Dipolar electromagnetic waves in coaxial structure filled by dissipative plasma with azimuth magnetic field
This report is devoted to the investigation of dispersion properties and spatial attenuation coefficient of the dipolar
 high-frequency electromagnetic wave that propagates along the coaxial magnetized waveguide structure with nonuniform
 azimuthal magnetic field, partially filled by...
Gespeichert in:
| Veröffentlicht in: | Вопросы атомной науки и техники |
|---|---|
| Datum: | 2009 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2009
|
| Schlagworte: | |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/88229 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Dipolar electromagnetic waves in coaxial structure filled by dissipative plasma with azimuth magnetic field / N.A. Azarenkov, V.P. Olefir, A.E. Sporov // Вопросы атомной науки и техники. — 2009. — № 1. — С. 77-79. — Бібліогр.: 7 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860245199514501120 |
|---|---|
| author | Azarenkov, N.A. Olefir, V.P. Sporov, A.E. |
| author_facet | Azarenkov, N.A. Olefir, V.P. Sporov, A.E. |
| citation_txt | Dipolar electromagnetic waves in coaxial structure filled by dissipative plasma with azimuth magnetic field / N.A. Azarenkov, V.P. Olefir, A.E. Sporov // Вопросы атомной науки и техники. — 2009. — № 1. — С. 77-79. — Бібліогр.: 7 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | This report is devoted to the investigation of dispersion properties and spatial attenuation coefficient of the dipolar
high-frequency electromagnetic wave that propagates along the coaxial magnetized waveguide structure with nonuniform
azimuthal magnetic field, partially filled by uniform collisional plasma. The influence of effective collision
frequency and the value of the direct current on the phase characteristics and the spatial attenuation coefficient of the
considered wave is studied. It was shown that it is possible to control effectively the dispersion properties and the
spatial attenuation of the considered wave by varying the value of the direct current.
Розглянуто дисперсійні властивості та коефіцієнт просторового загасання дипольної високочастотної хвилі,
що поширюється в коаксіальній магнітоактивній хвилеводній структурі з радіально неоднорідним
азимутальним магнітним полем, яка частково заповнена радіально однорідною плазмою з зіткненнями.
Досліджено вплив ефективної частоти зіткнень електронів та величини зовнішнього аксіального постійного
струму на фазові характеристики та коефіцієнт просторового загасання дипольної хвилі. Показана можливість
ефективного керування фазовими характеристиками та просторовим загасанням дипольної хвилі за допомогою
зовнішнього постійного струму.
Исследуются дисперсионные свойства и коэффициент пространственного затухания дипольной
высокочастотной электромагнитной волны, распространяющейся в коаксиальной магнитоактивной
волноводной структуре с радиально неоднородным азимутальным магнитным полем, частично заполненной
радиально однородной столкновительной плазмой. Изучено влияние эффективной частоты столкновений
электронов и величины внешнего аксиального постоянного тока на фазовые характеристики и коэффициент
пространственного затухания дипольной волны. Показана возможность эффективного управления фазовыми
характеристиками и коэффициентом пространственного затухания дипольной волны с помощью внешнего
постоянного тока.
|
| first_indexed | 2025-12-07T18:35:49Z |
| format | Article |
| fulltext |
DIPOLAR ELECTROMAGNETIC WAVES IN COAXIAL STRUCTURE
FILLED BY DISSIPATIVE PLASMA WITH AZIMUTH MAGNETIC FIELD
N.A. Azarenkov, V.P. Olefir, A.E. Sporov
V.N. Karazin Kharkov National University, Institute of High Technologies,
Department of Physics and Technology, Kharkov, Ukraine,
E-mail: vpolefir@gmail.com
This report is devoted to the investigation of dispersion properties and spatial attenuation coefficient of the dipolar
high-frequency electromagnetic wave that propagates along the coaxial magnetized waveguide structure with non-
uniform azimuthal magnetic field, partially filled by uniform collisional plasma. The influence of effective collision
frequency and the value of the direct current on the phase characteristics and the spatial attenuation coefficient of the
considered wave is studied. It was shown that it is possible to control effectively the dispersion properties and the
spatial attenuation of the considered wave by varying the value of the direct current.
PACS: 52.35g, 52.50.Dg
1. INTRODUCTION
Electrodynamic properties of coaxial plasma-metal
structures are the subject of intensive theoretical and
experimental studies at present time. Such structures are
widely used as the waveguide structures in the devices of
plasma electronics [1] and also as the discharge chambers
for gas discharge sustaining [2, 3]. The realized
experimental study of the coaxial waveguide structures
with a central metallic rod have shown that properties of
electromagnetic waves and gas discharge plasma
maintained by these waves, differ considerably from the
corresponding properties of cylindrical plasma – metal
waveguide structures without the central conductor [1, 4].
It is necessary to note that in spite of good plasma
parameters obtained in experimental devices with coaxial
structures, theoretical study of eigen waves properties of
coaxial waveguide structures and efficiency of such
structure usage in various applications is insufficient. This
especially relates to the theoretical study of propagation
and spatial attenuation of the electromagnetic eigen waves
with complex azimuthal wave field structure that propagate
along the coaxial structure with central metallic conductor
partially filled by dissipative plasma. These circumstances
greatly determine the urgency of presented work.
2. PROBLEM FORMULATION
Let’s consider a high–frequency electromagnetic wave
with azimuthal wavenumber 1=m that propagates in
cylindrical the coaxial magnetized waveguide structure,
partially filled by dissipative plasma. The waveguide
structure consists of the metallic rod of radius 1R , which
is placed at the axis of plasma column. The direct current
zJ flows along this rod, creating radially non–uniform
azimuthal magnetic field )(0 rH . This rod is surrounded
by the cylindrical plasma layer of radius 2R . The vacuum
region ( 32 RrR << ) separates the cylindrical plasma
layer from waveguide metallic wall with radius 3R . It
was assumed, that plasma density is radially uniform
(averaged over the plasma column cross-section) and
varies slightly along the plasma column. Such approach is
widely used for theoretical description of a gas discharge
sustained by the travelling surface waves [5, 6]. Plasma
was considered in the hydrodynamic approach as a cold
dissipative medium. The collisions were characterized by
the effective electron collisional frequency ν that is
constant in the whole volume of the cylindrical plasma
layer and is supposed to be small ( 1/ <ων , where ω is
wave frequency).
The permittivity tensor of magnetized plasma ε can
be written in the form [7]:
−
=
12
3
21
0
00
0
εε
ε
εε
i
i
ε , (1)
where
)]()[(
1
22
2
1 rc
p
ωωω
ωω
ε
−′
′
−= ,
)]()[(
)(
22
2
2 r
r
c
pc
ωωω
ωω
ε
−′
= ,
ωω
ω
ε
′
−=
2
3 1 p , νωω i+=′ , pω and )(rcω are electron
plasma and cyclotron frequencies, respectively.
Propagation of electromagnetic wave in the
waveguide structure is governed by the system of
Maxwell’s equations. In the case considered the solution
of the system of Maxwell’s equation in cylindrical
coordinate system ( r , ϕ , z ) (let assume that z – axis is
directed along the axis of waveguide structure) can be
found in the form:
( )][exp)(),(, 3 tmzkirHrEHE ωϕ −+= , (2)
where 3k is the complex axial wavevector, real part of it
determines the wavenumber and imaginary part
determines the wave spatial attenuation coefficient.
Taking into account (2) from the system of Maxwell’s
equations one can find, that in the region of cylindrical
plasma layer the ordinary differential equations that
govern the dipolar wave components can be written in the
following form:
+−=
−−−=
−++−=
+−+−=
z
z
zz
z
zz
zz
ECEC
dr
dH
HCEkHC
dr
dE
HCECHCEC
dr
dH
HCECHC
r
E
dr
dE
718
7
1
2
36
25411
321
ε
ε
ε
ε
ϕ
ϕ
ϕϕ
ϕ
ϕ
ϕϕ
, (3)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2009. № 1. 77
Series: Plasma Physics (15), p. 77-79.
where
1
3
1 εk
k
r
miC = ,
1
2
2 ε
ε
r
mC = ,
−=
1
2
2
3
1
εkr
mkiC ,
r
kC 1
1
2
34 −=
ε
ε
,
−+=
1
2
1
2
22
2
2
5 ε
εεk
r
m
k
iC ,
1
3
7 εk
k
r
miC = ,
( )1
22
3
1
6 ε
ε
kk
k
iC −= , ( )3
22
38 εkk
k
iC −= and ck /ω= is
the vacuum wavenumber. In the case considered this
system for arbitrary external parameters can be solved
only with the help of numerical methods.
In the cylindrical vacuum region the system of
Maxwell equations possesses the analytical solutions
expressed in the terms of modified Bessel functions.
These solutions contains the wave field constants, that can
be obtained with the help of boundary conditions
consisting in continuity of the tangential wave field
components at the plasma – vacuum interface. From such
conditions these constants can be written in the form:
++−=
−−=
−+=
+−−=
)()()(
)()()(
)()()(
)()()(
2
4
2
6
2
5
4
2
1
2
3
2
2
3
2
6
2
5
2
4
2
2
3
2
2
2
1
1
RHAREAREAA
RHAREAREiAA
RHARHAREAA
RHARHAREAA
p
z
pp
z
p
z
pp
z
pp
z
p
z
pp
z
p
z
ϕ
ϕ
ϕ
ϕ
, (4)
where )( 2
'
2
1 RKRA vmv κκ= ,
k
RKmkiA vm )( 232 κ= ,
k
RKRiA vmv )( 22
2
3 κκ= ,
k
RImkiA vm )( 235 κ= ,
)( 2
'
2
4 RIRA vmv κκ= ,
k
RIRiA vmv )( 22
2
6 κκ= , 22
3
2 kkv −=κ ,
prime denotes the derivative with respect to argument and
)( 2RE p
z , )( 2RH p
z , )( 2RE p
ϕ , )( 2RH p
ϕ are the wave fields
at the plasma – vacuum interface, obtained by the
numerical integration of the system of ordinary
differential equations (3).
The boundary conditions for )(rEz and )(rEϕ wave
field components at the waveguide metallic wall 3Rr =
gives the dispersion equation that can be written in the
following form:
=+
=+
0)()(
0)()(
3
'
43
'
3
3231
RKARIA
RKARIA
vmvm
vmvm
κκ
κκ
, (5)
3. RESULTS AND DISCUSSION
It is necessary to mention that, in the case when the
external current flows along the propagation direction of
the wave considered the dispersion equation (5) possesses
two solutions with different frequency values for the fixed
value of the dimensionless wavenumber 13)Re( Rk . One
of them with comparatively higher frequency will be
called further high frequency (HF) wave, and other – low
frequency (LF) wave.
Properties of these waves are substantially determined
by the direct current value. The influence of the direct
current value on the LF and HF dispersion properties is
shown on the Fig. 1. The dimensionless parameters
pωωµ /= and 13)Re( Rkx = were used to represent the
obtained results. The increase of the direct current value
leads to the decrease of the HF wave frequency and to the
increase of the LF wave frequency. So, for rather high
dimensionless direct current value ( 5.1)2/( 3 >= mceJj z )
the frequencies of HF and LF waves for rather high
13)Re( Rk values are close. In the limiting case, when the
azimuthal magnetic field )(0 rH trends to zero the LF
wave vanishes.
Fig. 1. The dependence of the wave frequency µ on the
wavenumber x for the LF and HF waves. Numbers on
the curve corresponds to different j values: 1 – 1.0=j ,
2 – 3.0=j , 3 – 5.0=j , 4 – 0.1=j , 5 – 5.1=j . Other
parameters are equal: 0.4/1 =cR pω , 0.5/2 =cR pω ,
0.6/3 =cR pω , 001.0/ =ων
The influence of the effective electron collisional
frequency ν on the LF and HF spatial attenuation is
shown on the Fig. 2. The dimensionless parameter
13)Im( Rk=α was used to represent the obtained results.
It was obtained that the increase of j value leads to the
increase of attenuation coefficient α of HF wave and to
the decrease of attenuation coefficient of LF wave. For
rather low direct current values ( 1.0<j ) the LF wave
strongly damps and therefore cannot propagate. It is
necessary to mention that the attenuation coefficient α
for the HF and LW waves has different behaviour in the
areas of rather high and rather low wavenumbers
13)Re( Rk . When 13)Re( Rk is rather low ( 3.0)Re( 13 <Rk
for HF wave and 5.0)Re( 13 <Rk for LF wave) the
attenuation coefficient decrease with the increase of
13)Re( Rk . In the next region the attenuation coefficient
increases with the increase of 13)Re( Rk value. Such
complicated behaviour may be very important for the
determination of the frequency range, where the
considered wave can maintain the stable discharge [6].
The influence of the effective collisional frequency
value on the dispersion and attenuation properties of the
HF and LW waves was also studied. Dispersion of the HF
and LF waves depends on ων / parameter rather weakly.
The increase of ων / value leads to the increase of the
78
attenuation coefficient α for the HF and LF waves. It is
necessary to note that the value of the attenuation
coefficient of the LF wave for the small ων / values (
001.0/ <ων ) is approximately of one order greater than
the value of attenuation coefficient of the HF wave. For
rather high ων / values ( 01.0/ ≈ων ) the attenuation
coefficients for the LF and HF waves are of one order. It
was obtained that the HF and LF waves in the region of
moderate ( ) 13Re Rk values ( ( ) 4Re5.0 13 << Rk ) have
rather small attenuation coefficient value. In other region
the value of the attenuation coefficient for both waves are
rather large.
Fig. 2. The dependence of the attenuation coefficient α
on the wavenumber x for the LF and HF waves. Problem
parameters are the same as for the Fig. 1
4. CONCLUSIONS
It was studied the influence of the effective collision
frequency and the value of the direct current on the phase
characteristics and the attenuation coefficient of the
electromagnetic dipolar wave that propagates along the
coaxial waveguide structure. It was shown that it is
possible to control effectively the dispersion properties
and the spatial attenuation of the dipolar wave by varying
the value of the direct current. The influence of the
dimensionless collision frequency on the dispersion and
attenuation properties of the HF and LF waves was study
as well. It was shown that the LF dipolar wave attenuates
more effectively than the HF wave.
REFERENCES
1.P.I. Markov, I.N. Onishchenko, G.V. Sotnikov //
Problems of Atomic Science and Technology. Series
“Plasma Physics” (8). 2002, v. 5, p. 86.
2.A. Schulz, M. Walter, J. Feichtinger, E. Räuchle and U.
Schumacher // International Workshop on Microwave
Discharges: Fundamentals and Applications, Greifswald,
Germany, 2003, p. 231.
3.O. Leroy, P. Leprince, C. Boisse-Laporte //
International Workshop on Microwave Discharges:
Fundamentals and Applications, Zvenigorod, Russia.
2006, p.137.
4.A.N. Kondratenko, V.M.Kuklin. Osnovy Plasmennoy
Elektroniki. Moscow: “Energoatomizdat”, 1988.
5.I. Zhelyazkov, V. Atanassov // Physics Reports. 1995,
v. 255, p. 79.
6.Z. Zakrzewski // Journal of Physics D: Applied
Physics. 1983, v. 16, p. 171.
7.V.P. Olefir, A.E. Sporov // Problems of Atomic Science
and Technology. Series “Plasma Phisics” (13) 2007, N1,
p. 69.
Article received 22.09.08
Revised version 1.10.08
ДИПОЛЬНЫЕ ЭЛЕКТРОМАГНИТНЫЕ ВОЛНЫ В КОАКСИАЛЬНОЙ СТРУКТУРЕ,
ЗАПОЛНЕННОЙ ДИССИПАТИВНОЙ ПЛАЗМОЙ С АЗИМУТАЛЬНЫМ МАГНИТЫМ ПОЛЕМ
Н.А. Азаренков, В.П. Олефир, А.Е. Споров
Исследуются дисперсионные свойства и коэффициент пространственного затухания дипольной
высокочастотной электромагнитной волны, распространяющейся в коаксиальной магнитоактивной
волноводной структуре с радиально неоднородным азимутальным магнитным полем, частично заполненной
радиально однородной столкновительной плазмой. Изучено влияние эффективной частоты столкновений
электронов и величины внешнего аксиального постоянного тока на фазовые характеристики и коэффициент
пространственного затухания дипольной волны. Показана возможность эффективного управления фазовыми
характеристиками и коэффициентом пространственного затухания дипольной волны с помощью внешнего
постоянного тока.
ДИПОЛЬНІ ЕЛЕКТРОМАГНІТНІ ХВИЛІ В КОАКСІАЛЬНІЙ СТРУКТУРІ,
ЩО ЗАПОВНЕНА ДИСИПАТИВНОЮ ПЛАЗМОЮ З АЗИМУТАЛЬНИМ МАГНІТНИМ ПОЛЕМ
М.О. Азарєнков, В.П. Олефір, О.Є. Споров
Розглянуто дисперсійні властивості та коефіцієнт просторового загасання дипольної високочастотної хвилі,
що поширюється в коаксіальній магнітоактивній хвилеводній структурі з радіально неоднорідним
азимутальним магнітним полем, яка частково заповнена радіально однорідною плазмою з зіткненнями.
Досліджено вплив ефективної частоти зіткнень електронів та величини зовнішнього аксіального постійного
струму на фазові характеристики та коефіцієнт просторового загасання дипольної хвилі. Показана можливість
ефективного керування фазовими характеристиками та просторовим загасанням дипольної хвилі за допомогою
зовнішнього постійного струму.
79
REFERENCES
|
| id | nasplib_isofts_kiev_ua-123456789-88229 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:35:49Z |
| publishDate | 2009 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Azarenkov, N.A. Olefir, V.P. Sporov, A.E. 2015-11-10T21:06:57Z 2015-11-10T21:06:57Z 2009 Dipolar electromagnetic waves in coaxial structure filled by dissipative plasma with azimuth magnetic field / N.A. Azarenkov, V.P. Olefir, A.E. Sporov // Вопросы атомной науки и техники. — 2009. — № 1. — С. 77-79. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.35g, 52.50.Dg https://nasplib.isofts.kiev.ua/handle/123456789/88229 This report is devoted to the investigation of dispersion properties and spatial attenuation coefficient of the dipolar
 high-frequency electromagnetic wave that propagates along the coaxial magnetized waveguide structure with nonuniform
 azimuthal magnetic field, partially filled by uniform collisional plasma. The influence of effective collision
 frequency and the value of the direct current on the phase characteristics and the spatial attenuation coefficient of the
 considered wave is studied. It was shown that it is possible to control effectively the dispersion properties and the
 spatial attenuation of the considered wave by varying the value of the direct current. Розглянуто дисперсійні властивості та коефіцієнт просторового загасання дипольної високочастотної хвилі,
 що поширюється в коаксіальній магнітоактивній хвилеводній структурі з радіально неоднорідним
 азимутальним магнітним полем, яка частково заповнена радіально однорідною плазмою з зіткненнями.
 Досліджено вплив ефективної частоти зіткнень електронів та величини зовнішнього аксіального постійного
 струму на фазові характеристики та коефіцієнт просторового загасання дипольної хвилі. Показана можливість
 ефективного керування фазовими характеристиками та просторовим загасанням дипольної хвилі за допомогою
 зовнішнього постійного струму. Исследуются дисперсионные свойства и коэффициент пространственного затухания дипольной
 высокочастотной электромагнитной волны, распространяющейся в коаксиальной магнитоактивной
 волноводной структуре с радиально неоднородным азимутальным магнитным полем, частично заполненной
 радиально однородной столкновительной плазмой. Изучено влияние эффективной частоты столкновений
 электронов и величины внешнего аксиального постоянного тока на фазовые характеристики и коэффициент
 пространственного затухания дипольной волны. Показана возможность эффективного управления фазовыми
 характеристиками и коэффициентом пространственного затухания дипольной волны с помощью внешнего
 постоянного тока. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Фундаментальная физика плазмы Dipolar electromagnetic waves in coaxial structure filled by dissipative plasma with azimuth magnetic field Дипольні електромагнітні хвилі в коаксіальній структурі, що заповнена дисипативною плазмою з азимутальним магнітним полем Дипольные электромагнитные волны в коаксиальной структуре, заполненной диссипативной плазмой с азимутальным магнитым полем Article published earlier |
| spellingShingle | Dipolar electromagnetic waves in coaxial structure filled by dissipative plasma with azimuth magnetic field Azarenkov, N.A. Olefir, V.P. Sporov, A.E. Фундаментальная физика плазмы |
| title | Dipolar electromagnetic waves in coaxial structure filled by dissipative plasma with azimuth magnetic field |
| title_alt | Дипольні електромагнітні хвилі в коаксіальній структурі, що заповнена дисипативною плазмою з азимутальним магнітним полем Дипольные электромагнитные волны в коаксиальной структуре, заполненной диссипативной плазмой с азимутальным магнитым полем |
| title_full | Dipolar electromagnetic waves in coaxial structure filled by dissipative plasma with azimuth magnetic field |
| title_fullStr | Dipolar electromagnetic waves in coaxial structure filled by dissipative plasma with azimuth magnetic field |
| title_full_unstemmed | Dipolar electromagnetic waves in coaxial structure filled by dissipative plasma with azimuth magnetic field |
| title_short | Dipolar electromagnetic waves in coaxial structure filled by dissipative plasma with azimuth magnetic field |
| title_sort | dipolar electromagnetic waves in coaxial structure filled by dissipative plasma with azimuth magnetic field |
| topic | Фундаментальная физика плазмы |
| topic_facet | Фундаментальная физика плазмы |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/88229 |
| work_keys_str_mv | AT azarenkovna dipolarelectromagneticwavesincoaxialstructurefilledbydissipativeplasmawithazimuthmagneticfield AT olefirvp dipolarelectromagneticwavesincoaxialstructurefilledbydissipativeplasmawithazimuthmagneticfield AT sporovae dipolarelectromagneticwavesincoaxialstructurefilledbydissipativeplasmawithazimuthmagneticfield AT azarenkovna dipolʹníelektromagnítníhvilívkoaksíalʹníistrukturíŝozapovnenadisipativnoûplazmoûzazimutalʹnimmagnítnimpolem AT olefirvp dipolʹníelektromagnítníhvilívkoaksíalʹníistrukturíŝozapovnenadisipativnoûplazmoûzazimutalʹnimmagnítnimpolem AT sporovae dipolʹníelektromagnítníhvilívkoaksíalʹníistrukturíŝozapovnenadisipativnoûplazmoûzazimutalʹnimmagnítnimpolem AT azarenkovna dipolʹnyeélektromagnitnyevolnyvkoaksialʹnoistrukturezapolnennoidissipativnoiplazmoisazimutalʹnymmagnitympolem AT olefirvp dipolʹnyeélektromagnitnyevolnyvkoaksialʹnoistrukturezapolnennoidissipativnoiplazmoisazimutalʹnymmagnitympolem AT sporovae dipolʹnyeélektromagnitnyevolnyvkoaksialʹnoistrukturezapolnennoidissipativnoiplazmoisazimutalʹnymmagnitympolem |