RF field pattern in the plasma cylinder of finite length for various antennas
The paper deals with numerical calculations of electromagnetic fields, which are launched in the plasma cylinder of finite length surrounded by metal vessel. The RF antenna is located at the end face of the cylinder and placed between two dielectric plates. Such configuration is typical for plasma s...
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| Published in: | Вопросы атомной науки и техники |
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| Date: | 2005 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Cite this: | RF field pattern in the plasma cylinder of finite length for various antennas / D.L. Grekov, D.V. Sklyarov // Вопросы атомной науки и техники. — 2005. — № 2. — С. 52-54. — Бібліогр.: 2 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859656808837152768 |
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| author | Grekov, D.L. Sklyarov, D.V. |
| author_facet | Grekov, D.L. Sklyarov, D.V. |
| citation_txt | RF field pattern in the plasma cylinder of finite length for various antennas / D.L. Grekov, D.V. Sklyarov // Вопросы атомной науки и техники. — 2005. — № 2. — С. 52-54. — Бібліогр.: 2 назв. — англ. |
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| description | The paper deals with numerical calculations of electromagnetic fields, which are launched in the plasma cylinder of finite length surrounded by metal vessel. The RF antenna is located at the end face of the cylinder and placed between two dielectric plates. Such configuration is typical for plasma sources used for technological purposes [1, 2]. The obtained outcomes can be used for improvement of the characteristics of similar systems.
В роботі виконаний числовий розрахунок електромагнітних полів, які генеруються в обмеженому металевими стінками плазмовому циліндрі. ВЧ поля генеруються антеною, розміщеною між двома діелектричними пластинами в торці циліндра. Така конфігурація характерна для плазмових джерел, які використовуються в промислових цілях. Отримані результаті можна використовувати для покращення характеристик подібних систем.
В работе проведен численный расчет электромагнитных полей, возбуждаемых в плазменном цилиндре ограниченной длины, заключенном в металлический кожух. ВЧ поля возбуждаются антенной, расположенной на торце цилиндра и помещенной между двух диэлектрических пластин. Такая конфигурация характерна для плазменных источников, используемых в технологических целях. Полученные результаты могут быть использованы для улучшения характеристик подобных систем.
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| first_indexed | 2025-12-07T13:40:01Z |
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RF FIELD PATTERN IN THE PLASMA CYLINDER OF FINITE LENGTH
FOR VARIOUS ANTENNAS
D.L. Grekov, D.V. Sklyarov
Institute of Plasma Physics, NSC KIPT, Kharkov, Ukraine
The paper deals with numerical calculations of electromagnetic fields, which are launched in the plasma
cylinder of finite length surrounded by metal vessel. The RF antenna is located at the end face of the cylinder and
placed between two dielectric plates. Such configuration is typical for plasma sources used for technological purposes
[1, 2]. The obtained outcomes can be used for improvement of the characteristics of similar systems.
PACS: 52.50.Qt
SETTING OF THE TASK
The scheme of device under consideration is
represented in Fig. 1. In calculations the radius of the
metal cylinder was a=23 cm , the length was
L=5 −10 cm , the thickness of dielectric plates were
(at the left on the right) g=0 . 1 −2 . 5 cm and
h−g=0 . 1 −0 . 5 cm . Three types of antennas
were considered in calculations and are shown in Fig. 2.
Plasma reactor
Dielectric plates
Antenna
z
r
ϕ
Metal walls
Fig. 1. The outline of plasma source and used in the
calculations coordinate system
R1
2.0 cm
R 23.0 cm
a
R 2
R 23.0 cm
R1
2.0 cm
b
2.0 cm
π20.0
0.0
13.0
87.0
0.1
ϕ
a
r
c
Fig. 2. The scheme of surveyed antennas: a – open ring,
b – the combination of azimuth and radial currents, c –
the spiral of Archimedes.
The working frequency of RF power supply is
f =13.5 MHz and the working range of pressures
of neutral gas is p=7 ⋅10−4−5 ⋅10−2 Torr .
TECHNIQUE OF SOLUTION
The hydrodynamic approximation was used for
plasma dielectric permeability. The density of plasma in
a device was considered as homogeneous. Then a plasma
dielectric permeability is ε p=1 −
ω pe
2
ω ωiν
, where
ω=2πf , ω pe= 4πe2 ne /me is plasma frequency
of electrons, ν is effective collision frequency. The
collisions of electrons with neutral atoms are dominant
for the range of pressures and electron temperature under
consideration. In spite of the fact that ν<<ω, the collision
frequency was taken into account in the vicinity of
eigenfrequencies of the device. The kinetic effects were
neglected in the consideration because ω p /kv T <<1 .
Here vT is electron thermal velocity and 1/k is the
RF field scale length. The electron mean free pass λe is
defined by electron – neutral atom collisions. For the
case under consideration λe ~ 0.5 cm and λe << a. So,
plasma density profile is defined by RF field pattern.
Maxwell equations were written for three
regions (two regions of dielectrics and one region of
plasma) in a cylindrical coordinate system and were
adjusted at boundaries. Set of the Maxwell's equations in
each region is written as
rot H k=
1
c
∂ Dk
∂ t
Dk=ε k
Ek
rot Ek=−1
c
∂ Bk
∂ t
div Dk=0
div Bk=0
, (1)
where k is index designating an appropriate region. In
the set of equations (1) the absence of external charges in
all three areas is taken into account. The currents and
charges of an antenna are taken into account in boundary
conditions.
Two independent modes, TE mode ( E z=0 ) and
TM mode ( H z=0 ), represent the solutions of the
system (1). They are connected through boundary
conditions on the antenna. Then, the combination of two
methods was used to solve the differential equations (1):
52 Problems of Atomic Science and Technology. Series: Plasma Physics (11). 2005. № 2. P. 52-54
the finite-differences along coordinates r and z and
Fourier series along coordinate ϕ . Application of
Fourier expansion allowed us to avoid introduction of a
three-dimensional grid and to reduce a set of Maxwell
equations to sequential solution of the differential
equations for two independent variables. Fifty harmonics
of Fourier series were used in numerical calculations.
Finally, the integral-differential equations for
Fourier harmonics were solved by the finite-differences
method. We employed the non -uniform grid in r and z
directions. It allowed us to get more accurate solutions in
the regions of field inhomogeneity with smaller amount
of nodes. Also, finite-differences method allows us to
solve the problem for the case of arbitrary density
distribution inside the device. In this specific case, the
grid consisted of 26 points along r, and 28 points along z.
BASIC RESULTS
As the result of the numerical calculations, the values
of the electromagnetic field components in grid points were
obtained. For example, in the Fig. 3 the RF field pattern in
plasma region is shown for density n=108 cm-3. As it is
seen in this figure, the electric field iterates the geometry
of the antenna. It vanishes while moving away the
antenna. Only the forced oscillations are exited in the
plasma at this density.
Fig. 3. Dependence E z=E z r ,ϕ at the point
z=0.5cm for the antenna type a,
I – current in the antenna
The dependencies of the modulus of the RF
electric field in plasma on the device parameters are
shown in Fig. 4 for ТМ and TE modes at plasma density
n=108 cm-3. As it is seen in Fig. 4a and Fig. 4b, the
change of the device length weakly influences the RF
field value in plasma region. The increase of width of the
first dielectric plate results in growth of TE mode value
(Fig. 4d), and increase of the width of second dielectric
plate leads to decrease of ТМ mode value (Fig. 4e).
Therefore, for increase of RF electric field value in
plasma region, it is necessary to increase width of the
first dielectric plate and to reduce the width of second
plate. When the values of RF fields are known, it is easy
to find the energy electromagnetic field in plasma region.
The ТМ mode plays the dominant role on initial stage of
discharge at plasma densities up to n=109 cm-3, as it is
shown in Fig. 5. When the plasma density increases
further, the contribution of the ТМ mode decreases, and
the contribution of the TE modes grows. The number of
RF energy peaks at densities up to n=108 cm-3 is due to
resonant excitation of eigenoscillations of ТМ mode.
4 5 6 7 8 9 10
0,00
0,02
0,04
TM moda
L cm a
4 5 6 7 8 9 10
0,0000
0,0002
0,0004 TE moda
L cm b
0,0 0,2 0,4 0,6 0,8 1,0
0,00
0,02
0,04 TM moda
g cm c
0,0 0,2 0,4 0,6 0,8 1,0
0,0000
0,0002
0,0004 TE moda
g cm d
0,0 0,2 0,4 0,6 0,8 1,0
0,00
0,02
0,04 TM moda
h−g cm e
0,0 0,2 0,4 0,6 0,8 1,0
0,0000
0,0002
0,0004
TE moda
g−h cm f
Fig. 4. The dependencies of the normalized modulus of
electric field in plasma 4π⋅c⋅∣E∣/ I on parameters of
the device
1E7 1E8 1E9 1E10 1E11 1E12
1E-4
1E-3
0,01
0,1
1
10
WeTm
WeTe
We
n cm-3
Fig. 5. Dependence of energy of RF electric field in
plasma c2⋅W e∣pl /16 π 2⋅I 2 on plasma density for
antenna of type c
Also, the antenna design influences the total
energy of RF electric field in plasma strongly. As it is
shown in Fig. 6, the antenna in the form of the spiral of
Archimedes has an advantage in comparison with
antennas of other types at small density about 2 . 2
53
time, and at increase of density of plasma about 16
time. It happens, because it is longer than others. The
value of a charge is identical to all types of antennas,
however, current value on an inlet of an antenna goes up
with antenna length increase. At low densities, ТМ mode
plays the dominant role. It is stimulated only by charge
on an antenna. And at major densities TE mode starts to
play a dominant role. This mode is stimulated by current
on an antenna. Thus, the positive effects from an
elongation of an antenna and from increase of an entry
current add and give such major benefit.
1E7 1E8 1E9 1E10 1E11 1E12
1E-4
1E-3
0,01
0,1
1
10 Tipe a
Tipe b
Tipe c
n sm-3
Fig. 6. Dependence of energy of an electric field in
plasma c2⋅W e∣pl /16 π 2⋅I 2 on density for different
types of antennas
Having received values of energy of electrical
and magnetic fields in the device it is possible to
calculate such macro characteristic of antennas as
capacity C=e2/ 2We and inductance
L=2c2 W h / I 2 . As main energy of an
electromagnetic field is concentrated in dielectric plates,
than capacity and inductance depend feebly on density of
plasma everywhere, except of regions of eigenmodes of
the device. Thus, for example, for an antenna of a type c
we have L==3 ⋅10−5 mh and
C=3 . 5 ⋅10−4 mfd . Also, knowing effective
frequency of collision, it is possible to find energy, which
is delivered to plasma heating. Then, the ohmic
resistance of an antenna loading equals
R= 1
I 2∫
V
E 2
8π
ω pe
2 ν
ω pe
2 ν2
dV . For the antenna of a
type c we have R=0 . 01 Om .
CONCLUSION
The calculations of electromagnetic fields in the
device established the base for antenna optimization. The
no uniform grid of splitting was adopted using the finite-
differences method. It permits to get more precise
solutions in the RF field strong inhomogeneity while
using of a fewer number of points. Also, a finite-
differences method allows us to solve the equations in
case of arbitrary distribution of particles density in a
source's volume. It enables us to receive self-consistent
solution later. Fourier’s decomposition has allowed to
reduce number of the finite-difference equations and to
increase speed of calculation considerably. The macro
characteristics (capacity, inductance and resistance) were
calculated for antennas. Also, the dependence of
integrated over source volume energy of RF electric field
on device parameters is obtained, that allows us to
estimate the influence of geometrical parameters change
on the source operation.
REFERENCES
1. N.А. Azarenkov, А.А. Bizyukov et al.// Proc. of Int.
Conf. on Vacuum Techn., Sudak. 2001, p.168.
2. Ho-Jun Lee, II-Dong Yang, Ki-Woong Whang//
Plasma Sources Sci. Techn. (5). 1996, p.383.
РАСПРЕДЕЛЕНИЕ ВЧ ПОЛЕЙ В ПЛАЗМЕННОМ ЦИЛИНДРЕ ОГРАНИЧЕННОЙ ДЛИНЫ ДЛЯ
РАЗЛИЧНЫХ АНТЕНН
Д.Л. Греков, Д.В. Скляров
В работе проведен численный расчет электромагнитных полей, возбуждаемых в плазменном цилиндре
ограниченной длины, заключенном в металлический кожух. ВЧ поля возбуждаются антенной, расположенной
на торце цилиндра и помещенной между двух диэлектрических пластин. Такая конфигурация характерна для
плазменных источников, используемых в технологических целях. Полученные результаты могут быть
использованы для улучшения характеристик подобных систем.
РОЗПОДІЛ ВЧ ПОЛЯ В ПЛАЗМОВОМУ ЦИЛІНДРІ ОБМЕЖЕНОЇ ДОВЖИНИ ДЛЯ РІЗНИХ АНТЕН
Д.Л. Греков, Д.В. Скляров
В роботі виконаний числовий розрахунок електромагнітних полів, які генеруються в обмеженому
металевими стінками плазмовому циліндрі. ВЧ поля генеруються антеною, розміщеною між двома
діелектричними пластинами в торці циліндра. Така конфігурація характерна для плазмових джерел, які
використовуються в промислових цілях. Отримані результаті можна використовувати для покращення
характеристик подібних систем.
54
|
| id | nasplib_isofts_kiev_ua-123456789-79347 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T13:40:01Z |
| publishDate | 2005 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Grekov, D.L. Sklyarov, D.V. 2015-03-31T13:55:38Z 2015-03-31T13:55:38Z 2005 RF field pattern in the plasma cylinder of finite length for various antennas / D.L. Grekov, D.V. Sklyarov // Вопросы атомной науки и техники. — 2005. — № 2. — С. 52-54. — Бібліогр.: 2 назв. — англ. 1562-6016 PACS: 52.50.Qt https://nasplib.isofts.kiev.ua/handle/123456789/79347 The paper deals with numerical calculations of electromagnetic fields, which are launched in the plasma cylinder of finite length surrounded by metal vessel. The RF antenna is located at the end face of the cylinder and placed between two dielectric plates. Such configuration is typical for plasma sources used for technological purposes [1, 2]. The obtained outcomes can be used for improvement of the characteristics of similar systems. В роботі виконаний числовий розрахунок електромагнітних полів, які генеруються в обмеженому металевими стінками плазмовому циліндрі. ВЧ поля генеруються антеною, розміщеною між двома діелектричними пластинами в торці циліндра. Така конфігурація характерна для плазмових джерел, які використовуються в промислових цілях. Отримані результаті можна використовувати для покращення характеристик подібних систем. В работе проведен численный расчет электромагнитных полей, возбуждаемых в плазменном цилиндре ограниченной длины, заключенном в металлический кожух. ВЧ поля возбуждаются антенной, расположенной на торце цилиндра и помещенной между двух диэлектрических пластин. Такая конфигурация характерна для плазменных источников, используемых в технологических целях. Полученные результаты могут быть использованы для улучшения характеристик подобных систем. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Basic plasma physics RF field pattern in the plasma cylinder of finite length for various antennas Розподіл ВЧ поля в плазмовому циліндрі обмеженої довжини для різних антен Распределение ВЧ полей в плазменном цилиндре ограниченной длины для различных антенн Article published earlier |
| spellingShingle | RF field pattern in the plasma cylinder of finite length for various antennas Grekov, D.L. Sklyarov, D.V. Basic plasma physics |
| title | RF field pattern in the plasma cylinder of finite length for various antennas |
| title_alt | Розподіл ВЧ поля в плазмовому циліндрі обмеженої довжини для різних антен Распределение ВЧ полей в плазменном цилиндре ограниченной длины для различных антенн |
| title_full | RF field pattern in the plasma cylinder of finite length for various antennas |
| title_fullStr | RF field pattern in the plasma cylinder of finite length for various antennas |
| title_full_unstemmed | RF field pattern in the plasma cylinder of finite length for various antennas |
| title_short | RF field pattern in the plasma cylinder of finite length for various antennas |
| title_sort | rf field pattern in the plasma cylinder of finite length for various antennas |
| topic | Basic plasma physics |
| topic_facet | Basic plasma physics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79347 |
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