Comparative analysis of the refraction of microwaves at different frequencies in an inhomogeneous plasma of a high power impulse reflex discharge
The trajectories of microwave rays at 36 and 71 GHz frequencies are calculated. A time dependences of an amplitude of scattered microwave signals at 36 and 71 GHz frequencies are experimentally measured. A comparison and analysis of experimental and calculated data, which are in satisfactory agree...
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| Цитувати: | Comparative analysis of the refraction of microwaves at different frequencies in an inhomogeneous plasma of a high power impulse reflex discharge / Yu.V. Kovtun, Y.V. Siusko, E.I. Skibenko // Вопросы атомной науки и техники. — 2018. — № 6. — С. 328-331. — Бібліогр.: 14 назв. — англ. |
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Kovtun, Yu.V. Siusko, Y.V. Skibenko, E.I. 2019-02-19T15:37:42Z 2019-02-19T15:37:42Z 2018 Comparative analysis of the refraction of microwaves at different frequencies in an inhomogeneous plasma of a high power impulse reflex discharge / Yu.V. Kovtun, Y.V. Siusko, E.I. Skibenko // Вопросы атомной науки и техники. — 2018. — № 6. — С. 328-331. — Бібліогр.: 14 назв. — англ. 1562-6016 PACS: 52.70.-m; 52.70.Gw; 52.80.Sm https://nasplib.isofts.kiev.ua/handle/123456789/149078 The trajectories of microwave rays at 36 and 71 GHz frequencies are calculated. A time dependences of an amplitude of scattered microwave signals at 36 and 71 GHz frequencies are experimentally measured. A comparison and analysis of experimental and calculated data, which are in satisfactory agreement, has been carried out. Проведено розрахунки траєкторії мікрохвильових променів на частотах 36 і 71 ГГц. Експериментально вимірянo залежності амплітуди розсіяних мікрохвильових сигналів на частотах 36 і 71 ГГц у часі. Проведено порівняння і аналіз експериментальних та розрахункових даних, що задовільно узгоджуються між собою. Проведены расчеты траектории микроволновых лучей на частотах 36 и 71 ГГц. Экспериментально измерены зависимости амплитуды рассеянных микроволновых сигналов на частотах 36 и 71 ГГц от времени. Проведено сравнение и анализ экспериментальных и расчетных данных, которые находятся в удовлетворительном согласии. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Диагностика плазмы Comparative analysis of the refraction of microwaves at different frequencies in an inhomogeneous plasma of a high power impulse reflex discharge Порівняльний аналіз рефракції мікрохвиль на різних частотах у неоднорідній плазмі потужного імпульсного відбивного розряду Сравнительный анализ рефракции микроволн на различных частотах в неоднородной плазме мощного импульсного отражательного разряда Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Comparative analysis of the refraction of microwaves at different frequencies in an inhomogeneous plasma of a high power impulse reflex discharge |
| spellingShingle |
Comparative analysis of the refraction of microwaves at different frequencies in an inhomogeneous plasma of a high power impulse reflex discharge Kovtun, Yu.V. Siusko, Y.V. Skibenko, E.I. Диагностика плазмы |
| title_short |
Comparative analysis of the refraction of microwaves at different frequencies in an inhomogeneous plasma of a high power impulse reflex discharge |
| title_full |
Comparative analysis of the refraction of microwaves at different frequencies in an inhomogeneous plasma of a high power impulse reflex discharge |
| title_fullStr |
Comparative analysis of the refraction of microwaves at different frequencies in an inhomogeneous plasma of a high power impulse reflex discharge |
| title_full_unstemmed |
Comparative analysis of the refraction of microwaves at different frequencies in an inhomogeneous plasma of a high power impulse reflex discharge |
| title_sort |
comparative analysis of the refraction of microwaves at different frequencies in an inhomogeneous plasma of a high power impulse reflex discharge |
| author |
Kovtun, Yu.V. Siusko, Y.V. Skibenko, E.I. |
| author_facet |
Kovtun, Yu.V. Siusko, Y.V. Skibenko, E.I. |
| topic |
Диагностика плазмы |
| topic_facet |
Диагностика плазмы |
| publishDate |
2018 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Порівняльний аналіз рефракції мікрохвиль на різних частотах у неоднорідній плазмі потужного імпульсного відбивного розряду Сравнительный анализ рефракции микроволн на различных частотах в неоднородной плазме мощного импульсного отражательного разряда |
| description |
The trajectories of microwave rays at 36 and 71 GHz frequencies are calculated. A time dependences of an
amplitude of scattered microwave signals at 36 and 71 GHz frequencies are experimentally measured. A comparison
and analysis of experimental and calculated data, which are in satisfactory agreement, has been carried out.
Проведено розрахунки траєкторії мікрохвильових променів на частотах 36 і 71 ГГц. Експериментально
вимірянo залежності амплітуди розсіяних мікрохвильових сигналів на частотах 36 і 71 ГГц у часі.
Проведено порівняння і аналіз експериментальних та розрахункових даних, що задовільно узгоджуються
між собою.
Проведены расчеты траектории микроволновых лучей на частотах 36 и 71 ГГц. Экспериментально
измерены зависимости амплитуды рассеянных микроволновых сигналов на частотах 36 и 71 ГГц от
времени. Проведено сравнение и анализ экспериментальных и расчетных данных, которые находятся в
удовлетворительном согласии.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149078 |
| citation_txt |
Comparative analysis of the refraction of microwaves at different frequencies in an inhomogeneous plasma of a high power impulse reflex discharge / Yu.V. Kovtun, Y.V. Siusko, E.I. Skibenko // Вопросы атомной науки и техники. — 2018. — № 6. — С. 328-331. — Бібліогр.: 14 назв. — англ. |
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ISSN 1562-6016. ВАНТ. 2018. №6(118)
328 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2018, № 6. Series: Plasma Physics (118), p. 328-331.
COMPARATIVE ANALYSIS OF THE REFRACTION OF MICROWAVES
AT DIFFERENT FREQUENCIES IN AN INHOMOGENEOUS PLASMA
OF A HIGH POWER IMPULSE REFLEX DISCHARGE
Yu.V. Kovtun, Y.V. Siusko, E.I. Skibenko
National Science Center “Kharkov Institute of Physics and Technology”,
Institute of Plasma Physics, Kharkiv, Ukraine
E-mail: Ykovtun@kipt.kharkov.ua; Zhenya-syusko@kipt.kharkov.ua
The trajectories of microwave rays at 36 and 71 GHz frequencies are calculated. A time dependences of an
amplitude of scattered microwave signals at 36 and 71 GHz frequencies are experimentally measured. A comparison
and analysis of experimental and calculated data, which are in satisfactory agreement, has been carried out.
PACS: 52.70.-m; 52.70.Gw; 52.80.Sm
INTRODUCTION
Among the methods of plasma diagnostics,
microwave methods occupy an important place [1-4].
The diagnostics methods that are based on the refraction
of microwave rays in plasma [3-7] are also applied. By
using the refraction, it is possible to determine a plasma
density distribution. An essential requirement for
application of this technique is using of narrow
microwave rays supposing the fulfilment of the
condition for geometric optics. These methods are
feasible only with inclined microwave probing. To have
a full set of data, the angle of transmitting horn antenna
has to be varied with respect to the plasma [6, 7], what
in practice is not always technically possible. For the
case when there is no possibility to vary this angle, it
was proposed [8, 9] to use the rays diverging from the
transmitting horn antenna, which are directed at oblique
angle to the plasma. In [10], calculations of the
deviation angle φ of a microwave ray from an angle of
its incidence ψ to no uniform plasma were made, which
showed that part of a microwave rays could fall into a
fixed horn antenna at a fixed angle with respect to the
plasma. Experimentally, microwave (f = 37 GHz)
scattering was registered at a fixed angle of ~ 60 ° and
~ 120° [10]. Experimental testing the method
interferometry of plasma by inclined microwave rays,
proposed in [8], was carried out in [11]. It has been
experimentally shown the possibility of determining an
average plasma electron concentration in the peripheral
layers. Thus, the purpose of this study is comparative
analysis of the refraction of microwave at different
frequencies in an inhomogeneous plasma which should
be useful to further developing the microwave methods
based on refraction and help to increase its
informatively and unambiguous measurements.
1. EXPERIMENTAL SETUP AND
DIAGNOSTIC TECHNIQUES
Experiments on the microwave refraction in the
plasma were carried out using the device “MAKET”
[12]. In the device a high-power impulse reflex
discharge in crossed E×B fields was realized. The
stainless steel discharge chamber had the following
dimensions: 20 cm in internal diameter, and 200 cm in
length. A pulsed magnetic field of the mirror
configuration (mirror ratio of 1.25, B ≤ 0.9 T) and
18 ms in duration was created by a solenoid composed
of six coils. The chamber was evacuated to a pressure of
1.33·10-4 Pa and then filled with the igniter gas (Ar) at a
pressure of 0.6 and 3 Pa. The plasma was produced by
discharging a capacitor bank (capacity 560 µF, voltage
≤ 5 kV) between cold cathodes (diameter 10 cm) and
the anode (the wall of the vacuum chamber). The
multicomponent gas-metal plasma was produced in the
mixture of the igniter gas and the sputtered cathode
material. The cathodes were made of a composite
material – Zr deposited on copper by the vacuum arc
method.
The microwave measuring system is schematically
represented in Fig. 1. Registration and measured of the
scattered signal was carried out by a receiving horn
antenna 5 shifted at the angle of 60 degrees with respect
to the radiating antenna axis and detector (diode) 2.
Pyramidal horn antennas were used for transmission
and receiving of a microwave radiation. A horn cross-
section size (antenna aperture) was a = b = 35 mm, axial
height is 92 mm. The horn antennas are mounted in
diagnostic ports the design of which does not provide
the variation of antenna tilt relatively to the plasma.
Inclined probing was realized due to microwaves rays
which directed to the plasma column obliquely. If the
horn antenna aperture is taking into account, the angle
of microwave radiation reception amounts to 60°± 9°.
Simultaneously with the measured of the scattered
signal, the microwave signal of the transmitted wave
through the center of the plasma formation was
measured by horn antenna 6 and detector 3. The mean
plasma density across the plasma column was measured
with using interferometer. Plasma was probed by
microwave (O-wave) at frequencies 36 and 71 GHz.
Fig. 1. Schematic representation of the measuring
system. 1 – generator; 2, 3 – detectors for receiving
microwave; 4 – the radiating horn antenna;
5, 6 – the receiving horn antennas
ISSN 1562-6016. ВАНТ. 2018. №6(118) 329
The space surrounding an antenna is usually
subdivided into three regions [13]: reactive near-field,
radiating near-field (Fresnel) and far-field (Fraunhofer)
regions. These regions are determined depending on the
distance from the antenna surface R: if R < (2·D2 / λ)
(where λ is the wavelength and D is the largest dimension
of the antenna) it is near-field region and if R > (2·D2 / λ) it
is far-field region. The calculation showed that the far-field
region is R > 31 cm and R > 65 cm for 36 and 71 GHz
frequencies respectively. The diameter of cylindrical anode
is less than this region. Thus plasma is located in the near-
field region of antenna. Therefore, the calculations of the
electric field and magnetic field components distribution at
the aperture of the horn antenna for the wave at 36 and
71 GHz frequencies were made. The basic wave mode for
the calculation was adopted as TE10. All other modes are
not essential for our waveguide. The calculations are
performed by the method of moments. The results of
calculation for waves at frequency 36 and 71 GHz are
shown in the Fig. 2.
2. REFRACTION OF MICROWAVES IN AN
INHOMOGENEOUS PLASMA CYLINDER
2.1. CALCULATION OF RAYS TRACING OF
MICROWAVES AT TWO FREQUENCIES IN
THE PLASMA CYLINDER
In the geometrical optics approximation, the
differential equation for the trajectory of a microwave
ray in a plasma cylinder looks like [5]:
2
2
2
2
O
2 sin)(
sin
r
R
rnr
R
dr
d
, (1)
where Ψ is the angle between the line of propagation
and the cylinder radius at the point of ray incidence on
the plasma cylinder; φ is the deviation angle of the
radius-vector from its initial position; R is the cylinder
radius; r is the current coordinate; n0 is the refraction
index for the O-wave. The deviation angle φ of the
microwave ray is dependent not only on the angle of the
ray incidence ψ and the plasma electron density, but
also on the plasma density profile.
In the case when the ratio of the effective collision
frequency to the probing frequency is veff / ω << 1, the
refraction index for the O-wave in the plasma is equal to
[14]:
2/1
cr.
p
2/1
2
2
p
O
)(
1
)(
1)(
N
rNr
rn
, (2)
Fig. 2. Distribution of the electric and magnetic fields
on the horn antenna aperture for wave at: a – 36 GHz;
b – 71 GHz
where ωp – frequency of plasma, ω – frequency of
probing wave.
Let's compare the influence of refraction on the
propagation of microwave rays at frequencies 36 and
71 GHz. The critical densities Ncr. for these frequencies
are 1.6·1013 and 6.3·1013 cm-3 respectively. The initial
conditions are chosen according to the geometry and
parameters of the experimental setup (see Fig. 1). The
microwave ray’s trajectory was calculated taking into
account the aperture of the horn antennas and taking the
density distribution in the form of Np(r) = Nmax·(1-
(r/R)2).
The calculation results obtained for the microwave
rays trajectory in the plasma cylinder for three different
cases are shown in Fig. 3. The axis of the radiating horn
antenna is situated at angle of φ = 0° (the angle of flare
is 9°), the axis of the receiving antenna is situated at
angle of φ = 300° (the angle of flare is 9°).
In the first case, when the maximum plasma density
is less than the critical Nmax < Ncr for both frequencies
36 and 71 GHz, the trajectory of microwave rays is
shown in Fig. 3,a. Microwave rays due to refraction
deviate from the rectilinear propagation and pass
through the plasma. In the second case (see Fig. 3,b) the
maximum plasma density is greater than the critical
density Nmax > Ncr. for a frequency of 36 GHz. Wherein
the microwave rays reflected from the plasma layer with
a critical density can fall into the receiving antenna 5
(see Fig. 1). For a frequency of 71 GHz Nmax < Ncr, the
microwave rays pass through the plasma. In the third
Fig. 3. Ray tracing of microwaves depending of different maximum values of density: a – Nmax = 8·1012 cm-3;
b – Nmax = 2·1013 cm-3, c – Nmax = 8·1013 cm-3. 1 – frequency 36 GHz; 2 – frequency 71 GHz; radius of layers
with critical density; 3 – Ncr. = 1.6·1013 cm-3; 4 – Ncr. = 6.3·1013 cm-3
330 ISSN 1562-6016. ВАНТ. 2018. №6(118)
case, the maximum plasma density is greater than the
critical Nmax > Ncr for both frequencies (see Fig. 3,c).
Microwave rays at a frequency of 71 GHz, reflected
from a plasma layer with a critical density, can hit the
horn antenna 5 (see Fig. 1). For a frequency of 36 GHz
calculations showed that when the radius of the plasma
layer with Ncr is greater than ~ 5.2…6.3 cm, microwave
rays do not enter the horn antenna 5 (see Fig. 1).
2.2. ATTENUATION OF MICROWAVE RAYS IN
PLASMA
Absorption coefficient the general form [14]:
ρ
0
ρ )(2
s
dss
c
,
(3)
where χ(s) absorption index in a given point s in the
plasma, Sp the path of a microwave ray in a plasma. In
the cylindrical layered medium equation 3 take form
[5]:
R
r
dr
Rrnr
rnr
r
c
0
2222
ρ
sin)(
)(
)(4
, (4)
where χ(r) absorption index in our case [14]:
2
1
2
2
ρ
2
2
ρc )1(
2
1
)(
r , (5)
where vc – effective collision frequency.
The time dependence of the maximum plasma
density (see Fig 4,a) for the calculation was given by
equation Np(t)=0.51·1021·(e-2016t – e-9626t). This
dependence is close to experimentally measured earlier
in work [10]. The horn antenna aperture, wave
frequency, distribution of plasma density and other
parameters is the same as in paragraph 2.1. Absorption
coefficient and absorption index were calculated by the
formulas 4 and 5. The effective collision frequency was
set equal to vc = 0.001·ω. (reflection from the opposite
surface). At a density greater than the critical, the
microwave signal does not pass through the plasma.
With decreasing density, the attenuation of the signal
decreases too, due to it its amplitude becomes higher.
Curve on Fig. 4,b curve 2 shows that when plasma
density reached value nearly 1∙1014 cm-3 the scattered
signal at 71 GHz frequency has a maximum value.
Fig. 4. Time dependences of: the plasma density (a); the
amplitude of microwave signal at 71 GHz frequency
transmitted through the center of plasma column (curve
1, b) and microwave scattered signal which hitting to
horn antenna situated at angle 60 degrees with respect
to the radiating antenna axis (curve 2, b)
3. EXPERIMENTAL RESULTS
The previous investigations of the plasma generated
in a high-power pulsed discharge [12] have
demonstrated that the time dynamics of the mean gas-
metal plasma density can be divided by convention into
three stages. The first stage presents the plasma creation
and its density increase up to Np = 1.7∙1013 cm-3. The
second stage is the plasma existence with the density
attaining Np~ 1014 cm-3 and more. The third stage
presents the plasma density decrease and decay.
In the present experiments simultaneously with
measurements of the scattered signal for wave at
36 GHz frequency (receiver antenna 5 (see Fig. 1)),
through probing interferometry of plasma (Fig. 5) was
made. And for wave at 71 GHz frequency transmitted
signal through the plasma was registered (Fig. 6).
According to the oscillogram of through probing
interferometry which is shown on Fig. 5 (curve 1) the
minimal amplitude of scatter signal for wave at 36 GHz
was registered when plasma density achieved the
critical density Ncr. This experimental result corresponds
to the calculated result (see Fig. 3,c). According to the
calculations it can be argued that the radius of the layer
with critical density is more than ~ 5.2…6.3 cm.
From Fig. 6 (curve 2) it is seen that the rise of the
scattered signal occurs approximately from 0.5 ms to
1.3 ms. At this time interval, the cutoff of the
transmitted signal Fig. 6 (curve 2) is observed.
Therefore, when plasma density is close or above the
critical (Ncr) for wave at 71 GHz frequency, the
maximum of the scattered signal is observed. This
experimental result is opposite the result for wave at
36 GHz frequency. The calculated result (see Figs. 3,c
and 4,b) is the same as experimental (see Fig. 6).
Fig. 5. Oscillogram of the thought probing
interferometr (1) and microwave scatter at angles
φ1 ≈ 60°± 9° (2). For both case the frequency of probing
rays is 36 GHz
Fig. 6. Time dependence of the amplitude of the
scattered signal at 71.45 GHz frequency at angle of 60°
(1) and the oscillograms of the signal transmitted
through the plasma (2)
ISSN 1562-6016. ВАНТ. 2018. №6(118) 331
CONCLUSIONS
The calculations of the ray trajectory at 36 and
71 GHz were performed. It is shown that, depending on
the maximum density of the plasma, three cases of
trajectory of microwaves with respect to the receiving
antenna are possible. The time dependence of the
amplitude of microwave scattered signal at 36 and
71 GHz frequencies were experimentally obtained. It
was found that at frequency 36 GHz the minimal
amplitude of receiving signal was registered when
plasma density in the layer achieved the density Ncr. In
contrast, for the same conditions, the maximum signal
amplitude was observed when probing frequency was
71 GHz. The experimental and calculation method
shows, that at a certain value of the plasma density, a
wave with a lower frequency is reflected or absorbed in
the plasma and becomes less informative. At the same
time, a wave with a higher frequency can still hit on the
receiving antenna. Therefore, the use of several
frequencies can make methods of plasma diagnostics
based on refraction more informative.
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Article received 26.09.2018
СРАВНИТЕЛЬНЫЙ АНАЛИЗ РЕФРАКЦИИ МИКРОВОЛН НА РАЗЛИЧНЫХ ЧАСТОТАХ
В НЕОДНОРОДНОЙ ПЛАЗМЕ МОЩНОГО ИМПУЛЬСНОГО ОТРАЖАТЕЛЬНОГО РАЗРЯДА
Ю.В. Ковтун, Е.В. Сюсько, Е.И. Скибенко
Проведены расчеты траектории микроволновых лучей на частотах 36 и 71 ГГц. Экспериментально
измерены зависимости амплитуды рассеянных микроволновых сигналов на частотах 36 и 71 ГГц от
времени. Проведено сравнение и анализ экспериментальных и расчетных данных, которые находятся в
удовлетворительном согласии.
ПОРІВНЯЛЬНИЙ АНАЛІЗ РЕФРАКЦІЇ МІКРОХВИЛЬ НА РІЗНИХ ЧАСТОТАХ
У НЕОДНОРІДНІЙ ПЛАЗМІ ПОТУЖНОГО ІМПУЛЬСНОГО ВІДБИВНОГО РОЗРЯДУ
Ю.В. Ковтун, Є.В. Сюсько, Є.І. Скибенко
Проведено розрахунки траєкторії мікрохвильових променів на частотах 36 і 71 ГГц. Експериментально
вимірянo залежності амплітуди розсіяних мікрохвильових сигналів на частотах 36 і 71 ГГц у часі.
Проведено порівняння і аналіз експериментальних та розрахункових даних, що задовільно узгоджуються
між собою.
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