Electromagnetic dipolar wave in magnetized non-uniform plasma column
It has been carried out theoretical study of phase characteristics, attenuation coefficient and wave field radial structure of the dipolar high frequency electromagnetic wave that propagates along the waveguide structure that consists of a slightly collisional non-uniform magnetized plasma column, e...
Збережено в:
| Опубліковано в: : | Вопросы атомной науки и техники |
|---|---|
| Дата: | 2005 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
|
| Теми: | |
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/78648 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Electromagnetic dipolar wave in magnetized non-uniform plasma column / V.P. Olefir, A.E. Sporov // Вопросы атомной науки и техники. — 2005. — № 1. — С. 72-74. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-78648 |
|---|---|
| record_format |
dspace |
| spelling |
Olefir, V.P. Sporov, A.E. 2015-03-19T17:09:32Z 2015-03-19T17:09:32Z 2005 Electromagnetic dipolar wave in magnetized non-uniform plasma column / V.P. Olefir, A.E. Sporov // Вопросы атомной науки и техники. — 2005. — № 1. — С. 72-74. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.35.Hr, 52.80.Pi https://nasplib.isofts.kiev.ua/handle/123456789/78648 It has been carried out theoretical study of phase characteristics, attenuation coefficient and wave field radial structure of the dipolar high frequency electromagnetic wave that propagates along the waveguide structure that consists of a slightly collisional non-uniform magnetized plasma column, enclosed by dielectric tube that is surrounded by vacuum and placed within a cylindrical metal waveguide. External steady magnetic field is directed along the axis of the waveguide system. The axial electron density distribution of gas discharge maintained by the wave considered in the diffusion controlled regime was studied as well. Проведено теоретичне дослідження фазових характеристик, коефіцієнта просторового загасання та радіальної структури поля дипольної електромагнітної хвилі, що розповсюджується вздовж структури, яка складається з неоднорідної магнітоактивної плазми з малою частотою зіткнень електронів, обмеженої діелектричною трубкою, оточеною вакуумом та розташованою всередині циліндричного металевого хвилеводу. Зовнішнє магнітне поле спрямоване вздовж осі структури. Досліджено також аксіальний розподіл густини плазми в розряді, що підтримується дипольною хвилею та протікає в дифузійному режимі. Проведено теоретическое исследование фазовых характеристик, коэффициента пространственного затухания и радиальной структуры поля дипольной электромагнитной волны, распространяющейся вдоль структуры, состоящей из слабостолкновительной неоднородной магнитоактивной плазмы, ограниченной диэлектрической трубкой, окруженной вакуумом и помещенной внутрь цилиндрического металлического волновода. Внешнее магнитное поле направлено вдоль оси структуры. Исследовано также аксиальное распределение плотности плазмы в разряде, поддерживаемом дипольной волной и протекающем в диффузионном режиме. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Basic plasma physics Electromagnetic dipolar wave in magnetized non-uniform plasma column Електромагнитна дипольна хвиля в магнітоактивному неоднорідному стовпі плазми Электромагнитная дипольная волна в магнитоактивном неоднородном столбе плазмы Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Electromagnetic dipolar wave in magnetized non-uniform plasma column |
| spellingShingle |
Electromagnetic dipolar wave in magnetized non-uniform plasma column Olefir, V.P. Sporov, A.E. Basic plasma physics |
| title_short |
Electromagnetic dipolar wave in magnetized non-uniform plasma column |
| title_full |
Electromagnetic dipolar wave in magnetized non-uniform plasma column |
| title_fullStr |
Electromagnetic dipolar wave in magnetized non-uniform plasma column |
| title_full_unstemmed |
Electromagnetic dipolar wave in magnetized non-uniform plasma column |
| title_sort |
electromagnetic dipolar wave in magnetized non-uniform plasma column |
| 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 |
2005 |
| language |
English |
| container_title |
Вопросы атомной науки и техники |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| format |
Article |
| title_alt |
Електромагнитна дипольна хвиля в магнітоактивному неоднорідному стовпі плазми Электромагнитная дипольная волна в магнитоактивном неоднородном столбе плазмы |
| description |
It has been carried out theoretical study of phase characteristics, attenuation coefficient and wave field radial structure of the dipolar high frequency electromagnetic wave that propagates along the waveguide structure that consists of a slightly collisional non-uniform magnetized plasma column, enclosed by dielectric tube that is surrounded by vacuum and placed within a cylindrical metal waveguide. External steady magnetic field is directed along the axis of the waveguide system. The axial electron density distribution of gas discharge maintained by the wave considered in the diffusion controlled regime was studied as well.
Проведено теоретичне дослідження фазових характеристик, коефіцієнта просторового загасання та радіальної структури поля дипольної електромагнітної хвилі, що розповсюджується вздовж структури, яка складається з неоднорідної магнітоактивної плазми з малою частотою зіткнень електронів, обмеженої діелектричною трубкою, оточеною вакуумом та розташованою всередині циліндричного металевого хвилеводу. Зовнішнє магнітне поле спрямоване вздовж осі структури. Досліджено також аксіальний розподіл густини плазми в розряді, що підтримується дипольною хвилею та протікає в дифузійному режимі.
Проведено теоретическое исследование фазовых характеристик, коэффициента пространственного затухания и радиальной структуры поля дипольной электромагнитной волны, распространяющейся вдоль структуры, состоящей из слабостолкновительной неоднородной магнитоактивной плазмы, ограниченной диэлектрической трубкой, окруженной вакуумом и помещенной внутрь цилиндрического металлического волновода. Внешнее магнитное поле направлено вдоль оси структуры. Исследовано также аксиальное распределение плотности плазмы в разряде, поддерживаемом дипольной волной и протекающем в диффузионном режиме.
|
| issn |
1562-6016 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/78648 |
| citation_txt |
Electromagnetic dipolar wave in magnetized non-uniform plasma column / V.P. Olefir, A.E. Sporov // Вопросы атомной науки и техники. — 2005. — № 1. — С. 72-74. — Бібліогр.: 6 назв. — англ. |
| work_keys_str_mv |
AT olefirvp electromagneticdipolarwaveinmagnetizednonuniformplasmacolumn AT sporovae electromagneticdipolarwaveinmagnetizednonuniformplasmacolumn AT olefirvp elektromagnitnadipolʹnahvilâvmagnítoaktivnomuneodnorídnomustovpíplazmi AT sporovae elektromagnitnadipolʹnahvilâvmagnítoaktivnomuneodnorídnomustovpíplazmi AT olefirvp élektromagnitnaâdipolʹnaâvolnavmagnitoaktivnomneodnorodnomstolbeplazmy AT sporovae élektromagnitnaâdipolʹnaâvolnavmagnitoaktivnomneodnorodnomstolbeplazmy |
| first_indexed |
2025-11-26T14:04:34Z |
| last_indexed |
2025-11-26T14:04:34Z |
| _version_ |
1850624278461939712 |
| fulltext |
ELECTROMAGNETIC DIPOLAR WAVE
IN MAGNETIZED NON-UNIFORM PLASMA COLUMN
V.P. Olefir, A.E. Sporov
Kharkiv National University, Institute of High Technologies,
Department of Physics and Technology, Kurchatov av. 31, 61108 Kharkiv, Ukraine,
E-mail: olefir@pht.univer.kharkov.ua; Fax: (057)3353977; Tel: (057)3351563
It has been carried out theoretical study of phase characteristics, attenuation coefficient and wave field radial
structure of the dipolar high frequency electromagnetic wave that propagates along the waveguide structure that consists
of a slightly collisional non-uniform magnetized plasma column, enclosed by dielectric tube that is surrounded by
vacuum and placed within a cylindrical metal waveguide. External steady magnetic field is directed along the axis of
the waveguide system. The axial electron density distribution of gas discharge maintained by the wave considered in the
diffusion controlled regime was studied as well.
PACS: 52.35.Hr, 52.80.Pi
1. INTRODUCTION
The intensive theoretical and experimental studies of
gas discharges sustained by high-frequency travelling
surface wave (SW) are stipulated by their wide practical
using in numerous technological applications [1]. The SW
that sustains the discharge is the eigen wave of discharge
structure. This is the characteristic feature of such
discharges and leads to the strong influence of the SW
properties on the axial distribution of discharge
parameters. In real discharge systems plasma density is
always non-uniform in radial direction and the conditions
of upper hybrid resonance may take place at the periphery
of plasma column [2]. The efficiency of energy transfer
from SW into gas discharge plasma can be increased
substantially in such regions, where electromagnetic
waves transform into plasma waves [3]. This process can
affects greatly the plasma density axial structure in SW
sustained gas discharges. The main aim of this report is to
determine the influence of plasma density radial profile
on the SW properties and on the plasma density axial
structure in the discharges sustained by the dipolar SW in
diffusion controlled regime.
2. THEORETICAL FORMULATION
The SW considered propagates in magnetized
waveguide structure that consists of radially non-uniform
plasma column with radius R p enclosed by dielectric
tube with thickness Δ that is surrounded by vacuum and
placed within a cylindrical metal waveguide with radius
Rm . External steady magnetic field B0 is directed
along the axis of the waveguide structure. Plasma is
considered in hydrodynamic approximation as cold and
slightly absorbing medium with constant effective
electron-neutral collision frequency ν in the discharge
volume. In the considered case this frequency is much
less than SW generator frequency ω . Plasma density
radial profile n r was chosen in Bessel–like form
given by n r =n 0 J 0 μ r R p
−−1 , where J 0 is
the Bessel function and μ is the parameter, which
characterizes the plasma density non-uniformity. This
non-uniformity parameter μ can varies from μ=0
(radially uniform profile) to μ=2 . 405 (perfect
ambipolar diffusion profile). The SW propagation is
governed by the system of Maxwell equations. This wave
possesses all six components of electromagnetic field. For
arbitrary discharge parameters (plasma density radial
profile, external magnetic field value, geometrical
parameters of discharge structure) in the case when
waveguide is filled by radially non-uniform magnetized
plasma this system can be solved only with the help of
numerical methods. In the case considered, when plasma
density, SW wavelength and it’s amplitude vary slightly
along the discharge column at the distances of the wave
length order, the solution of the system of Maxwell
equations in cylindrical coordinate system r ,ϕ , z for
SW field components E , H can be found in WKB
form:
E , H r ,ϕ , z , t =E , H r expi [∫z0
z
k 3 z
' d z '−ω t ]
, (1)
where k3 is SW axial wavenumber.
Applying expression (1) to the system considered one
can reduce it into the system of four ordinary differential
equations for the tangential SW components in plasma
column ( 0rR p ). In spite of the low value of
collision frequency ν << ω it is necessary to keep
imaginary addends in the expressions of the permittivity
tensor ε1,2,3 of magnetized plasma. These imaginary
addends give the possibility to carry out the numerical
integration of the system of ordinary differential
equations in the region when upper hybrid resonance
occurs. In dielectric and vacuum regions the system of
Maxwell equations can be solved analytically and one can
obtain the expressions for tangential wave field
components [4]. The local dispersion equation can be
obtained by applying the conditions of continuity of the
tangential field components at the plasma-glass tube and
glass tube-vacuum region interfaces. The condition of
vanishing of the SW electric field at the waveguide
metallic wall is also applied.
Therefore, the complex local dispersion equation is
obtained, the real part of its complex solution for
72 Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 72-74
wavenumber gives wavelength and imaginary part gives
SW attenuation coefficient. To solve the dispersion
equation one must firstly solve the system of ordinary
differential equations under the fixed values of k3 and
ω . Then, one solve the local dispersion equation and
find the eigen value of k3 or ω .
In the case considered it is possible to obtain axial
electron density variation as an intricate function of
attenuation coefficient. The axial profile of dimensionless
density N=ω pe
2 ω−2 can be theoretically determined
from the energy balance equation of gas discharge
stationary state in diffusion controlled regime [1]. When
mean power that maintains an electron in the discharge
and electron effective collision frequency for momentum
transfer ν are constant in discharge volume, one can
obtain equation that governs plasma density axial
distribution in the form:
d N
d ξ
=− 2Nα
νω−11 −dα /dN Nα−1
, (2)
where α=Im k3 R p is the dimensionless attenuation
coefficient and ξ=νz ωR p
−1 is the dimensionless
axial coordinate [1].
It is necessary to mention that the SW can maintain
the stable discharge in diffusion regime only at the
regions in the phase diagrams where the Zakrzewski’s
stability condition is fulfilled. In dimensionless variables
this condition can be written as [1, 5]:
d
dN
∣α∣
N
0 . (3)
3. DISCUSSION
To determine axial distribution of plasma density in
gas discharge it is necessary firstly to find the phase
properties and attenuation coefficient of the wave. Unlike
the usual dispersion equation connecting wave frequency
and wave length under the fixed value of plasma density,
the local dispersion equation in the considered case,
(when wave frequency is fixed and is determined by the
generator's frequency ω ), connects local value of
plasma density and wavelength. Some results of
numerical solution of the local dispersion equation for
different external discharge parameters are presented in
the Fig. 1-4. The calculations were carried out for the
dimensionless parameters =ωc ω−1 ,
σ=R pωc−1 , δ=ΔR p
−1 , η=Rm R p
−1 and
ν=νω−1 (where ωc is electron cyclotron frequency
and c is light velocity in vacuum).
Fig. 1, 2 present the influence of the vacuum gap
thickness on the SW properties. The numerical
calculations have shown that at a fixed wavelength the
decrease of the vacuum gap thickness leads to the
decrease the wave phase velocity (Fig. 1) and to the
increase of its attenuation coefficient α (Fig. 2), as in
the case of symmetric waves. It is necessary to mention
the fact that at some value of parameter η the SW
attenuation coefficient increases sharply (curves
corresponds to η=1 . 7 ÷1 . 74 at Fig. 2), but the
wavenumber remains finite. Thus, variation of the
parameter η value strongly affects the region on phase
diagrams where SW can maintain the stable discharge in
diffusion controlled regime. At all figures the boundaries
of the stable regions on phase and attenuation diagrams
are marked by circles (left boundary) and triangles (right
boundary). The existence on the same phase curve the
regions with two opposite slopes leads to the strong
restriction of the stable discharge region (compare the
curves corresponds to η=1 . 5, 1 . 6 and
η=1 . 7 ÷1 . 74 on Figs. 1, 2).
0 1 2 3 4 5
0.26
0.28
0.30
0.32
0.34
0.36
0.38
0.40
1.74
1.73
1.72
1.7
1.6
1.5
ωω-1
p
Re(k
3
)R
p
Fig. 1. The dependence of the SW phase properties on the
value of the vacuum gap thickness for radially uniform
plasma. Numbers at the curves correspond to the
parameter η value. Other dimensionless parameters are
equal to ν=0 . 001 , εd=4 . 5 , =0 . 2 ,
σ=0 .3 , δ=0 .3 and m=−1
0 1 2 3 4 5
0.0
0.1
0.2
0.3
0.4
0.5
Re(k
3
)R
p
Im(k
3
)R
p
1.74
1.73
1.72
1.7
1.6
1.5
Fig. 2. The dependence of the SW attenuation coefficient
α on the value of the vacuum gap thickness for radially
uniform plasma. The parameters are the same as in Fig. 1
The increase of dimensionless plasma column radius
σ (when σ1 ) leads to the decrease of SW phase
velocity and SW attenuation coefficient. The analysis has
shown that one can mark out the regions with two
different SW behavior. When parameter σ is rather
small ( σσ cr ) the dispersion equation possesses the
solutions with Re k 3R p=0 . When σσ cr there is
a region on the phase curve at small Re k 3R p values
where SW cannot exist.
In real conditions the dimensions of discharge vessel
are fixed and they are determined by the diameter of
dielectric and metal tubes, where the discharge occurs.
73
So, it is possible to control discharge parameters due to
variation of an external magnetic field value. The
dependence of the phase and attenuation properties of the
wave on the several values of dimensionless magnetic
field value are given in Fig. 3, 4. The study has
shown that the increase of the parameter results in
the retardation of the wave in the region of small
Re k 3R p values and acceleration of SW in the region
of large Re k 3R p (Fig. 3). The SW attenuation
coefficient grows with the increase of the parameter
value (Fig. 4).
0 1 2 3 4 5
0.2
0.3
0.4
0.5
0.6
0.7
2.0
1.5
0.9
0.6
0.2
Re(k
3
R
p
)
ωω-1
p
Fig. 3. The dependence of the SW phase properties on the
external magnetic field value for radially uniform plasma.
Numbers at the curves corresponds to the parameter
value. Other parameters are equal to δ=0 .3 ,
η=1 . 5 , ν=0 . 001 , εd=4 . 5 , σ=0 .3 and
m=−1
Also it was shown that the increase of the non-
uniformity parameter μ value leads to the decrease of
the SW phase velocity and to the attenuation coefficient
α growth. It was obtained that α essentially increases
when the wave frequency became close to the upper
hybrid frequency. The maximum possible density that can
be maintained in the discharge by the SW considered
grows with the increase of parameter μ value. At the
same time the dimensional length of the discharge
becomes smaller.
0 1 2 3 4 5
0.00
0.01
0.02
0.03
0.04
0.05
0.15
0.16
0.17
0.18
2.0
1.5
0.9
0.6
0.2
Im(k
3
R
p
)
Re(k
3
R
p
)
Fig. 4. The dependence of the SW attenuation coefficient
α on the external magnetic field value for radially
uniform plasma. The parameters are the same as in Fig. 3
REFERENCES
[1] M. Moisan, Z. Zakrzewski. // Journal of Physics D:
Applied Physics (24). 1991, p. 1025.
[2] I. Peres, M. Fortin, J. Margot. // Phys. Plasmas (3).
1996, p. 1754.
[3] N.I. Karbushev, U.A. Kolosov, A.I. Polovkov. //
Phisica Plasmy .(18). 1992, p. 54.
[4] V.P. Olefir, N.A. Azarenkov, A.E. Sporov. //
Conference Proceedings Vol.1 (Intern. Conf on
Math. Methods in Electromagnetic Theory, 2000,
Kharkiv, Ukraine)./ KONTRAST Publishing Center,
Kharkiv, 2000, p. 329
[5] Z. Zakrzewski. // Journal of Physics D: Applied
Physics (16). 1983, p. 171.
[6] J. Margot-Chaker, M. Moisan, V.M.M. Glaude, P.
Lauque, J. Paraszczak, G. Sauvé. // J. Appl. Phys.
(66). 1989, p. 4134.
ЭЛЕКТРОМАГНИТНАЯ ДИПОЛЬНАЯ ВОЛНА В МАГНИТОАКТИВНОМ НЕОДНОРОДНОМ
СТОЛБЕ ПЛАЗМЫ
В.П. Олефир, А.Е.Споров
Проведено теоретическое исследование фазовых характеристик, коэффициента пространственного
затухания и радиальной структуры поля дипольной электромагнитной волны, распространяющейся вдоль
структуры, состоящей из слабостолкновительной неоднородной магнитоактивной плазмы, ограниченной
диэлектрической трубкой, окруженной вакуумом и помещенной внутрь цилиндрического металлического
волновода. Внешнее магнитное поле направлено вдоль оси структуры. Исследовано также аксиальное
распределение плотности плазмы в разряде, поддерживаемом дипольной волной и протекающем в
диффузионном режиме.
ЕЛЕКТРОМАГНИТНА ДИПОЛЬНА ХВИЛЯ В МАГНІТОАКТИВНОМУ НЕОДНОРІДНОМУ СТОВПІ
ПЛАЗМИ
В.П. Олефір, А.Е.Споров
Проведено теоретичне дослідження фазових характеристик, коефіцієнта просторового загасання та радіальної
структури поля дипольної електромагнітної хвилі, що розповсюджується вздовж структури, яка складається з
неоднорідної магнітоактивної плазми з малою частотою зіткнень електронів, обмеженої діелектричною
74
трубкою, оточеною вакуумом та розташованою всередині циліндричного металевого хвилеводу. Зовнішнє
магнітне поле спрямоване вздовж осі структури. Досліджено також аксіальний розподіл густини плазми в
розряді, що підтримується дипольною хвилею та протікає в дифузійному режимі.
75
|