remove components of the background noise. Spectrograms
were calculated as well in order to also have a visual representation of the spectrum as it
changes in time. They are formed as the dependency of frequency on time while the power
at each frequency at a given moment in time is represented by color. This is accomplished
for the complex data of the DBS signals.
The complex DBS signal spectrum is calculated so as to investigate the Doppler shift
and consequently the rotation velocity. The velocity spectrum reveals some oscillatory
phenomena. The modulus of the complex DBS signal showcases the behavior of the
fluctuation amplitude. The calculation of the coherence spectrum leads to the examination
of the relation between oscillations of various DBS signals.
Correlation analysis of DBS signals can be used for obtaining information on radial
correlation properties of turbulence and therefore on the turbulence spectrum with respect
to radial wave numbers [34]. However for us the main goal was the detection of periodic
components in the Doppler backscattering radiation, as well as the definition of the charac-
teristics of such periodic processes. For this purpose, the calculation of cross-correlation
functions (CCFs) between velocities measured at different radii or between amplitudes
of DBS signals at different radii, and between the amplitude and velocity obtained at the
same radius was performed. It was also possible to obtain correlation functions between
the DBS signals and other diagnostic signals.
The processes of coupling between spectral components of interacting waves could
be revealed via bicoherence analysis. Cross-bicoherence as a measure of phase coupling
between three spectral components of signals is described by the following expressions:
2
Yk∗ ( f 3 )Yi ( f 1 )Yj ( f 2 )
b2 ( f 1 , f 2 ) = 2
; f3 = f1 ± f2
h|Yk ( f 3 )|2 ih Yi ( f 1 )Yj ( f 2 ) i
where Yi (f), Yj (f), Yk (f) are spectra of amplitude of the complex output signal of the IQ
detector or spectra of E × B velocity determined from the Doppler frequency shift.
3. Application Results
3.1. Geodesic Acoustic Mode
DBS was implemented to study geodesic acoustic modes (GAMs) on the Globus-M toka-
mak in the Ohmic phase of discharges at relatively low plasma density (n ≈ (2–3) × 1019 m−3)
when the toroidal ion drift was directed away from the X-point [35–37]. All DBS sys-
tems (see Table 1) and in some experiments even their combinations were used to ob-
tain information about various properties of GAMs presented in Table 3 (see the end of
Section 3.1). GAMs were identified through spectral analysis of the perpendicular veloc-
ity V⊥ (t) = VE×B (t) + Vphase (t). Since GAMs lead to oscillations of VE×B (t), they can be
detected by DBS. The measured Doppler frequency shift was obtained either from the
spectrum shift of the IQ detector signal or as the phase derivative of the complex signal.
GAMs manifest themselves as coherent oscillations in the frequency domain of 23–28 kHz
in the case of deuterium plasma and around 36 kHz in hydrogen plasma [38,39]. These
frequencies are within the large orbit drift width limit when compared with theoretical
predictions [40].V⊥(t) = VE×B(t) + Vphase(t). Since GAMs lead to oscillations of VE×B(t), they can be detected by
DBS. The measured Doppler frequency shift was obtained either from the spectrum shift
of the IQ detector signal or as the phase derivative of the complex signal. GAMs manifest
themselves as coherent oscillations in the frequency domain of 23–28 kHz in the case of
Appl. Sci. 2021, 11, 8975 deuterium plasma and around 36 kHz in hydrogen plasma [38,39]. These frequencies are
6 of 19
within the large orbit drift width limit when compared with theoretical predictions [40].
The study of the temporal evolution of GAMs showed that they do not exist contin-
ually; rather, an intermittent increase and decrease of GAM amplitude was observed.
ThereThewerestudy
twoof the temporaltimes
characteristic evolution of GAM
for the GAMslevelshowed that they
changes [39]. do
Thenot exist
first onecontinu-
is the
ally; rather, an intermittent increase and decrease of GAM amplitude was observed. There
duration of a quasi-coherent GAM burst which was about 0.2 ms with an interval of 0.4
were two characteristic times for the GAM level changes [39]. The first one is the duration
ms between bursts. This behavior corresponds to the well-known predator-prey model
of a quasi-coherent GAM burst which was about 0.2 ms with an interval of 0.4 ms between
[41]. Another timescale is a very slow evolution of the GAM level with a period of about
bursts. This behavior corresponds to the well-known predator-prey model [41]. Another
5 ms. This is also the characteristic time of the evolution of the ion pressure gradient on
timescale is a very slow evolution of the GAM level with a period of about 5 ms. This is
Globus-M.
also the characteristic time of the evolution of the ion pressure gradient on Globus-M.
The GAMs velocity amplitude V⊥(t) was recalculated to the radial electric field Er
The GAMs velocity amplitude V⊥ (t) was recalculated to the radial electric field Er
assuming that the phase velocity Vphase(t) induced by GAM oscillations is relatively small.
assuming that the phase velocity Vphase (t) induced by GAM oscillations is relatively small.
The amplitude of the electric field oscillations reached up to 3 kVm−−11, which sometimes
The amplitude of the electric field oscillations reached up to 3 kVm , which sometimes
exceeded the mean value of the radial electric field causing a velocity reversal at a certain
exceeded the mean value of the radial electric field causing a velocity reversal at a certain
phase of the GAMs oscillations [39].
phase of the GAMs oscillations [39].
Initially the GAM location was studied by varying the probing frequencies from shot
Initially the GAM location was studied by varying the probing frequencies from
to shot while all plasma parameters were kept identical. These experiments showed that
shot to shot while all plasma parameters were kept identical. These experiments showed
GAMs exist in a very narrow layer of a few centimeters inside the separatrix [39]. The
that GAMs exist in a very narrow layer of a few centimeters inside the separatrix [39].
obtained radial profile of the GAM velocity amplitude is presented in Figure 2. A clear
The obtained radial profile of the GAM velocity amplitude is presented in Figure 2. A
maximum and decrease in amplitude is observed in this several centimeter layer. The
clear maximum and decrease in amplitude is observed in this several centimeter layer.
GAM
The GAMfrequency was also
frequency was investigated in different
also investigated locations
in different and itand
locations wasit determined
was determined that
no significant
that change
no significant of its of
change values was present.
its values Experiments
was present. with awith
Experiments foura frequency DBS
four frequency
scheme confirmed the narrow localization of GAM [42]. Only the peripheral
DBS scheme confirmed the narrow localization of GAM [42]. Only the peripheral DBS DBS channel
could
channelregister
couldGAM oscillations
register near the normalized
GAM oscillations minor radius
near the normalized minor0.95, whereas
radius 0.95,the other
whereas
channels did not detect oscillations exceeding the background level at
the other channels did not detect oscillations exceeding the background level at the GAM the GAM fre-
quency. This narrow area of GAM existence might be caused by the
frequency. This narrow area of GAM existence might be caused by the prevention of prevention of GAMs
development
GAMs developmentby Landau dampingdamping
by Landau induced induced
by the steep q-value
by the steepdecrease in the edge
q-value decrease re-
in the
gion of Globus-M. The width of the GAMs existence layer was about
edge region of Globus-M. The width of the GAMs existence layer was about 1 cm with 1 cm with the GAM
frequency
the GAM not changing
frequency notsignificantly within this within
changing significantly area [39]. Such
this areaobservations correspond
[39]. Such observations
to the global GAM eigenmode nature which was predicted in work
correspond to the global GAM eigenmode nature which was predicted in work [43]. [43].
0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62
5 70
a sep. 60
4
VExB, km/s
fGAM, kHz
50
3 40
2 30
20
1
10
600 0
fGAM=22.4 kHz (deuterium)
b
Te, eV
fGAM=38 kHz (hydrogen)
400
200
0
0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62
R, m
Figure
Figure2.2.Radial
Radialprofiles
profilesof:
of:(a)
(a)GAM
GAMamplitude
amplitudeand
andfrequency;
frequency;(b)
(b)electron
electrontemperature
temperature [39].
[39].
Poloidal correlation DBS using two microwave schemes with the cut-offs positioned at
different poloidal angles (−30◦ and 45◦ ) of the same minor cross-section was employed in
Globus-M to study the poloidal structure of GAMs [32,44]. The zero phase delay between
the GAM oscillations in the two simultaneously detected DBS signals was discovered by
coherent spectrum analysis of the velocity oscillations, which is presented in Figure 3. The
observation is consistent with an m = 0 mode structure of the GAM E × B flow as predicted
by theory in [41].Poloidal correlation DBS using two microwave schemes with the cut-offs positioned
at different poloidal angles (−30° and 45°) of the same minor cross-section was employed
in Globus-M to study the poloidal structure of GAMs [32,44]. The zero phase delay be-
tween the GAM oscillations in the two simultaneously detected DBS signals was discov-
Appl. Sci. 2021, 11, 8975 ered by coherent spectrum analysis of the velocity oscillations, which is presented in7 of 19
Figure 3. The observation is consistent with an m = 0 mode structure of the GAM E×B flow
as predicted by theory in [41].
−4
...
φ(f), rad
0.8 m=0 fGAM −2
...
C(f)
−0
...
0.4
−2
0.0
0 10 20 30 40 50
f, kHz
Figure 3. Coherence spectrum C(f) and cross-phase spectrum φ(f) of two Doppler shift oscillations
Figure 3. Coherence
recorded spectrum
by reflectometers C(f) and at
positioned cross-phase spectrum
poloidal angles −30◦ϕ(f)
andof45two Doppler
◦ , (#34504, shift
time = oscillations
170 ms) [44].
recorded by reflectometers positioned at poloidal angles −30° and 45°, (#34504, time = 170 ms) [44].
Cross-bicoherence analysis of perpendicular velocity and amplitude of the complex
DBSCross-bicoherence analysis
signal was successfully usedofto
perpendicular velocity
demonstrate the and amplitude
interaction of the
between the GAM complex
oscilla-
DBS
tionssignal was successfully
and plasma turbulenceused to demonstrate
[32,44,45]. The resultsthe
of interaction
this analysisbetween
indicatethe
thatGAM oscil-
a nonlinear
lations and plasma turbulence [32,44,45]. The results of this analysis indicate that a
interaction takes place that manifests itself in the appearance of the amplitude oscillationnon-
linear interaction takes place that manifests itself in the appearance of the amplitude
at the GAMs frequency fGAM . This can be caused by the influence of turbulent Reynolds os-
cillation
stress onatzonal
the GAMs frequency
flows or GAMs [41].fGAM. This can be caused by the influence of turbulent
Reynolds stress on zonal flows or GAMs [41].
Table 3. Properties of GAMs in Globus-M.
Table 3. Properties of GAMs in Globus-M.
Investigated Property Range of Values Notes
Investigated Property
Mode of operation
Range of Values
Ohmic heating regime
Notes
not detected in H-mode
Mode of operation Ohmic heating regime not detected in H-mode
23–28 (D) Gao formula, influenced by
f, kHz 23–28
f, kHz ~36 (H)(D) Gao formula, influenced
isotope effect [40] by
~36 (H) isotope effect [40]
consistent with the inverse of the
Spectral peak width ∆f, kHz 2–6 consistent
Spectral peak width ∆f, kHz 2–6 GAM with
burst the inverse of
lifetime
the GAM burst lifetime
Type burst Predator-prey model [41]
Type burst Predator-prey model [41]
determined as the time of
tlifetime, ms 0.2–0.4 determined
damping of as thethe time of
velocity
tlifetime, ms 0.2–0.4 damping of the
autocorrelation functionvelocity
autocorrelation
assumption of relation function
to the
Modulation frequency f mod , Hz 300 assumption of relation
evolution of the ion pressureto the
Modulation frequency fmod, Hz 300 gradient
evolution of the ion pressure
exceeds the gradient
mean radial electric
Amplitude, kV m−1 up to 3
exceeds the field
mean radial
Amplitude, kV m−1 up to 3
related to electric
the sharp field
decrease in
Location R, m 0.56 the safetyto
related factor values decrease
the sharp followed
by Landau damping [41]
in the safety factor values
Location R, m 0.56 globalfollowed
GAM eigenmode nature
Location width, cm 1 by1
Landau
2
3 3
= LT ρi[41]
damping
λGAM [43]
global
Linear GAM eigenmode
dynamics of zonal flow
Poloidal structure m=0
Location width, cm 1 modes [41]
nature =L [43]
the influence of turbulent
Non-linear interaction with
present Reynolds stress on zonal flows or
turbulences
GAMs [41]
3.2. Limit Cycle Oscillations
The four-frequency microwave DBS system was used to study a variety of limit cycle
oscillations (LCO) characteristics (see Table 4 in the end of Section 3.2) on Globus-M. LCOs
were discovered in plasma discharges with neutral beam injection (NBI) when the direction
of the magnetic field was favorable for transition to H-mode (i.e., the toroidal ion drift wasAppl. Sci. 2021, 11, 8975 8 of 19
directed towards the X-point). LCOs were found in the form of low-frequency (5–9 kHz)
oscillations in E × B drift velocity with the duration of their existence ranging from 2
to 20 ms [46]. Low frequency LCOs (~6 kHz) led to a transition to H-mode while high
frequency LCOs (~8.5 kHz) resulted in the transition to L-mode or even in a disruption. The
LCO frequencies in Globus-M are much higher in comparison to medium size devices [47].
A strong radial dependence of LCO frequency was not predicted by the model of limit
cycle oscillations induced by a predator-prey coupling of turbulence with zonal flows [48].
However, it is in accordance with the Stringer spin-up mechanism [49]. The multichannel
DBS system made it possible to estimate the velocity shear ωs of the oscillations at LCO
frequency. The amplitude of these oscillations was about 105 s−1 , but it increased up to
106 s−1 just before L-H transition in the case of the low frequency LCOs. The transition
to H-mode after these LCOs can be caused by an increase in the efficiency of the action
of the oscillating velocity shear on the plasma turbulence while decreasing its oscillation
frequency [50,51]. A periodic suppression of the turbulence power was observed as well.
However, in the event of the high LCO frequency, the turbulence level would decrease not
to zero, but to a certain value, after which it began to increase (standard oscillations). For
the lower LCO frequency, the turbulence level decreased periodically to zero. Such bursty
dynamics were also observed on TCV [52].
Table 4. Properties of LCO in Globus-M.
LCO in Discharges with LCO in Discharges
Investigated Property Notes
H-Mode without H-Mode
Additional heating NBI not detected in Ohmic phase
the higher LCO frequencies predicted by
f, kHz ~6 ~8.5
Stringer spin-up [49]
Spectral peak width ∆f, corresponds to the calculation of spectra in
1.5 1.5
kHz a 512 ms window
the duration of the LCO phase tends to be
Duration of LCO phase τ, closer to the value of 2 ms in discharges
2–20
ms with H-mode and to the values of 20 ms
without H-mode
Velocity shear, s−1 order of 105 –106 order of 105
a significant increase before no significant changes predator-prey model [48]
Velocity shear behavior
transition to H-mode in behavior
Turbulence suppression present during LCO
Turbulence modulation, % 98 81 dependence of the onset of the transition
on frequency corresponds to the transition
standard oscillations appearance model developed for the case
Type bursty dynamics
around a certain value of the appearance of zonal flows [51]
possibly, the significant coupling indicates
Nonlinear coupling of that LCOs are dominated by zonal flows;
present
turbulence similar results were obtained in the HL-2A
tokamak in the ‘type-Y’ LCO phase [53]
2 cm inside the separatrix which is similar
Location ρ ~0.75
to other tokamaks
close to the radial wavelength of the zonal
Location width ∆ρ ~0.4 √
flows λ ZF ∼ ρi a [41]Appl. Sci. 2021, 11, 8975 9 of 19
Auto-bicoherence analysis of the perpendicular velocity demonstrated the nonlinear
coupling of the broadband turbulence and velocity oscillations at the LCOs frequency in
the case of high frequency LCOs [46]. It is possible to assume that this significant coupling
indicates that LCOs are dominated by zonal flows caused by Reynolds stress [41]. Similar
results were obtained in the HL-2A tokamak in the ‘type-Y’ LCO phase [53].
The radial scale of the observed flow is estimated to be 4 cm [42,46]. This scale is
close to the radial wavelength of the zonal flows [41]. The maximum of the amplitude
profile of the velocity oscillations at LCO frequency was located at about 2 cm inside the
separatrix. Moreover, the velocity profile maximum moves from the boundary to the core
region during the LCO period. This was investigated by studying phase relations between
the perpendicular velocity and turbulence amplitude for two radial positions, which are
presented in the form of Lissajous phase diagrams in Figure 4. It was demonstrated
that at R = 54.4 cm the clockwise direction in the figure corresponds to a predator-prey
model [48], while at R = 56.6 cm the counterclockwise direction was associated with a
transition to H-mode in work [53]. Using DBS it was possible to observe both trajectories
simultaneously. The calculated autocorrelation and cross-correlation functions of amplitude
and perpendicular velocity lead to the estimation of the velocity of the movement to be
about 3 km s−1 . Apart from that, it was shown that the amplitude oscillations that occur at
Appl. Sci. 2021, 11, x FOR PEER REVIEWdifferent cutoff positions are approximately in-phase. From all the obtained data we 9 ofcould
20
conclude that it is impossible to apply the known 0D predator-prey models to explain the
observed differences at different radii.
/ −0
#37000
R = 54.4 cm
/ −0
#37000
R = 56.6 cm
−2 −2
V, km/s
V, km/s
−4 −4
−6 −6
−8
a −8
b
0 1 2 3 4 5 0 1 2 3 4 5
A, a.u. A, a.u.
(a) (b)
Figure 4. Lissajous
Figure diagrams
4. Lissajous of perpendicular
diagrams rotation
of perpendicular velocity
rotation and DBS
velocity signal
and DBSamplitude for dif- for
signal amplitude
ferent radii (a) R = 54.4 cm, (b) R = 56.6 cm [46].
different radii (a) R = 54.4 cm, (b) R = 56.6 cm [46].
Quasi-Coherent
Table 4. Fluctuations
Properties of LCO in Globus-M.
Quasi-coherent fluctuations (QCFs) were also discovered in the spectra of the DBS
LCO in Discharges with LCO in Discharges without
Investigated Property amplitude fluctuations. Their main properties are presented in Table 5.Notes
QCFs appear in the
H-Mode H-Mode
form of a spectral peak at the 110 kHz frequency with a spectral width of ∆fQC = 80 kHz [54].
Additional heating QC fluctuations with similarNBIparameters were observed on notthe detected in Ohmic
T-10 tokamak phase in
[55]. Unlike
T-10, the fluctuations in Globus-M were observed during the theI-phase
higherdischarge
LCO frequencies
with LCOs.
f, kHz ~6
QCFs were strongly modulated by LCO.~8.5 They were observedpredicted
by twoby Stringer spin-DBS
high-frequency
channels of 39 and 48 GHz at once. It corresponds to the normalized upminor
[49] radii values
from ρ = 0.6 to ρ = 0.7. ASTRA 7 and GENE simulations showed corresponds to the in
an increase diffusion
calcula-
Spectral peak width ∆f, kHz coefficient caused
1.5 by the ion temperature 1.5gradient (ITG) instability
tion of spectra in a 512location.
in the QCF ms
Auto-bicoherence analysis of the DBS amplitude fluctuations demonstrated window nonlinear
coupling of the broadband turbulence and QCFs. High level of cross-coherence of velocity
the duration of the LCO
fluctuations and DBS amplitude (about 0.8 at QCFs frequencies) indicates the presence
phase tends to be closer to
QCFs in velocity. Low level of coherence of DBS amplitude and magnetic field fluctuations
the value of 2 ms in dis-
Duration of LCO phase τ, ms (Appl. Sci. 2021, 11, 8975 10 of 19
Table 5. Properties of QCFs in Globus-M.
Investigated Property Range of Values Notes
f, kHz 110 similar to values on other
Spectral peak width ∆f, kHz 80 tokamaks like T-10 [55]
Type burst
tlifetime , ms 0.1–0.2 modulated by LCO
Location ρ 0.65 in the QCF location there is an
observed increase in diffusion
Location width ∆ρ 0.1 coefficient caused by ITG
present only during a certain
Mode of operation I-phase
phase of LCO
a peak of summed bicoherence at
Non-linear interaction with the QCFs frequency demonstrates
present
turbulences the existence of a relationship
with turbulent fluctuations
Coherence of velocity fluctuations 0.8 near QCFs
and DBS amplitude frequencies
Coherence of DBS amplitude and less than 0.3 near
not of a magnetic nature
magnetic field fluctuations QCFs frequencies
3.3. Filaments
Appl. Sci. 2021, 11, x FOR PEER REVIEW For the first time DBS diagnostics was implemented to study filaments [56].11Such of 20
an implementation is possible when the poloidal size of the filaments is close to π/k⊥
(1–3 cm in the case of DBS on Globus-M), where k⊥ is the wave vector of the incident wave
in the cutoff region. Such filaments were discovered using DBS inside the separatrix in
H-mode with NBI [31,57] and in Ohmic H-mode with high MHD activity [58,59]. Fila-
ELMy H-mode with NBI [31,57] and in Ohmic H-mode with high MHD activity [58,59].
ments were observed as a sequence of bursts of quasi-coherent fluctuations (BQFs) in the
Filaments were observed as a sequence of bursts of quasi-coherent fluctuations (BQFs)
IQ DBS signals. The frequency of IQ signal oscillations during a burst was used to calcu-
in the IQ DBS signals. The frequency of IQ signal oscillations during a burst was used
late the poloidal velocity of the filaments. The distance between filaments in the perpen-
to calculate the poloidal velocity of the filaments. The distance between filaments in the
dicular direction was calculated by measuring the temporal delay between adjacent
perpendicular direction was calculated by measuring the temporal delay between adjacent
bursts.
bursts.The
Thefour
fourfrequency
frequencyDBSDBSscheme
schemeallows
allowsone
onetotoestimate
estimatethe
theradial
radialsize
sizeofoffilaments.
filaments.
The
The reconstruction of the location and spatial distribution of filaments inthe
reconstruction of the location and spatial distribution of filaments in the Globus-M
Globus-M
tokamak
tokamakisispresented
presentedin inFigure
Figure5.5.
Sideview
Figure5.5.Side
Figure viewofof the
the magnetic
magnetic surface
surface of of
thethe Globus-M
Globus-M tokamak.
tokamak. TheThe reconstruction
reconstruction of the
of the
locationofoffilaments
location filaments(I–V)
(I–V)at
atfixed
fixedtime.
time. Filaments
Filaments are
are conventionally
conventionally shown by lines directed along
along magnetic
magnetic field lines.
field lines. The arrows
The arrows indicate
indicate the direction
the direction of theofmotion
the motion
of theoffilaments.
the filaments. The
The rectangle
rectangle denotes
denotes the the of
location location
the DBSof receiving
the DBS receiving antenna [59].
antenna [59].
Intotal,
In total, three types
typesof
offilaments
filamentswere discovered.
were One
discovered. Oneof them is ELM
of them filaments.
is ELM They
filaments.
werewere
They observed during
observed ELMsELMs
during triggered by sawtooth
triggered oscillations
by sawtooth [60] in
oscillations discharges
[60] with
in discharges
H-mode initiated by NBI when plasma density was relatively small n < 1.2 × 10 19 m−193 [61].
with H-mode initiated by NBI when plasma density was relatively small e ne < 1.2 × 10 m−3
[61]. If the plasma density was higher, the waveform during ELMs ceased to resemble
quasi-coherent oscillations, although the signal level increased greatly during ELMs. Ap-
parently, this is due to the fact that the poloidal size of the filament depends on the density
and, when the critical value is exceeded, it greatly differs from π/k⊥. Measured parametersAppl. Sci. 2021, 11, 8975 11 of 19
If the plasma density was higher, the waveform during ELMs ceased to resemble quasi-
coherent oscillations, although the signal level increased greatly during ELMs. Apparently,
this is due to the fact that the poloidal size of the filament depends on the density and,
when the critical value is exceeded, it greatly differs from π/k⊥ . Measured parameters of
ELM filaments can be found in Table 6.
Table 6. Properties of filaments in Globus-M.
Investigated Property ELM Filament Inter-ELM Filament MHD Induced Filament
Radial size, cm 2–6Appl. Sci. 2021, 11, 8975 12 of 19
the amplitude of the Alfven perpendicular velocity, radial electric field can be extracted
from the measurements. Studies were conducted in the Globus-M tokamak with early
neutral beam injection at the stage of growth of the plasma current [66,67]. Initially, the
detection of toroidal Alfven eigenmodes (TAE) using DBS was confirmed by comparing the
experimentally obtained frequency of the fluctuations presented in Table 7 to the Alfven
continuum frequency gaps f TAE = v A /4πqR, where v A = B/µ0 ρ D is the Alfven velocity
(B-magnetic field, ρ D -mass density of plasma ions), q is the safety factor, and R is the major
radius [68]. The results of the calculations were similar to those acquired in experiments.
Apart from that, the calculated spectrograms of rotation velocity determined using the
DBS method highlighted the fact that the frequency of the TAE decreases with time, which
corresponds to the concept of the slowing down of the Alfven wave. These properties
were also observed in the spectrograms of the magnetic probe signals that confirmed
the observation of Alfven eigenmodes. The nature of the TAE varied depending on the
characteristics of the injected beam (it was shown that the isotope of the injected particles
had an effect on what type of Aflven mode could develop) as well as the plasma density.
The instability was observed either in the form of a short burst lasting from 0.1 up to 0.5 ms
or as continuous oscillations of several ms. The length of the TAE burst apparently can be
defined through a predator-prey model [69].
The DBS measurements were used to calculate various properties of the Alfven eigen-
modes such as the amplitude of the radial electric field and accordingly their magnetic
field. The obtained values are presented in Table 7 as well as works [70–72]. It is worthy
of note that the magnetic field amplitude determined using DBS was compared with the
measurements of the magnetic probes B MP located on the wall of the vacuum chamber.
Appl. Sci. 2021, 11, x FOR PEER REVIEW 13 of 20
It was observed that the B MP values were generally significantly smaller than those cal-
culated from the DBS measurements, which seems to indicate the spatial damping of the
instability [71].
While several DBS systems were used to study the location of the Alfven eigenmodes,
While several DBS systems were used to study the location of the Alfven eigenmodes,
the four-frequency system had yielded the best results. The toriodal number n = 1 TAE
the four-frequency system had yielded the best results. The toriodal number n = 1 TAE
was detected in the area with major radii values of 0.50–0.56 m. It was noted that a clear
was detected in the area with major radii values of 0.50–0.56 m. It was noted that a clear
maximum of the amplitude for this n was not determined. However, the location of TAE
maximum of the amplitude for this n was not determined. However, the location of TAE
with higher toriodal number values (n = 2, 3) was determined to be closer to the periphery
with higher toriodal number values (n = 2, 3) was determined to be closer to the periphery
with R ~ 0.51–0.59 m. The examples of profiles obtained for a variety of Alfven eigenmodes
with R ~ 0.51–0.59 m. The examples of profiles obtained for a variety of Alfven eigenmodes
is presented in Figure 6. It clearly highlights that there is a possibility of the existence of
is presented in Figure 6. It clearly highlights that there is a possibility of the existence of the
the toroidal Alfven eigenmodes in the core plasma regions. The shift of the main TAE
toroidal Alfven eigenmodes in the core plasma regions. The shift of the main TAE harmonic
harmonic
(i.e., with (i.e.,
n = 1)with n =inner
to the 1) to the innerregions
plasma plasmaappears
regionstoappears to be
be related torelated to the increas-
the increasing plasma
ing plasma
current current [73].
[73].
Distributionof
Figure6.6.Distribution
Figure ofamplitudes
amplitudes of magnetic field
field oscillations
oscillationsfor
forvarious
varioustoroidal
toroidalmode
modenumbers
num-
bers
n inndischarges
in discharges
withwith different
different plasma
plasma currents:
currents: (a) (a) # 37001,
# 37001, t =t 141.2
= 141.2
ms;ms;(b)
(b)# #36988,
36988,t t==147.5
147.5ms;
ms;
(c) #(c)36944,
# 36944, t = 146.2
t = 146.2 ms;ms; q— stability
q—stability factor
factor (#),(○),
n = n1 =(squares),
1 (squares), 2 (circles),
2 (circles), 3 (triangles)
3 (triangles) [73].[73].
Table 7. Properties of Alfven eigenmodes in Globus-M.
Investigated Property Range of Values Notes
Additional heating NBI only observed during NBIAppl. Sci. 2021, 11, 8975 13 of 19
Table 7. Properties of Alfven eigenmodes in Globus-M.
Investigated Property Range of Values Notes
Additional heating NBI only observed during NBI
vA
f, kHz ~99–160 Alfven continuum frequency gaps f TAE = 4πqR [68]
the decrease of the TAE frequency is related to the
Spectral peak width ∆f, kHz 80
slowing down of the Alfven wave
Type continuous or burst dependent on the injected beam parameters [69]
tlifetime (for burst type), ms ~0.1–0.5 predator-prey model [69]
Radial electric field amplitude, kV m−1 ~0.5–3 the oscillations of the Alfven magnetic field are
accompanied by the oscillations of the measured electric
Magnetic field amplitude, 10−4 T ~6–25 field according to Maxwell’s equation Bfθ = Eer [73]
vA
shift of TAE to the inner plasma regions is related to the
Location R, m ~0.50–0.56
increasing plasma current
different toroidal numbers correspond to different TAE
Toroidal number, n 1–3
harmonics
3.5. Turbulence
The four frequency DBS system was used to study turbulence in H-mode with and
without ELMs. The experiments were performed in the Globus-M spherical tokamak
operated in H-mode initiated by NBI. Plasma density fluctuations as well as plasma
velocity fluctuations were investigated during the transition to the ELM-free H-mode.
Studies showed a decrease in both plasma density and plasma velocity fluctuation near the
separatrix in the absence of ELMs [74,75].
A more in-depth study of turbulence during ELMs allowed us to identify two types
of ELMs and two corresponding types of transition to the ELM-free H-mode [76]. Low-
frequency ELMs in the Globus-M tokamak are characterized by the transition to the
ELM-free regime during plasma current decrease alongside a similar change in the current
density profile. This transition is associated with a decrease in the intensity of sawtooth
oscillations. The level of turbulence at the periphery in this case varies only slightly, which
was demonstrated by analyzing the amplitude of the complex DBS signal as demonstrated
in Figure 7a. It can be assumed that the transport does not change, which is indicated by
the constancy of the Dα level and average density.
High-frequency ELMs are characterized by a spontaneous transition to the ELM-free
regime. The peripheral turbulence amplitude decreases during this transition (as seen
in Figure 7b), which was accompanied by the typical features of peripheral transport
suppression: the electron density increases and Dα emission drops. A study of the turbu-
lence amplitude spectra during this regime led to the discovery of quasi-coherent (QC)
fluctuations in the ELM-free H-mode in the highest frequency (48 GHz) channel with a the
cutoff radius of ρ = 0.6 [77]. The properties of these fluctuations were similar to the QCFs
observed in I-phase (see Table 5), except for the fact that the QC fluctuations in ELM-free
H-mode were not modulated by anything. They existed continuously during the period of
ELM-free H-mode. Such QCFs were not detected in the spectra of the complex IQ signal.
This, apparently, indicates that the poloidal scale of the fluctuations is much larger than the
method resolution of π/k⊥ .ations in the ELM-free H-mode in the highest frequency (48 GHz) channel with a the cut-
off radius of = 0.6 [77]. The properties of these fluctuations were similar to the QCFs
observed in I-phase (see Table 5), except for the fact that the QC fluctuations in ELM-free
H-mode were not modulated by anything. They existed continuously during the period
of ELM-free H-mode. Such QCFs were not detected in the spectra of the complex IQ sig-
Appl. Sci. 2021, 11, 8975 14 of 19
nal. This, apparently, indicates that the poloidal scale of the fluctuations is much larger
than the method resolution of π/k⊥.
Evolutionofof
Figure7.7.Evolution
Figure DBS
DBS amplitude
amplitude forfor different
different cut-off
cut-off radii.
radii. (a)(a) low-frequency
low-frequency ELMs,
ELMs, (b)(b) high-
high-
frequency
frequencyELMs.
ELMs.The
Theturbulence
turbulenceamplitude
amplitudeofofeach
eachDBS-channel
DBS-channelisiscalculated
calculatedinindifferent
differentarbi-
arbitrary
trary
unitsunits
[76].[76].
4.4.Conclusions
Conclusions
InInsummary,
summary,thetheDBS
DBSdiagnostics
diagnosticswas
wassuccessfully
successfullyused
usedtotostudy
studyperipheral
peripheralplasma
plasma
processes in the Globus-M tokamak. The application of this method was implemented on
processes in the Globus-M tokamak. The application of this method was implemented ona
spherical tokamak for the first time. Subsequently, DBS was implemented on
a spherical tokamak for the first time. Subsequently, DBS was implemented on the spher- the spherical
tokamak
ical tokamak MAST
MAST[8].[8].
The simultaneous applicationofofseveral
The simultaneous application severalDBS
DBSsystems
systemslocated
locatedatatdifferent
differentpoloidal
poloidal
angles and with different probing frequencies made it possible to determine
angles and with different probing frequencies made it possible to determine the spatial the spatial
structure of different plasma processes. As a result, geodesic acoustic modes, limit cy-
cle oscillations, quasi-coherent fluctuations, filaments, Alfven eigenmodes, and plasma
turbulence were investigated.
Two types of systems were used to study the radial distribution of GAMs: (1) two
single-frequency systems with the possibility to change the probing frequency in the
ranges of 18–26 GHz and 27–38 GHz, (2) a four-frequency system with fixed probing
frequencies of 20, 29, 39, and 48 GHz. It turned out that the very narrow localization of
GAMs near the periphery could only be studied in detail with the first type of system.
It is worth noting, however, that discharge repetition in this case required much effort
and additional diagnostics of various plasma parameters. It was not possible to construct
a radial profile of the GAM oscillation amplitude using a four-frequency system, as the
cut-offs for the selected frequencies were spaced much farther apart than the size of the
GAM localization layer. Therefore, GAMs were only detected on the peripheral channel of
the four-frequency system, whereas on other channels they were not observed. It was also
useful for the purpose of GAM research to use poloidally spread single-frequency DBS
systems positioned in a manner so that their cut-offs were located on the same magnetic
surface. Such an application of DBS diagnostics in this configuration allowed for the
determination of the poloidal mode number of the GAM velocity oscillations to be m = 0.
A four-frequency DBS system was used with the intent to study LCO. In contrast to
GAMs, the localization of the LCO turned out to be much wider, and all four DBS channels
were able to detect oscillations at this frequency, albeit with different amplitudes. The study
of fluctuations in the velocity and amplitude of turbulence at different radii had made it
possible to investigate the characteristic properties of the development of LCO. The phase
relationship between oscillations of velocity and turbulence amplitude near the top of the
pedestal region corresponded to the interaction of zonal fluxes and turbulence observed
on other devices (see [78], for example). Yet near the separatrix where both velocity and
turbulence fluctuations were observed, their phase coupling changed and the velocity
started to increase slightly earlier than the level of turbulence. These results contradictAppl. Sci. 2021, 11, 8975 15 of 19
the known zero-dimensional model of the interaction of zonal flows and turbulence [48]
and indicate that the description of LCO should be at least one-dimensional. A study of
the spectral characteristics of the LCO oscillations on Globus-M showed an increase in
their frequency when compared to larger devices. The dependence of the frequency of
oscillations on the size of the devices cannot be predicted by a predator-prey model of
coupling of zonal flows with turbulence.
DBS was first utilized for filament research. Subsequently, the detection of filaments
using DBS on the ASDEX Upgrade tokamak was reported [79]. The use of various probing
frequencies on Globus-M made it possible to detect them both near the separatrix and
in the more inner plasma regions. The simultaneous use of several probing frequencies
allowed one to study their radial size. It had been found that the filaments that develop
during ELMs are radially longer than the filaments that develop during inter-ELM periods.
The use of poloidally spread DBS schemes helped investigate the localization of filaments
and track their movement in the poloidal direction. The poloidal rotation velocity of the
filaments, determined from the phase delay between the signals of the two poloidally
spread antennas of the DBS diagnostic, was equal to the one determined from the Doppler
frequency shift. Full-wave simulations of scattering on the filaments later confirmed the
correctness of the interpretation of the obtained experimental data.
For the first time, the DBS method had also been used to perform research into
Alfven oscillations that had been detected in the phase derivative of the complex DBS
signal. Alfven fluctuations in the phase of the complex IQ signal were detected in the
DIII-D tokamak using reflectometry [80]. On Globus-M the application of a four-frequency
probing system enabled us to study the radial distribution of the TAE amplitude. It was
noted that there were no fluctuations in the probing frequencies corresponding to the
regions near the separatrix. The largest oscillation amplitude values were recorded on the
highest frequency channel. Such measurements demonstrated the need to develop the DBS
diagnostics with a higher frequency range for the inner plasma area with the goal of TAE
detection in the core region.
The study of turbulence spectra led to the discovery of quasi-coherent fluctuations.
Such fluctuations were detected in the ELM-free H-mode and I-phase near the top of the
pedestal. The development of the QCFs was accompanied by a sharp increase in the local
diffusion rate leading to the deformation of the density profile. The appearance of the QCF
is associated with the development of ITG instability.
All of the operational DBS systems are now utilized on the new and improved Globus-
M2 tokamak. Moreover, the DBS diagnostic continues to evolve in response to the de-
mand associated with the development of the scientific plans for the modernization of
the tokamak. In particular, an additional six-channel DBS circuit with a frequency range
of 50–75 GHz has recently been installed for core region research. In experiments that
aimed to completely replicate the Globus-M working conditions that were favorable for
the development of TAEs, the use of a high-frequency DBS system allowed to observe
the decline in the TAE amplitude in the central region of the discharge and thus the final
localization profile of these oscillations was determined [81].
Author Contributions: Conceptualization, A.Y. and V.B.; methodology, A.P. (Alexander Petrov);
software, A.P. (Anna Ponomarenko); validation, A.Y., A.P. (Alexander Petrov) and A.P. (Anna
Ponomarenko); formal analysis, A.Y.; investigation, A.Y.; resources, A.Y.; data curation, A.Y.; writing—
original draft preparation, A.Y. and A.P. (Alexander Petrov); writing—review and editing, A.Y.;
visualization, A.Y.; supervision, A.Y.; project administration, A.Y.; funding acquisition, A.Y. All
authors have read and agreed to the published version of the manuscript.
Funding: This research was funded by Ministry of Science and Higher Education of the Russian
Federation: 0784-2020-0020.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.You can also read
