Influence of collisions and plasma radial non‑uniformity on electromagnetic wave in coaxial structure with azimuth external magnetic field
This report is devoted to the investigation of dispersion properties, attenuation coefficient and radial wave field structure of high-frequency electromagnetic wave that propagates in coaxial magnetized waveguide structure with non-uniform azimuth magnetic field, partially filled by radial non-unifo...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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Olefir, V.P. Sporov, A.E. 2017-01-04T12:18:02Z 2017-01-04T12:18:02Z 2007 Influence of collisions and plasma radial non‑uniformity on electromagnetic wave in coaxial structure with azimuth external magnetic field / V.P. Olefir, A.E. Sporov // Вопросы атомной науки и техники. — 2007. — № 1. — С. 69-71. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.35.-g, 52.50.Dg https://nasplib.isofts.kiev.ua/handle/123456789/110413 This report is devoted to the investigation of dispersion properties, attenuation coefficient and radial wave field structure of high-frequency electromagnetic wave that propagates in coaxial magnetized waveguide structure with non-uniform azimuth magnetic field, partially filled by radial non-uniform collisional plasma. The influence of geometric parameters of waveguide structure, plasma non-uniformity, effective collision rate, direction and value of azimuth magnetic field on phase characteristics, attenuation coefficient and radial wave field structure of the considered wave is studied. It was shown that it is possible to control effectively the dispersion properties and spatial attenuation of the considered wave by varying the value and direction of external azimuth magnetic field. Досліджено дисперсійні властивості, коефіцієнт просторового загасання та радіальну структуру поля високочастотної електромагнітної хвилі, що розповсюджується в коаксіальній магнітоактивній хвилевідній структурі з радіально неоднорідним азимутальним магнітним полем, частково заповненою радіально неоднорідною плазмою із зіткненнями. Вивчено вплив геометричних параметрів хвилевідної структури, радіальній неоднорідності густини плазми, ефективної частоти зіткнень електронів, напрямку та величини постійного току на фазові характеристики, коефіцієнт просторового загасання та радіальну структуру поля досліджуваної хвилі. Показано можливість ефективного керування дисперсійними властивостями та коефіцієнтом просторового загасання зміною величини та напрямку постійного струму. Исследованы дисперсионные свойства, коэффициент пространственного затухания и радиальная структура поля высокочастотной электромагнитной волны, распространяющейся в коаксиальной волноводной структуре, частично заполненной радиально неоднородной столкновительной плазмой, которая находится в радиально неоднородном азимутальном магнитном поле. Изучено влияние геометрических параметров волноводной структуры, радиальной неоднородности плотности плазмы, эффективной частоты столкновений электронов, величины и направления постоянного тока на фазовые характеристики, коэффициент пространственного затухания и радиальную структуру поля рассматриваемой волны. Показана возможность эффективного управления дисперсионными свойствами и коэффициентом пространственного затухания путем изменения величины и направления постоянного тока. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Basic plasma physics Influence of collisions and plasma radial non‑uniformity on electromagnetic wave in coaxial structure with azimuth external magnetic field Вплив зіткнень та радіальної неоднорідності плазми на електромагнітні хвилі в коаксіальній структурі з зовнішнім азимутальним магнітним полем Влияние столкновений и радиальной неоднородности плазмы на электромагнитные волны в коаксиальной структуре с внешним азимутальным магнитным полем Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Influence of collisions and plasma radial non‑uniformity on electromagnetic wave in coaxial structure with azimuth external magnetic field |
| spellingShingle |
Influence of collisions and plasma radial non‑uniformity on electromagnetic wave in coaxial structure with azimuth external magnetic field Olefir, V.P. Sporov, A.E. Basic plasma physics |
| title_short |
Influence of collisions and plasma radial non‑uniformity on electromagnetic wave in coaxial structure with azimuth external magnetic field |
| title_full |
Influence of collisions and plasma radial non‑uniformity on electromagnetic wave in coaxial structure with azimuth external magnetic field |
| title_fullStr |
Influence of collisions and plasma radial non‑uniformity on electromagnetic wave in coaxial structure with azimuth external magnetic field |
| title_full_unstemmed |
Influence of collisions and plasma radial non‑uniformity on electromagnetic wave in coaxial structure with azimuth external magnetic field |
| title_sort |
influence of collisions and plasma radial non‑uniformity on electromagnetic wave in coaxial structure with azimuth external magnetic field |
| author |
Olefir, V.P. Sporov, A.E. |
| author_facet |
Olefir, V.P. Sporov, A.E. |
| topic |
Basic plasma physics |
| topic_facet |
Basic plasma physics |
| publishDate |
2007 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Вплив зіткнень та радіальної неоднорідності плазми на електромагнітні хвилі в коаксіальній структурі з зовнішнім азимутальним магнітним полем Влияние столкновений и радиальной неоднородности плазмы на электромагнитные волны в коаксиальной структуре с внешним азимутальным магнитным полем |
| description |
This report is devoted to the investigation of dispersion properties, attenuation coefficient and radial wave field structure of high-frequency electromagnetic wave that propagates in coaxial magnetized waveguide structure with non-uniform azimuth magnetic field, partially filled by radial non-uniform collisional plasma. The influence of geometric parameters of waveguide structure, plasma non-uniformity, effective collision rate, direction and value of azimuth magnetic field on phase characteristics, attenuation coefficient and radial wave field structure of the considered wave is studied. It was shown that it is possible to control effectively the dispersion properties and spatial attenuation of the considered wave by varying the value and direction of external azimuth magnetic field.
Досліджено дисперсійні властивості, коефіцієнт просторового загасання та радіальну структуру поля високочастотної електромагнітної хвилі, що розповсюджується в коаксіальній магнітоактивній хвилевідній структурі з радіально неоднорідним азимутальним магнітним полем, частково заповненою радіально неоднорідною плазмою із зіткненнями. Вивчено вплив геометричних параметрів хвилевідної структури, радіальній неоднорідності густини плазми, ефективної частоти зіткнень електронів, напрямку та величини постійного току на фазові характеристики, коефіцієнт просторового загасання та радіальну структуру поля досліджуваної хвилі. Показано можливість ефективного керування дисперсійними властивостями та коефіцієнтом просторового загасання зміною величини та напрямку постійного струму.
Исследованы дисперсионные свойства, коэффициент пространственного затухания и радиальная структура поля высокочастотной электромагнитной волны, распространяющейся в коаксиальной волноводной структуре, частично заполненной радиально неоднородной столкновительной плазмой, которая находится в радиально неоднородном азимутальном магнитном поле. Изучено влияние геометрических параметров волноводной структуры, радиальной неоднородности плотности плазмы, эффективной частоты столкновений электронов, величины и направления постоянного тока на фазовые характеристики, коэффициент пространственного затухания и радиальную структуру поля рассматриваемой волны. Показана возможность эффективного управления дисперсионными свойствами и коэффициентом пространственного затухания путем изменения величины и направления постоянного тока.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/110413 |
| citation_txt |
Influence of collisions and plasma radial non‑uniformity on electromagnetic wave in coaxial structure with azimuth external magnetic field / V.P. Olefir, A.E. Sporov // Вопросы атомной науки и техники. — 2007. — № 1. — С. 69-71. — Бібліогр.: 6 назв. — англ. |
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2025-11-25T20:29:31Z |
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2025-11-25T20:29:31Z |
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| fulltext |
Problems of Atomic Science and Technology. 2007, 1. Series: Plasma Physics (13), p. 69-71 69
INFLUENCE OF COLLISIONS AND PLASMA RADIAL
NON-UNIFORMITY ON ELECTROMAGNETIC WAVE IN
COAXIAL STRUCTURE WITH AZIMUTH EXTERNAL MAGNETIC FIELD
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: olefir@pht.univer.kharkov.ua
This report is devoted to the investigation of dispersion properties, attenuation coefficient and radial wave field
structure of high-frequency electromagnetic wave that propagates in coaxial magnetized waveguide structure with non-
uniform azimuth magnetic field, partially filled by radial non-uniform collisional plasma. The influence of geometric
parameters of waveguide structure, plasma non-uniformity, effective collision rate, direction and value of azimuth
magnetic field on phase characteristics, attenuation coefficient and radial wave field structure of the considered wave is
studied. It was shown that it is possible to control effectively the dispersion properties and spatial attenuation of the
considered wave by varying the value and direction of external azimuth magnetic field.
PACS: 52.35.-g, 52.50.Dg
1. INTRODUCTION
The study of eigen electromagnetic waves of plasma
filled metal waveguide structures is of a great importance
for plasma electronics, various plasma technologies, etc.
Among different types of plasma filled waveguide
structures it is possible to separate the cylindrical devices
with coaxial elements. The realized experimental study of
coaxial waveguide structures with 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
central conductor [1]. Properties of plasma maintained in
coaxial structure with dielectric rod inside have been
study in paper [2]. It is necessary to note that in spite of
perfect plasma parameters obtained in experimental
devices with coaxial structures, theoretical study of eigen
wave properties of coaxial waveguide structures and
efficiency of such structure use in various applications is
insufficient. This especially concerns the theoretical study
of plasma density, radial non–uniformity and electron
collision rate influence on the phase characteristics and
spatial attenuation of electromagnetic eigen waves of
coaxial structure with central metal conductor. These
circumstances greatly determine the urgency of
theoretical study of eigen wave properties of coaxial
structures.
2. TASK SETTING
Let us consider the axially–symmetric (azimuth
wavenumber 0=m ) high–frequency electromagnetic
wave that propagates in the cylindrical coaxial
magnetized waveguide structure, partially filled by radial
non–uniform dissipative plasma. Let suppose that the
wave propagates along z – axis of cylindrical coordinate
system ( r , ϕ , z ), which is directed along the axis of
waveguide structure The waveguide structure consists of
metal rod of radius 1R , which is placed at the axis of
plasma column. The direct current zJ flows along this
rod, creating radial non–uniform azimuth magnetic field
)(0 rH . This rod is enclosed by the cylindrical plasma
layer with radius 2R . The vacuum region ( 32 RrR << )
separates the cylindrical plasma layer from waveguide
metal wall with radius 3R . It was supposed, that plasma
density is radial non–uniform and possesses the bell–
shaped profile of the following form:
( ) ( ) ( )( )22
maxmax exp −−−= δµ rrrrnrn . (1)
Here, maxr – is the radius value where plasma density
culminates its maximum, parameters δr and µ
( 10 ≤≤ µ ) describes the width and the slope of the bell–
shaped profile, respectively. Plasma was considered in the
hydrodynamic approach as cold medium with collisions,
that were characterized by the effective collision rate ν .
This quantity is constant in the whole volume of
cylindrical plasma layer and is supposed to be small
( 1/ <ων , where ω is wave frequency).
From the system of Maxwell equations one can find,
that the electromagnetic field of considered axially
symmetric E –wave consists of only three components
zE , rE and ϕH . In the region of cylindrical plasma
layer ( 21 RrR << ) the equations that govern these
components of E –wave can be written in the form [3]:
−+
−
=
+−=
+=
ϕ
ϕ
ϕ
ϕ
ε
ε
ε
εε
ε
κ
ε
ε
ε
ε
ε
H
r
kEik
rd
Hd
H
k
iEk
rd
Ed
EiH
k
kE
z
p
z
z
zr
1
1
2
3
1
2
1
2
2
1
2
1
2
3
1
2
1
3
, (2)
where
( )
( ) ( )( )r
r
c
p
22
2
1 1
ωωω
ωω
ε
−′
′
−= ,
( ) ( )
( ) ( )( )r
rr
c
pc
22
2
2
ωωω
ωω
ε
−′
= ,
( )
ωω
ω
ε
′
−=
rp
2
3 1 , νωω i+=′ , ( )rpω and ( )rcω are
electron plasma and cyclotron frequencies, respectively,
( )rkkp 1
22
3
2 εκ −= , ck /ω= is the vacuum wavenumber,
3k is complex axial wavevector, real part of it determines
the wavenumber and imaginary part determined wave
attenuation coefficient.
mailto:olefir@pht.univer.kharkov.ua
70
It is necessary to mention, that in spite of low value of
effective electron collision frequency ( ων < ) it is
necessary to keep imaginary terms in the expressions for
components of permittivity tensor of magnetized plasma.
This imaginary terms give the possibility to carry out
numerical integration of the system (2) in the region
where the conditions of upper hybrid resonance may take
place [4].
In the cylindrical vacuum region ( 32 RrR << ) the
wave components ( )rEz , ( )rEr and ( )rHϕ can be
analytically expressed in terms of Bessel functions:
( ) ( )
( ) ( )( )
=
−−=
+=
ϕ
ϕ κκ
κκ
H
k
k
E
rKCrIC
k
kiH
rKCrICE
r
vv
v
vvz
3
1211
0201
, (3)
where 22
3
2 kkv −=κ , 1,0I , 1,0K are Bessel functions of
the first kind and second kind, 1C and 2C are the wave
field constants. The boundary conditions for ( )rEz and
( )rHϕ consisting in continuity of these quantities at
plasma-vacuum interface ( 2Rr = ) give the linear system
for the matching constants 1C and 2C .
The boundary condition for ( )rEz wave field
component at the waveguide metallic wall 3Rr =
consisting in the vanishing ( )3REz gives the dispersion
equation that can be written in the following form:
( ) ( ) 0302301 =+ RKCRIC vv κκ , (4)
The initial conditions for integration of the system of
ordinary differential equations (2) can be obtained from
the conditions at the inner conductive rod.
The obtained dispersion equation (4) is solved in
complex algebra. For this purpose the system of ordinary
differential equations was numerically solved with the
help of Badler and Deuflhard version of semi-implicit
extrapolation method [5]. This method gives the
possibility to obtain accurately numerical solution even in
the region where the conditions of upper hybrid resonance
take place. The dispersion equation (4) was solved with
the help of Muller method [5].
3. MAIN RESULTS
In the case when external current flows along the
propagation direction of the considered wave the
dispersion equation (4) possesses two solutions with
different values of frequency for the fixed value of
dimensionless wavenumber ( ) 13Re Rk . One of them with
comparatively more high frequency will be called further
high frequency (HF) wave, and other — low frequency
(LF) wave. Properties of these waves substantially
determined by the value and direction of direct current.
Thus, in the limiting case, when the azimuth magnetic
field ( )rH0 trends to zero the LF wave vanishes. The
increase of the direct current 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 ( 0.2)2/( 3 ≈= cmeJj ez ) the frequencies of HF and
LF waves for rather high ( ) 13Re Rk values are close.
The influence of parameter ων / value on the
dispersion and attenuation properties of HF and LW
waves was study for the case of radial uniform plasma
( 0=µ ). For rather small values of effective collision rate
( 1/ <ων ) the increase of ων / value leads to the
increase of the LF dimensionless frequency pωω / and
attenuation coefficient ( ) 13Im Rk . Dispersion and
attenuation properties of HF wave depend on the ων /
parameter much weaker. It is necessary to note that the
attenuation coefficient value of LF wave is approximately
of one order greater than the value of attenuation
coefficient of LF wave.
The influence of plasma density radial profile (non-
uniformity parameter µ value) on the dimensionless
frequency and attenuation coefficient for HF and LF wave
at fixed point of dispersion curve (for ( ) 01.0Re 13 =Rk ) is
shown on Fig. 1. Other external parameters were equal to
0.4/)( max11 == crRr pω , 0.5/)( max22 == crRr pω ,
0.6/)( max33 == crRr pω , 001.0/ =ων , 5.4max =r ,
1.0=δr , 0.2)2/( 3 == mceJj z . One can see that the
increase of non–uniformity parameter µ leads to the
increase of the dimensionless wave frequency of HF wave
and to the decrease of the dimensionless wave frequency
of LF wave. The wave attenuation coefficient shows more
complicated behaviour (Fig. 2). The calculations carried
out have shown that the spatial attenuation coefficient for
HF wave possesses the maximum in the range of rather
small µ values ( 2.0≈µ ). In contrast, the attenuation
coefficient for LF possesses the minimum for
approximately the same µ values. Such complicated
dependence may be very important for the determination
of the frequency range, where the considered wave can
maintain the stable discharge [6].
0,0 0,2 0,4 0,6 0,8 1,0
0,0004
0,0005
0,0006
0,0007
0,0017
0,0018
0,0019
0,0020
0,0021
0,0022
0,0023
0,0024
HF Wave
LF Wave
µ
ω / ω
p
Fig. 1. The dependence of dimensionless wave
frequency pωω / on the non–uniformity parameter µ for
the fixed point on the dispersion curve ( ( ) 01.0Re 13 =Rk )
71
0,0 0,2 0,4 0,6 0,8 1,0
0,0000
0,0001
0,0002
0,0003
0,0004
0,0055
0,0060
0,0065
0,0070
0,0075
0,0080
0,0085
0,0090
HF Wave
LF Wave
µ
Im(k3) R1
Fig. 2. The dependence of attenuation coefficient
( ) 13Im Rk on the non–uniformity parameter µ for the
fixed point on the dispersion curve ( ( ) 01.0Re 13 =Rk )
CONCLUSIONS
The influence of plasma density radial non–
uniformity, electron effective collision frequency,
direction and direct current value on phase characteristics,
attenuation coefficient and radial wave field structure of
the considered wave was studied. It was shown that it is
possible to control effectively the dispersion properties of
E –wave by varying the value and direction of direct
current. The influence of dimensionless collision rate on
the dispersion and attenuation properties of HF and LF
waves was studied as well. It was shown that LF wave
attenuates more effectively than HF wave. It was shown
also that in the case of bell–shaped radial plasma density
profile the increase of plasma density radial non–
uniformity results in the growth of wave frequency of HF
wave and in the decrease of wave frequency of LF wave.
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2. E. Rauchle. Duo-plasmaline, a surface wave
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Workshop on Micrmtave Discharges: Fundamentals and
Applications, Abbaye de Fomevraud, France, 1997.
3. Yu.A. Akimov, M.P. Azarenkov, V.P. Olefir,
A.E. Sporov //Problems of Atomic Science and
Technology. Ser.”Plasma Physics”(8). 2002, N5, p. 63.
4. N.A. Azarenkov, V.P. Olefir, A.E. Sporov. Gas
Discharge Sustained by Potential Surface Waves in
Magnetized Waveguide Structure Filled by Radially Non–
Uniform Plasma // 29th EPS Conference on Plasma Phys.
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B.P. Flannery, Numerical Recipes in C. The Art of
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edition, Cambridge, 1996.
6. Z. Zakrzewski // Journal of Physics D: Applied
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