The HF field pattern in the magnetized plasma cylinder of finfte lenght
The PR-1 device is the wide-aperture source of homogeneous plasma. It is using for plasma processing of big diameter samples such as parts of HF antenna and elements of vessel of fusion devices. The paper presented deals with investigation of HF field pattern of the operation regime with external ma...
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| Zitieren: | The HF field pattern in the magnetized plasma cylinder of finfte lenght / D.L. Grekov, N.A. Azarenkov, A.A. Bizyukov, V.P. Olefir // Вопросы атомной науки и техники. — 2003. — № 1. — С. 133-136. — Бібліогр.: 2 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859632944270802944 |
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| author | Grekov, D.L. Azarenkov, N.A. Bizyukov, A.A. Olefir, V.P. |
| author_facet | Grekov, D.L. Azarenkov, N.A. Bizyukov, A.A. Olefir, V.P. |
| citation_txt | The HF field pattern in the magnetized plasma cylinder of finfte lenght / D.L. Grekov, N.A. Azarenkov, A.A. Bizyukov, V.P. Olefir // Вопросы атомной науки и техники. — 2003. — № 1. — С. 133-136. — Бібліогр.: 2 назв. — англ. |
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| description | The PR-1 device is the wide-aperture source of homogeneous plasma. It is using for plasma processing of big diameter samples such as parts of HF antenna and elements of vessel of fusion devices. The paper presented deals with investigation of HF field pattern of the operation regime with external magnetic field. It is shown that the HF fields penetrate into the plasma volume better as compared with the case when magnetic field is turned off. So the plasma flow of greater density could be generated.
Установка ПР-1 являє собою широкоапертурне джерело однорідної плазми, яке сконструйоване для обробки примірників великого діаметру, таких як елементи конструкції ВЧ антен та складові частини камери термоядерних установок. В роботі досліджено розподіл електромагнітних полів в камері установки, що працює в режимі з зовнішнім магнітним полем. Доведено, що в цьому режимі ВЧ поля краще проникають в плазму, ніж в режимі без магнітного поля. Тому в режимі з зовнішнім магнітним полем можливо створювати потік плазми з більшою густиною.
Установка ПР-1 предназначена для плазменной обработки образцов большого диаметра, таких как элементы конструкции ВЧ антенн и элементы камеры установок для магнитного удержания плазмы. В работе проведено изучение распределения ВЧ полей в объеме установки в режиме с внешним магнитным полем. Показано, что в этом случае ВЧ поля лучше проникают в плазму, чем без магнитного поля. Это позволит создавать плазменные потоки большей плотности.
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THE HF FIELD PATTERN IN THE MAGNETIZED PLASMA
CYLINDER OF FINFTE LENGHT
D.L. Grekov, N.A. Azarenkov*, A.A. Bizyukov*, V.P. Olefir*
Institute of Plasma Physics of National Science Center “Kharkov Institute of Physics
and Technology”, Academicheskaja st. 1, 61108, Kharkov, Ukraine;
*-Department of Physics and Technology, Kharkiv National University, Kharkov,
Svobody sq. 4, 61108, Kharkiv, Ukraine
The PR-1 device is the wide-aperture source of homogeneous plasma. It is using for plasma processing of big diameter
samples such as parts of HF antenna and elements of vessel of fusion devices. The paper presented deals with investiga-
tion of HF field pattern of the operation regime with external magnetic field. It is shown that the HF fields penetrate
into the plasma volume better as compared with the case when magnetic field is turned off. So the plasma flow of
greater density could be generated.
PACS: 52.35.Hr
INTRODUCTION
The device РR-1 represents the wide-aperture homo-
geneous plasma source intended for processing of the pat-
tern in diameter more than 30 cm. It can be the compo-
nent of the high-frequency (HF) antenna of the thermonu-
clear traps, elements of the chambers coating of the instal-
lations etc. The theoretical and experimental research of
the plasma creation in this installation by HF fields with
frequency f=13.56 MHz was carried out earlier [1,2] in
operational modes without external magnetic field. The
presence of the solenoid allows to carry out the experi-
ments with external axial magnetic field B
about 100 Gs.
The present activity is devoted to investigation the influ-
ence of the external magnetic field value on the HF field
spatial distribution in device volume. It is allows to make
the conclusion about uniformity of spatial distribution of
HF field in the plasma and about the possibility of using
the external magnetic field for regimes of the work of the
device РR-1 with greater plasma density.
The framework of the device PR-1 is the metal cylin-
der of radius 5.22=a cm and altitude l < a. The dielec-
tric plate (I) with width g and permittivity dε is stacked
on the cylinder bottom and separates the antenna from the
chamber bottom. The antenna is covered with dielectric
plate (II) with width gh − and permittivity dε .
z
g
l
h
0
I
II
III
B0
1
Fig.1. The cross-section of the device PR-1 along the
cylindrical chamber axis. The antenna is located between
dielectric plate (I) and (II). The plasma occupies the re-
gion (III), 1 – the solenoid for creating the external mag-
netic field
The plasma is formed in region (III), having the alti-
tude l-h along the chamber axis (axes Z in further consid-
eration). Accordingly the experiment [2], the plasma in
the region (III) is uniform. Therefore at the further consid-
eration will be used the model of the homogeneous plas-
ma cylinder.
THE BASIC EQUATIONS
Let us to study the spatial distribution of HF fields ex-
ited by the generator with frequency f=13.56 MHz. We
accept that the external magnetic field value is equal to
100 Gs. In this case the field frequency fπω 2= located
in interval ceLH ωωω < << , where LHω is low hybrid
frequency, ceω is electron cyclotron frequency. In an ef-
fective range of pressure of neutral gas (
Toppp 42 107105 −− ⋅÷⋅= ) the inequalities
ωνν < << < aeff ( effν is the effective collisions frequen-
cy of electrons with ions, aν is the frequency of elastic
collisions of electrons with atoms) are executed. There-
fore we neglected the collisions in plasma permittivity
tensor. The components of the tensor permittivity are:
2222
1 //1 cepepi ωωωωε +−= ,
cepe ω ωωε /2
2 −= , 22
3 /1 ωωε pe−= ,
where piω and peω are the ions and electrons plasma
frequencies. We assume that the relation of a HF of fields
to azimuth coordinate ϕ looks like )exp( ϕim and from
axial coordinate z is )exp( zk| | , where | |k is longitudinal
component of the wave vector in relation to the external
magnetic field. From the Maxwell equations can be ob-
tained the system of related equations described the be-
haviour of the HF fields in plasma
[ ]
01
)(
1)(
2
2
2
2
2
22
12
2
2
2
2
1
=
−
−−+
+
−
+
||
||
||
z
z
z
E
r
m
dr
dr
dr
d
r
N
BN
c
B
r
m
dr
dr
dr
d
r
N
ε
εεω
ε
,
Problems of Atomic Science and Technology. 2003. № 1. Series: Plasma Physics (9). P. 133-136 133
[ ]
[ ] 0)(
1)(
1
2
2
22
132
2
2
2
2
2
2
11
2
2
2
=−++
+
−
−+
+
−
||
||
||
z
z
z
EN
c
E
r
m
dr
dr
dr
d
r
N
B
r
m
dr
dr
dr
d
r
N
εεεω
εεε
ε
(1)
( ω/ckN | || | = ). The solutions of this system are
( )xNBZB Fmz ⊥= and ( )xNCZE Smz ⊥= . Here ( )xZm
are the cylindrical functions that are finite at 0=x ,
crx /ω= . By an index F is denote the smaller on abso-
lute value and index S is denote the greater radial index of
refraction, which are determined by equation:
−+−
−++−
±++−
=
| |
| |
| |
2/1
2
2
22
131
22
131
2
2
2
131
2
2
1
2
,
])[(4
)])(([
))((
2
1
εεεε
εεεε
εεεε
ε
N
N
N
N SF (2)
We will to note the oscillations with SN the as F-mode,
and the oscillation with SN as S-mode.
0
0
VIIIIIII
⊥N
2
2
| |N
Fig.2. The dependence of radial refraction
parameters 2
⊥N of the F-mode and S-mode on 2
| |N
As can see from fig.2 depending on 2
| |N one of modes
can be surface (on radius), and second propagating (zone
I, IV); both modes can be propagating on radius (zone II),
or surface (zone III). Thus each of modes has all three
components (r, j, z) both magnetic and electrical field. As
( )xZE mz ~ , and ( ) ( )xZxZE mm ′+ βαϕ ~ (
( ) ( ) dxxdZxZ mm /=′ ), the fulfillment of the boundary con-
ditions on the device lateral 0=
= ar
Eϕ and 0== arzE
is possible only for a superposition of modes. Let's write
zE of the F-modes as zBkE zFz ∂∂= / , and zB of the S-
modes as zEkB zSz ∂∂= / . The obvious kind of the fac-
tors Fk and Sk can be easy finding from equations (1).
From conditions on a lateral wall can be obtained the fol-
lowing transcendental equation:
( )
( ) ( )
( )
( )
( )
( ) ( )[ ]
0
2
2
1
22
2
2
2
1
2
=
−+′′
+′
′′−
−′
−+′′
+′
′
| |
| |
| || |
εε
ε
εε
ε
NkaNZN
aNZk
a
m
aNZkN
aNZ
NkNaNZN
aNZ
a
m
SSmS
SmS
FmF
Sm
FFmF
Fm
, (3)
where caa /ω=′ . This equation determines the row of
values ∞=| | 2,1,2 qN q , which are excited in plasma.
The appropriate values of FqN and SqN can be obtained
from equation (2). The obvious kind of the dependence of
the plasma fields on z is determined by boundary condi-
tions ( ) 0=rEr and ( ) 0=ϕ rE on the chamber back at
1=z . From them follows: )](cos[~ zlNE qz −| | (or
)]([~ zlNchE qz −| | ) and )](sin[~ zlNB qz −| | (or
)]([~ zlNshB qz −| | ). Thus, the general solution for m-th
harmonics of the HF field in plasma can be written as
∑
∞
=
| | +−=
1
)]()()][(cos[
q
SqmFqmFqqqzm xNZxNZkzlNCE (4)
Using (4), it is easy to receive expressions for a remaining
component electrical and magnetic field in plasma.
THE FEATURES OF THE ELECTROMAG-
NETIC FIELD DISTRIBUTION IN
MAGNETIZED PLASMA
For example let's analyze the excitation of HF fields
by surface charge with m=2. It is known that the solution
in dielectric represents the superposition of TM-waves
( ∑ ±
= ±
s
msmzm imzk
a
rjJAE )exp()exp( ms|| ϕ , 0=zB )
and TE-waves
( ∑ ±
′= ±
p
mpmzm imzk
a
rjJBB )exp()exp( '
mp||
ϕ , 0=zE ).
Here msj is the s-th root of a cylindrical functions of or-
der m, mpj′ is p-th root of the derivative of cylindrical
functions of order m,
( ) 2/12222 // cajk dmsms εω−=| | , ( ) 2/12222'' // cajk dmsms εω−=| | .
In the case of the non-magnetized plasma the solution
have the same structure but in expression of | |k instead
22 /1 ωωε pep −= it is necessary to use dε . Let suppose
that the surface charge on the antenna has such radial de-
pendence ( )arjJ /~ 5,22 .
Thus in case of non-magnetized plasma the HF field
of ТМ-mode both in dielectric and plasma has the same
radial distribution. The TE-mode is not excited in this
case.
The external magnetic field completely changes the
situation. In order to find the HF field in plasma it is nec-
essary to fulfill the boundary conditions on interface of
dielectric (II)-plasma (III): zIIIzIId EE 3εε = ,
IIIII EE ϕϕ = and zIIIzII BB = .
134
0 5 1 0 1 5 2 0
1 0 - 5
1 0 - 1
1 0 3
q
F
S
Fig.3. The amplitudes of the spatial harmonics (n.u.) in
plasma with 3910.2 −= cmne ; surface charge 5=s . The
harmonics of the curve F have 02 >| | qN , ones of the
curve S correspond to 02 <| | qN . The arrows are marked
position of the root with 5,2j
It results in the infinite system of linear equations con-
cerning amplitudes qC . We do not present its here be-
cause of its cumbersome. The amplitudes qC were deter-
mined by numerical methods. Because the values of
aNj FqFq ′= / , and aNj SqSq ′= / are not equal 5,2j de-
termined the HF field radial structure in dielectric, the
spectrum of harmonics (fig. 3) is excited in plasma. For
these harmonics is 0≠zB . It results in appearance of the
TE-mode in dielectric due to continuity of the zB -com-
ponent on plasma-dielectric interface. Also, there is the
essential modification of the ТМ-mode field. As one can
see from fig. 4 the field of this mode increase in center of
the chamber and is decrease on its periphery.
0 . 0 0 . 5 1 . 0
- 3 0
- 1 5
0
1 5
a/r
zE
Fig. 4. The radial structure of the HF field in dielectric
(n.u.) (♦ ) is the case of magnetized plasma, (•) is the case
of non-magnetized plasma
These effects are stipulated by interaction of HF field
with magnetized plasma. Let's analyze distribution of a
HF of fields in plasma volume. As one can see from fig.
5,6 the HF field concentrated mainly in the central part of
plasma volume. Thus the field smoothly decreases from
the plasma-dielectric interface in the contrary to the case
of non-magnetized plasma. Such behavior HF field along
an axis z is stipulated by excitation of considerable num-
ber of harmonics with 02 <| | qN that dependent from z
proportionally ( )]cos[ zlN q −| | .
zE
Fig.5. The distribution components zE in plasma volume
at 3910.2 −= cmne
Er
Fig.6. The distribution components rE in plasma volume
at 3910.2 −= cmne
CONCLUSION
The HF field pattern in the PR-1 device in operational
mode with an external magnetic field was studied. Con-
sidering the excitation of HF field by one azimuth and ra-
dial harmonics of a surface charge with frequency 13
MHz as the example, it was shown, that the presence of a
magnetic field changes the HF field pattern both in dielec-
tric, and in plasma. When the external magnetic field is
turned off, the HF fields of the antenna is strongly
screened by a surface charge on boundary dielectric -
plasma and sharply decrease in plasma along axis of the
device. The presence of a magnetic field results in more
uniform distribution of fields along Z-axis and focusing
them in center of plasma. Also, absolute value of of elec-
tric field considerably increases. The obtained qualitative
conclusions can be generalized on the case of superposi-
tion of azimuth and radial harmonics at calculations of the
actual antenna. So, the presence of an external magnetic
field will allow to proceed to operational modes of the de-
vice with greater plasma density.
135
This work was partially supported by the Science
and Technology Center in Ukraine (STCU, Project
#1112).
REFERENCES
[1] D.L. Grekov, N.А. Azarenkov, А.А Bizyukov,
V.P.Olefir. Distribution of electromagnetic fields in
the installation PR-1 // Radio physics and radio as-
tronomy. (7) 2002 , №3, p. 321-326.
[2] N.А. Azarenkov, А.А.Bizyukov, А.V.Gapon, D.L.-
Grekov, А.F. Tseluiko, А.G. Chunadra. A surface
waves plasma source // Applied physics. 2002, №5,
p. 36-42.
РОЗПОДІЛ ВЧ ПОЛІВ В ПЛАЗМІ УСТАНОВКИ ПР-1 В МАГНІТНОМУ ПОЛІ
Д.Л.Греков, М.О.Азаренков, О.А.Бізюков, В.П.Олефір
Установка ПР-1 являє собою широкоапертурне джерело однорідної плазми, яке сконструйоване для обробки
примірників великого діаметру, таких як елементи конструкції ВЧ антен та складові частини камери
термоядерних установок. В роботі досліджено розподіл електромагнітних полів в камері установки, що працює
в режимі з зовнішнім магнітним полем. Доведено, що в цьому режимі ВЧ поля краще проникають в плазму, ніж
в режимі без магнітного поля. Тому в режимі з зовнішнім магнітним полем можливо створювати потік плазми з
більшою густиною.
РАСПРЕДЕЛЕНИЕ ВЧ ПОЛЕЙ В ПЛАЗМЕ УСТАНОВКИ ПР-1 В МАГНИТНОМ ПОЛЕ
Д.Л. Греков, Н.А. Азаренков, А.А. Бизюков, В.П. Олефир
Установка ПР-1 предназначена для плазменной обработки образцов большого диаметра, таких как элементы
конструкции ВЧ антенн и элементы камеры установок для магнитного удержания плазмы. В работе проведено
изучение распределения ВЧ полей в объеме установки в режиме с внешним магнитным полем. Показано, что в
этом случае ВЧ поля лучше проникают в плазму, чем без магнитного поля. Это позволит создавать плазменные
потоки большей плотности.
136
D.L. Grekov, N.A. Azarenkov*, A.A. Bizyukov*, V.P. Olefir*
Institute of Plasma Physics of National Science Center “Kharkov Institute of Physics
and Technology”, Academicheskaja st. 1, 61108, Kharkov, Ukraine;
*-Department of Physics and Technology, Kharkiv National University, Kharkov,
Svobody sq. 4, 61108, Kharkiv, Ukraine
Introduction
The basic equations
The features of the electromagnetic field distribution in magnetized plasma
Conclusion
References
Д.Л.Греков, М.О.Азаренков, О.А.Бізюков, В.П.Олефір
Д.Л. Греков, Н.А. Азаренков, А.А. Бизюков, В.П. Олефир
|
| id | nasplib_isofts_kiev_ua-123456789-110618 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T13:12:40Z |
| publishDate | 2003 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Grekov, D.L. Azarenkov, N.A. Bizyukov, A.A. Olefir, V.P. 2017-01-05T19:01:06Z 2017-01-05T19:01:06Z 2003 The HF field pattern in the magnetized plasma cylinder of finfte lenght / D.L. Grekov, N.A. Azarenkov, A.A. Bizyukov, V.P. Olefir // Вопросы атомной науки и техники. — 2003. — № 1. — С. 133-136. — Бібліогр.: 2 назв. — англ. 1562-6016 PACS: 52.35.Hr https://nasplib.isofts.kiev.ua/handle/123456789/110618 The PR-1 device is the wide-aperture source of homogeneous plasma. It is using for plasma processing of big diameter samples such as parts of HF antenna and elements of vessel of fusion devices. The paper presented deals with investigation of HF field pattern of the operation regime with external magnetic field. It is shown that the HF fields penetrate into the plasma volume better as compared with the case when magnetic field is turned off. So the plasma flow of greater density could be generated. Установка ПР-1 являє собою широкоапертурне джерело однорідної плазми, яке сконструйоване для обробки примірників великого діаметру, таких як елементи конструкції ВЧ антен та складові частини камери термоядерних установок. В роботі досліджено розподіл електромагнітних полів в камері установки, що працює в режимі з зовнішнім магнітним полем. Доведено, що в цьому режимі ВЧ поля краще проникають в плазму, ніж в режимі без магнітного поля. Тому в режимі з зовнішнім магнітним полем можливо створювати потік плазми з більшою густиною. Установка ПР-1 предназначена для плазменной обработки образцов большого диаметра, таких как элементы конструкции ВЧ антенн и элементы камеры установок для магнитного удержания плазмы. В работе проведено изучение распределения ВЧ полей в объеме установки в режиме с внешним магнитным полем. Показано, что в этом случае ВЧ поля лучше проникают в плазму, чем без магнитного поля. Это позволит создавать плазменные потоки большей плотности. This work was partially supported by the Science and Technology Center in Ukraine (STCU, Project #1112). en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Low temperature plasma and plasma technologies The HF field pattern in the magnetized plasma cylinder of finfte lenght Розподіл Вч полів в плазмі установки ПР-1 в магнітному полі Распределение ВЧ полей в плазме установки ПР-1 в магнитном поле Article published earlier |
| spellingShingle | The HF field pattern in the magnetized plasma cylinder of finfte lenght Grekov, D.L. Azarenkov, N.A. Bizyukov, A.A. Olefir, V.P. Low temperature plasma and plasma technologies |
| title | The HF field pattern in the magnetized plasma cylinder of finfte lenght |
| title_alt | Розподіл Вч полів в плазмі установки ПР-1 в магнітному полі Распределение ВЧ полей в плазме установки ПР-1 в магнитном поле |
| title_full | The HF field pattern in the magnetized plasma cylinder of finfte lenght |
| title_fullStr | The HF field pattern in the magnetized plasma cylinder of finfte lenght |
| title_full_unstemmed | The HF field pattern in the magnetized plasma cylinder of finfte lenght |
| title_short | The HF field pattern in the magnetized plasma cylinder of finfte lenght |
| title_sort | hf field pattern in the magnetized plasma cylinder of finfte lenght |
| topic | Low temperature plasma and plasma technologies |
| topic_facet | Low temperature plasma and plasma technologies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/110618 |
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