Gas discharge in plasma-metal waveguide with varying radius of metal enclosure partially filled by radially non-uniform magnetized plasma
The article presents the results of theoretical study of phase and attenuation characteristics of the symmetric electromagnetic wave in long waveguide structure that partially filled by radially non-uniform plasma immersed in external steady magnetic field. The results of theoretical study of statio...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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irk-123456789-1946462023-11-28T12:40:53Z Gas discharge in plasma-metal waveguide with varying radius of metal enclosure partially filled by radially non-uniform magnetized plasma Azarenkov, N.A. Olefir, V.P. Sporov, A.E. Basic plasma physics The article presents the results of theoretical study of phase and attenuation characteristics of the symmetric electromagnetic wave in long waveguide structure that partially filled by radially non-uniform plasma immersed in external steady magnetic field. The results of theoretical study of stationary gas discharge sustained by this wave in the considered waveguide structure with slightly varying radius of metal enclosure in the framework of electrodynamic model are presented as well. It was studied the influence of the effective plasma collision frequency on the phase and attenuation wave properties and on the plasma density axial distribution in gas discharge considered for different radial plasma density profiles. Представлено результати теоретичного дослідження фазових характеристик та просторового загасання симетричної електромагнітної хвилі в довгій хвилеводній плазмово-металевій структурі, що частково заповнена радіально-неоднорідною плазмою, яка знаходиться у зовнішньому аксіальному постійному магнітному полі. В межах електродинамічної моделі стаціонарного газового розряду отримано аксіальний розподіл густини плазми, що підтримується власною симетричною хвилею структури. Досліджено також впливи ефективної частоти зіткнень електронів плазми на фазові характеристики та просторове загасання хвилі, а також на аксіальний розподіл густини плазми в газових розрядах, що підтримуються нею, за різних радіальних розподілів густини плазми. Представлены результаты теоретического исследования фазовых свойств и пространственного затухания симметричной электромагнитной волны в длинной волноводной плазменно-металлической структуре, частично заполненной радиально-неоднородной плазмой, помещенной во внешнее аксиальное постоянное магнитное поле. Представлены результаты теоретического исследования аксиального распределения плотности плазмы в стационарном газовом разряде, поддерживаемом симметричной волной, в рассматриваемой волноводной структуре, полученные в рамках электродинамической модели разряда. Исследованы также влияния эффективной частоты столкновений электронов плазмы на фазовые свойства и пространственное затухание волны, а также на аксиальное распределение плотности плазмы в газовых разрядах, поддерживаемых этой волной, для различных радиальных профилей плотности плазмы. 2020 Article Gas discharge in plasma-metal waveguide with varying radius of metal enclosure partially filled by radially non-uniform magnetized plasma / N.A. Azarenkov, V.P. Olefir, A.E. Sporov // Problems of atomic science and tecnology. — 2020. — № 6. — С. 69-73. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.35-g, 52.50.Dg http://dspace.nbuv.gov.ua/handle/123456789/194646 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Basic plasma physics Basic plasma physics |
| spellingShingle |
Basic plasma physics Basic plasma physics Azarenkov, N.A. Olefir, V.P. Sporov, A.E. Gas discharge in plasma-metal waveguide with varying radius of metal enclosure partially filled by radially non-uniform magnetized plasma Вопросы атомной науки и техники |
| description |
The article presents the results of theoretical study of phase and attenuation characteristics of the symmetric electromagnetic wave in long waveguide structure that partially filled by radially non-uniform plasma immersed in external steady magnetic field. The results of theoretical study of stationary gas discharge sustained by this wave in the considered waveguide structure with slightly varying radius of metal enclosure in the framework of electrodynamic model are presented as well. It was studied the influence of the effective plasma collision frequency on the phase and attenuation wave properties and on the plasma density axial distribution in gas discharge considered for different radial plasma density profiles. |
| format |
Article |
| author |
Azarenkov, N.A. Olefir, V.P. Sporov, A.E. |
| author_facet |
Azarenkov, N.A. Olefir, V.P. Sporov, A.E. |
| author_sort |
Azarenkov, N.A. |
| title |
Gas discharge in plasma-metal waveguide with varying radius of metal enclosure partially filled by radially non-uniform magnetized plasma |
| title_short |
Gas discharge in plasma-metal waveguide with varying radius of metal enclosure partially filled by radially non-uniform magnetized plasma |
| title_full |
Gas discharge in plasma-metal waveguide with varying radius of metal enclosure partially filled by radially non-uniform magnetized plasma |
| title_fullStr |
Gas discharge in plasma-metal waveguide with varying radius of metal enclosure partially filled by radially non-uniform magnetized plasma |
| title_full_unstemmed |
Gas discharge in plasma-metal waveguide with varying radius of metal enclosure partially filled by radially non-uniform magnetized plasma |
| title_sort |
gas discharge in plasma-metal waveguide with varying radius of metal enclosure partially filled by radially non-uniform magnetized plasma |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2020 |
| topic_facet |
Basic plasma physics |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/194646 |
| citation_txt |
Gas discharge in plasma-metal waveguide with varying radius of metal enclosure partially filled by radially non-uniform magnetized plasma / N.A. Azarenkov, V.P. Olefir, A.E. Sporov // Problems of atomic science and tecnology. — 2020. — № 6. — С. 69-73. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT azarenkovna gasdischargeinplasmametalwaveguidewithvaryingradiusofmetalenclosurepartiallyfilledbyradiallynonuniformmagnetizedplasma AT olefirvp gasdischargeinplasmametalwaveguidewithvaryingradiusofmetalenclosurepartiallyfilledbyradiallynonuniformmagnetizedplasma AT sporovae gasdischargeinplasmametalwaveguidewithvaryingradiusofmetalenclosurepartiallyfilledbyradiallynonuniformmagnetizedplasma |
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2025-07-16T22:02:45Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2020. №6(130)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2020, № 6. Series: Plasma Physics (26), p. 69-73. 69
https://doi.org/10.46813/2020-130-069
GAS DISCHARGE IN PLASMA-METAL WAVEGUIDE WITH VARYING
RADIUS OF METAL ENCLOSURE PARTIALLY FILLED BY RADIALLY
NON-UNIFORM MAGNETIZED PLASMA
N.A. Azarenkov, V.P. Olefir, A.E. Sporov
V.N. Karazin Kharkiv National University, Kharkiv, Ukraine
E-mail: sporov@karazin.ua, vpolefir@karazin.ua
The article presents the results of theoretical study of phase and attenuation characteristics of the symmetric
electromagnetic wave in long waveguide structure that partially filled by radially non-uniform plasma immersed in
external steady magnetic field. The results of theoretical study of stationary gas discharge sustained by this wave in
the considered waveguide structure with slightly varying radius of metal enclosure in the framework of
electrodynamic model are presented as well. It was studied the influence of the effective plasma collision frequency
on the phase and attenuation wave properties and on the plasma density axial distribution in gas discharge
considered for different radial plasma density profiles.
PACS: 52.35-g, 52.50.Dg
INTRODUCTION
Till now the intensive theoretical and experimental
studies of plasma sources with the specified plasma
parameters are carried out in different laboratories over
the world [1, 2]. One of the possible kind of plasma
sources are the microwave gas discharges in rather long
and narrow tubes that are sustained by the eigen waves
of the discharge structure. This is the characteristic
feature of such discharges that is used in modeling of
stationary plasma density axial distribution in the
framework electrodynamic approach [2]. Such modeling
consists of the detailed description of wave propagation
and attenuation, and using the model equation for the
description the discharge features [2, 3].
The plasma – metal waveguides with slightly
varying radius of metal enclosure along the discharge
are used as a chambers for gas discharges [4]. In the
previous studies it was carried out the investigation of
axial structure of gas discharge in such waveguides
under the assumption of radially uniform magnetized
plasma [5]. But usually in such discharges plasma
density is strongly non-uniform in radial direction. The
aim of this work is to study influence of variable radius
of metal waveguide and plasma density radial profile on
the properties of the discharge that is sustained by the
symmetric wave which is promising for gas discharge
sustaining [1, 2].
1. BASIC EQUATIONS
Let us consider the model of the stationary stage of
gas discharge in diffusion controlled regime that
sustains by the symmetric electromagnetic wave in
rather long magnetized plasma – metal waveguide
structure with variable radius of metal enclosure in the
framework of electromagnetic approach. The considered
electromagnetic symmetric wave propagates along three
component waveguide structure that is composed of the
plasma column with radius Rp, vacuum region Rp<r<R
and cylindrical metal enclosure of radius R. External
steady magnetic field 0 0(0,0, )B B is directed along
the axis of the structure. Plasma was considered in the
hydrodynamic approach as a cold, weakly absorbing
media with constant effective collisional frequency
that is considered to be small compared to the given
wave frequency and is constant in axial and radial
directions [6]. The case when only one mode with the
specified azimuthal wave number is excited in the
discharge structure is considered. It was supposed that
all geometric, plasma and wave parameters slightly vary
in axial direction on the distances of wavelength order,
so the WKB approach can be used to obtain the solution
of the system of Maxwell equations [7]. This solution
can be found in the form:
( ') '3
0
, , , ,, ( , , ) , ( , )e ,
z
i t k z dz
z
r z r zE H r z E H r z
(1)
where is the wave frequency; k3 is the axial
wavenumber, E, H – amplitude of electric and magnetic
wave fields, respectively. It was considered the case
when the variation variable A value along the discharge
at the distances of the order of wavelength is small as
compared with the magnitude of this variable, therefore
1
3
A
A k
z
, where symbol A denotes E, H, k3, or n.
Thus, in further description all terms of order
3
1
lnO A
k z
were neglected [7].
It was also considered that radial plasma density
distribution can be expressed in the Bessel-like form as:
n(r) = n(0) J0(δr). Here J0 is the Bessel function of the
first kind and δ is plasma density non-uniformity
parameter, that varies from δ = 0 (radially uniform
plasma) up to δ = 2.405 (strong radially non-uniform
plasma that corresponds to ambipolar diffusion regime).
In such case one can obtain the equations for radial
wave components in plasma region have the following
form:
3
3 2
1 1
( ) ( )
( )
( ) ( ) ( )
( ) ( )
p p
r
p p p
z
k
H r E r
k
k i r
E r H r E r
k r r
,
(2)
https://doi.org/10.46813/2020-130-069
70 ISSN 1562-6016. ВАНТ. 2020. №6(130)
where ε1,2,3(r) are the components of permittivity tensor
of magnetized collisional plasma [6] that depends on
radial coordinate r throw the dependence of n(r). The
ordinary differential equations for other wave field
components in plasma region can be written as:
2 2
3 2 3 1
1 1
3 2
1 1
3
( ) ( )
( ) ( )
( ) ( )
1
( ) ( )
( )
( ) ( )
( ) ( )
1
( ) ( ) ( ),
p
p pz
p
p p
z
p
p pz
p
p p
z
k r k k rdE
E r i H r
d r r k r
dE
E r ikH r
d r r
p rk rdH
H r i E r
d r r k r
dH
H r ik r E r
d r r
(3)
where 2 2 2 2
1 3 1 2( ) ( )( ( )) ( ) p r r k k r k r , k=ω/c – is
the vacuum wavenumber.
The expressions for wave field components in
vacuum region can be written as:
1 0 2 0
' '
3 0 4 0
' '
3 1 0 3 2 0
3 0 4 0
' '
1 0 2 0
' '
3 3 0 3 4 0
( ) ( ) ( )
( ) ( )
( )
( ) ( )
( )
( ) ( ) ( )
( ) ( )
( )
( ) ( )
( )
z
r
z
r
E r A I r A K r
i k A I r i k A K r
E r
i k A I r i k A K r
E r
H r A I r A K r
i k A I r i k A K r
H r
i k A I r i k A K r
H r
,
(4)
where 2 2 2
3k k is the transverse wave number in
vacuum and А1-4 are field constants that can be obtained
from the boundary conditions and a stroke denotes
derivative by argument.
Taking into account boundary conditions on the
plasma – vacuum interface (the continuity of tangential
wave field components at r = Rp) it is possible to obtain
such expressions for field constants А1-4:
2
0
1 1
2
0
2 1
2
0
3 1
2
0
4 1
( )
( ) ( )
( )
( ) ( )
( )
( ) ( )
( )
( ) ( ).
p pP P
p p z p p
p pP P
p p z p p
p pP P
p p z p p
p pP P
p p z p p
R K R
A R K R E R i H R
k
R I R
A R I R E R i H R
k
R K R
A R K R H R i E R
k
R I R
A R I R H R i E R
k
(5)
In these formulas it is supposed that the expressions
for wave field components at plasma-vacuum interface
E
p
(Rp), H
p
(Rp) are obtained with the help of numerical
integration of the system of ordinary differential
equations (3).
The final equation (local dispersion equation) can be
obtained from the boundary conditions at vacuum –
metal interface (the vanishing of the wave tangential
components at r=R):
1 0 2 0
3 1 4 1
( ) ( ) 0
( ) ( ) 0.
A I R A K R
A I R A K R
(6)
The solution of the local dispersion equation (6)
connects the values of local density n and complex axial
wave vector k3 at the given wave frequency value ω. So,
from this equation (6) it is possible to obtain the
dependence of attenuation coefficient α = Im(k3) upon
the plasma density n. This dependence can be used to
determine the density axial gradient dn/dz for the
discharges in the diffusion controlled regime from the
relation [2, 3]:
2
1
d n n
n dd z
d n
. (7)
The axial plasma density profile n(z) in gas
discharge sustained by the symmetric wave in the
considered waveguide structure in diffusion controlled
regime can be obtained as a result of numerical
integration of the ordinary differential equation (7).
It is necessary to mention that surface wave can
sustain the stable discharge in the diffusion controlled
regime only when the Zakrzewski’s stability condition
is fulfilled [8]:
0
d
d n n
. (8)
It is necessary to check the fulfillment of this
criterion (8) when solving the ordinary differential
equation (7).
2. MAIN RESULTS
The electromagnetic wave that sustains the
discharge is the eigen wave of the discharge structure on
the whole length of the plasma column. So, the ability
of gas discharge sustaining by this wave is mainly
determined by the electrodynamic properties of the
wave considered. Because of that, the study consists of
two stages: 1) the detailed investigation of the phase and
attenuation properties of the wave; 2) the study of the
axial structure of gas discharge sustained by the wave
considered at stage 1.
The studied wave possesses all six components of
electric and magnetic wave field, so the determination
of wave field components in plasma region (the solution
of system (3)) for arbitrary problem parameters is
possible only with the help of numerical methods. To
carry out the study the following dimensionless
variables and parameters were introduced: wave
frequency μ = ω/ωp, axial wave number x = Re(k3)Rp,
attenuation coefficient α = Im(k3)Rp, effective collision
frequency
1 , external magnetic field value
Ω = ωCe/ω, radius of plasma column σ = Rω/c, radius of
metal enclosure η = R/Rp, axial coordinate
/ / pz R .
At first, the influence of the collision frequency on
phase and attenuation properties of the symmetric wave
was studied for the case of radially uniform plasma. In
the case considered the local dispersion equation (6) has
one solution for the problem parameters set. The
obtained solutions are presented on the Fig. 1
(dimensionless frequency via axial wave number) and
ISSN 1562-6016. ВАНТ. 2020. №6(130) 71
on the Fig. 2 (attenuation coefficient via axial wave
number).
Fig. 1. The dependence of dimensionless eigen wave
frequency μ via the dimensionless wave number x for
different values. Problem parameters are the
following: Ω = 0.6, σ = 0.5, η = 1.5, δ = 0. Numbers
just near the curves correspond to different values:
1 – = 0.005; 2 – = 0.05; 3 – = 0.1; 4 – = 0.5;
5 – = 1.0; 6 – = 5.0; 7 – = 10.0
These solutions were obtained for the low collisional
( 1.0, curve 1), moderate collisional ( ~ 1.0,
curves 2-5) and strong collisional ( > 1.0, curves 6, 7)
regimes. It was obtained that the wave considered has
difference behavior and regions of existence for
different collisional frequency values. The greater the
, the shorter is the normalized frequency μ = ω/ωp
region of the wave existence. Also the maximum
possible normalized frequency of this wave decreased
with the increasing of .
Fig. 2. The dependence of dimensionless attenuation
coefficient α on the dimensionless wave number x for
different values. Problem parameters and curve
numbering are the same as for the Fig. 1
The influence of the effective electron collision
frequency on the spatial attenuation coefficient
α = Im(k3)R was also studied. The results of the study
are presented on the (see Fig. 2). It was obtained that the
increase of the effective collision frequency value
leads to the substantially increase of the wave
attenuation coefficient. It is necessary to mention that
the value of collision frequency have some different
influence on the wave attenuation in the region of small,
moderate and strong values.
Fig. 3. The dependence of dimensionless eigen wave
frequency μ via the dimensionless wave number x for
different non-uniformity parameter values δ. Problem
parameters are the following: Ω = 0.6, σ = 0.5, η = 1.5,
= 0.001. Numbers just near the curves correspond to
different δ values: 1 – δ = 0; 2 – δ = 0.6; 3 – δ = 1.0;
4 – δ = 1.4; 5 – δ = 1.6; 6 – δ = 1.8; 7 – δ = 2.0;
8 – δ = 2.2; 9 – δ = 2.4
Fig. 4. The dependence of dimensionless attenuation
coefficient on the dimensionless wave number x for
different δ values. Problem parameters and curve
numbering are the same as for Fig. 3
The influence of plasma density non-uniformity on
the phase and attenuation properties at gradually
increasing non-uniform parameter value δ from 0 up to
2.4 is studied. The numerical results of the influence of
non-uniformity parameter δ on the normalized wave
frequency μ = ω/ωp are presented on the Fig. 3. It is
shown that the dispersion has different behavior in the
case of uniform and slightly non-uniform (curves 1-3),
moderate (curves 4-8) and strong non-uniform plasma
(curve 9). Generally, for the non-uniform plasma the
increase of the non-uniformity parameter δ leads to the
decrease of the symmetric wave phase velocity
Vph = / x for the fixed x value.
The results of studying the influence of radial
plasma density non-uniformity on the wave attenuation
coefficient are presented on the Fig. 4. The gradual
increasing on plasma density radial non-uniformity
parameter leads to substantial increasing on attenuation
coefficient α (see curves 1-9 in Fig. 4).
72 ISSN 1562-6016. ВАНТ. 2020. №6(130)
Fig. 5. The axial distribution on dimensionless
plasma density N = ωp
2
/ ω
2
along the discharge via the
dimensionless axial coordinate ξ for different non-
uniformity values δ. Problem parameters are the
following: Ω = 0.6, σ = 0.5, η = 1.5, = 0.01. Numbers
just near the curves correspond to different values:
1 – δ = 0; 2 – δ = 1.0; 3 – δ = 1.6; 4 – δ = 2.0. Solid
line corresponds to the constant, dashed line – to the
increasing and dotted line – to the decreasing radius of
waveguide metal wall along the discharge
Fig. 6. The axial variation of dimensionless waveguide
metal radius (parameter η) along the discharge via the
dimensionless axial coordinate ξ. Numbers just near the
curves corresponds: 1 – to the constant, 2 – to the
increasing and 3 – to the decreasing radius of
waveguide metal wall along the discharge
The results of numerical solution of the equation (7)
to obtain plasma density axial distribution in the
discharge sustained by symmetric waves are represented
in Fig. 5. The Fig. 6 presents the appropriate lows of
metal enclosure variation. Numbers on the curves 1, 2,
3, 4 corresponds to the case of δ = 0, 1.0, 1.6, 2.0,
respectively. The results are presented for three cases of
parameter η varying along the discharge: constant η
value along the discharge – solid line in Fig. 5 (see
curve 1 in Fig. 6); increasing η value along the
discharge – dashed line in Fig. 5 (see curve 2 in Fig. 6);
and decreasing η value along the discharge – dotted line
in Fig. 5 (see curve 3 in Fig. 6).
The increase of non-uniformity parameter δ leads to
the growth of the axial gradients of plasma density
distributions and to the decrease of gas discharge
normalized length max max / / pz R . It was also
obtained that the maximum possible value of the plasma
density, that can be obtained in such discharges also
increased with the increase of the parameter δ (see the
dependence of normalized values of
μ = ω/ωp = 1/sqrt(N) for different δ values in Fig. 3). It
is shown that the influence of metal enclosure varying
radius is much smaller for the case of strong radially
non-uniformity that in the case of radially uniform
plasma [5].
The decrease of the discharge length with the
increase of the plasma density non-uniformity parameter
δ can be explained due to the substantial increase of the
attenuation coefficient (see Fig. 4). Such behavior of
via δ is caused by the increased Joule heat losses due
to the increase of the wave field strength under plasma
density non-uniformity parameter growth.
CONCLUSIONS
It was studied the influence of slightly varying radi-
us of metal enclosure and strong plasma density radial
non-uniformity on the phase and attenuation properties
of electromagnetic symmetric wave in three component
waveguide structure partially filled by collisional,
radially non-uniform magnetized plasma. The axial
structure of gas discharge sustained by this wave for
different values of effective collisional frequency and
plasma density radial profiles was studied also. It was
shown that the influence of variable radius of
waveguide metal enclosure in the case of radially non-
uniform plasma on the axial plasma density profile in
the considered discharge is similar to the case of
radially uniform plasma. But it is necessary to mention
that this influence becomes much smaller with the
increase of plasma non-uniformity parameter .
This work was supported by the Ministry of
Education and Science of Ukraine, under the grant
0118U002023.
REFERENCES
1. I. Zhelyazkov, V. Atanassov. Axial structure of
low-pressure high-frequency discharges sustained by
travelling electromagnetic surface waves // Physics
Reports. 1995, v. 255, № 2-3, p. 79-201.
2. H. Schlüter, A. Shivarova. Travelling-wave-
sustained discharges // Physics Reports. 2007, v. 443,
№ 4-6, p. 121-255.
3. C.M. Ferreira. Modelling of a low-pressure plasma
column sustained by a surface wave // J. of Phys. D:
Appl. Phys. 1983, v. 16, № 9, p. 1673-1685.
4. J. Wolinska-Szatkowska. Surface wave discharge in
a conical tube // J. of Phys. D: Appl. Phys. 1987, v. 20,
p. 977-978.
5. N.A. Azarenkov, V.P. Olefir, A.E. Sporov.
Electromagnetic model of gas discharge in long tube of
slightly varying radius // Problems of Atomic Science
and Technology. Series «Plasma Physics» (25). 2018,
№ 6, p. 113-116.
6. A.N. Kondratenko. Surface and volume waves in
bounded plasma. Мoscow: “Energoatomizdat”, 1985.
7. G.G. Lister, T.R. Robinson. Strongly damped
surface waves in plasmas. I. The WKB approximation //
J. of Phys. D: Appl. Phys. 1991, v. 24, № 11, p. 1993-
1999.
ISSN 1562-6016. ВАНТ. 2020. №6(130) 73
8. M. Moisan, Z. Zakrzewski. Plasma sources based
on the propagation of electromagnetic surface waves //
J. of Phys. D: Appl. Phys. 1991, v. 24, № 7, p. 1025-
1048.
Article received 18.10.2020
ГАЗОВЫЙ РАЗРЯД В ПЛАЗМЕННО-МЕТАЛЛИЧЕСКОМ ВОЛНОВОДЕ С ИЗМЕНЯЮЩИМСЯ
РАДИУСОМ МЕТАЛЛИЧЕСКОЙ СТЕНКИ, ЧАСТИЧНО ЗАПОЛНЕННОМ РАДИАЛЬНО
НЕОДНОРОДНОЙ МАГНИТНО-АКТИВНОЙ ПЛАЗМОЙ
Н.А. Азаренков, В.П. Олефир, А.Е. Споров
Представлены результаты теоретического исследования фазовых свойств и пространственного затухания
симметричной электромагнитной волны в длинной волноводной плазменно-металлической структуре,
частично заполненной радиально-неоднородной плазмой, помещенной во внешнее аксиальное постоянное
магнитное поле. Представлены результаты теоретического исследования аксиального распределения
плотности плазмы в стационарном газовом разряде, поддерживаемом симметричной волной, в
рассматриваемой волноводной структуре, полученные в рамках электродинамической модели разряда.
Исследованы также влияния эффективной частоты столкновений электронов плазмы на фазовые свойства и
пространственное затухание волны, а также на аксиальное распределение плотности плазмы в газовых
разрядах, поддерживаемых этой волной, для различных радиальных профилей плотности плазмы.
ГАЗОВИЙ РОЗРЯД У ПЛАЗМОВО-МЕТАЛЕВОМУ ХВИЛЕВОДІ ЗІ ЗМІННИМ РАДІУСОМ
МЕТАЛЕВОЇ СТІНКИ, ЧАСТКОВО ЗАПОВНЕНОМУ РАДІАЛЬНО-НЕОДНОРІДНОЮ
МАГНІТНО-АКТИВНОЮ ПЛАЗМОЮ
М.О. Азарєнков, В.П. Олефір, О.Є. Споров
Представлено результати теоретичного дослідження фазових характеристик та просторового загасання
симетричної електромагнітної хвилі в довгій хвилеводній плазмово-металевій структурі, що частково
заповнена радіально-неоднорідною плазмою, яка знаходиться у зовнішньому аксіальному постійному
магнітному полі. В межах електродинамічної моделі стаціонарного газового розряду отримано аксіальний
розподіл густини плазми, що підтримується власною симетричною хвилею структури. Досліджено також
впливи ефективної частоти зіткнень електронів плазми на фазові характеристики та просторове загасання
хвилі, а також на аксіальний розподіл густини плазми в газових розрядах, що підтримуються нею, за різних
радіальних розподілів густини плазми.
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