The influence of anomalous skin-effect no the discharge sustained by surface wave
In the present work the non self-consistent theory of the discharge sustained by SW. In the approximation of the set field analytical ratio for EEDF are found. The approached distributions of discharge parameters, such as plasma density, spatial diffusion coefficient, frequencies of elementary proce...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
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| Цитувати: | The influence of anomalous skin-effect no the discharge sustained by surface wave / N.A. Azarenkov, Vladimir V. Gushchin, Valery V. Gushchin // Вопросы атомной науки и техники. — 2005. — № 1. — С. 66-68. — Бібліогр.: 6 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859865249143848960 |
|---|---|
| author | Azarenkov, N.A. Gushchin, Vladimir V. Gushchin, Valery V. |
| author_facet | Azarenkov, N.A. Gushchin, Vladimir V. Gushchin, Valery V. |
| citation_txt | The influence of anomalous skin-effect no the discharge sustained by surface wave / N.A. Azarenkov, Vladimir V. Gushchin, Valery V. Gushchin // Вопросы атомной науки и техники. — 2005. — № 1. — С. 66-68. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | In the present work the non self-consistent theory of the discharge sustained by SW. In the approximation of the set field analytical ratio for EEDF are found. The approached distributions of discharge parameters, such as plasma density, spatial diffusion coefficient, frequencies of elementary processes (excitation, ionization, etc.), and quantities of inelastic processes are received. It is shown, that under certain conditions the contribution to them from bounce electrons can become determining.
В даній роботі побудовано самоузгоджену теорію розряду, що підтримується ПХ. У наближенні заданого поля знайдено аналітичні рішення для ФРЕЕ. Отримано наближені розподіли характеристик розряду, таких як густина плазми, коефіцієнт просторової дифузії, частоти елементарних процесів (збудження, іонізації та ін.) та кількості процесів. Показано, що за певних умов bounce електрони можуть відігравати визначну роль.
В данной работе построена несамосогласованная теория разряда, поддерживаемого ПВ. В приближении заданного поля найдены аналитические решения для ФРЭЭ. Получены приближенные распределения разрядных характеристик, таких как плотность плазмы, коэффициент пространственной диффузии, частоты элементарных процессов (возбуждения, ионизации и т.п.) и количество неупругих процессов. Показано, что при определенных условиях вклад от bounce электронов может стать определяющим.
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| first_indexed | 2025-12-07T15:47:46Z |
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| fulltext |
THE INFLUENCE OF ANOMALOUS SKIN-EFFECT ON THE DISCHARGE
SUSTAINED BY SURFACE WAVE
N.A.Azarenkov, Vladimir V.Gushchin, Valery V.Gushchin
Depart. of Physics & Technology, V.N. Karazin Kharkov National University, Ukraine
In the present work the non self-consistent theory of the discharge sustained by SW. In the approximation of
the set field analytical ratio for EEDF are found. The approached distributions of discharge parameters, such as plasma
density, spatial diffusion coefficient, frequencies of elementary processes (excitation, ionization, etc.), and quantities of
inelastic processes are received. It is shown, that under certain conditions the contribution to them from bounce elec
trons can become determining.
PACS: 52.50-b; 52.80 Pi; Dg.52.25. Fi.
1.INTRODUCTION
In the theory of the discharge sustained by sur
face waves (SW), effects of spatial nonlocality and
nonequlibrity are essential. The full system of the equa
tions is self-coordinated, (it is resulted in [1]) and can be
strictly solved only numerically. However in the given re
port we want to reveal influence of anomalous skin-effect
on the discharge characteristics. Therefore we shall con
struct the phenomenological kinetic theory - electron en
ergy distribution function (EEDF) we shall find in ap
proximation of the set field. For this purpose we shall
present fields distributions in a modelling kind. We
choose distributions of potential of a spatial charge field
as, close to observed on experiment:
Φs x =Φwall {1 −4x2
d 2 } (1)
where: Φwall - a wall potential of the discharge chamber;
d - thickness of a plasma layer;
At the description of nonequilibrium and nonlo
cal plasma the most convenient method simplifying re
search of the kinetic equation (KE) is nonlocal approach
[2,3]. Within the framework of this method all particles
are separated on the flying and trapped. The last make os
cillations inside the potential hole created by a field of a
spatial charge. By virtue of that basically collision be
tween themselves (without the change of energy), it is
possible to count their movement collisionless. Therefore
EEDF of trapped electrons depends only on full energy
ε=weΦ s x (here w=mv2
2
- electron kinetic en
ergy), that has experimental confirmation [4]. This fact al
lows transferring the KE - the six-dimensional equation in
patrician derivatives - in the one-dimensional ordinary
differential equation (ODE). Such simplification is
achieved by averaging the equation on the cross-section
accessible to particles with energy ε :
∑ νk
¿ εε k
¿ ׿
d
dε
{D ε
∂ f 0
0 ε
∂ ε
V ε f 0
0 ε }=¿
¿
¿
ε k
¿ε
ε
f 0
0 εεk
¿ −νk
¿ w f 0
0 ε
f 0
0 ε ׿
¿−¿
¿ν ion ε − ε2I
ε f 0
0 ε2I νion ε2I
¿¿
(2)
where such designations are entered: εk
¿ , I - excitation
potentials on k power level and shock ionization of neu
tral atom from the basic condition accordingly; ν k
¿ , ν ion
- frequencies of excitation on k power level and the shock
ionization, average on cross-section section, accordingly;
the badge A means procedure of averaging on the cross-
section section accessible to particles with energy ε .
The power diffusion coefficients are determined as the
sum of three composes: D ε=D xD zDql , where
first two composed describe the diffusion due to anomalous
skin-effect on the bounce electrons which obvious kind is re
sulted in [1], and the third composed corresponds to the qua
sylinear diffusion arising in a vicinity of a point of a plasma
resonance, determined according to [5].
2. BASIC ASSUMPTIONS
However to find analytical solutions of the equa
tion (2) without simplifying assumptions is not probably.
Therefore we break space of energy into ranges, in each
of which the kind of the collision integral becomes sim
pler. So the second composed in the left part (2) describes
change of the EEDF due to elastic collisions, and the right
part of this equation - due to inelastic collisions. Thus the
first and the third composed in the right part take into ac
count return of electrons in low-energy area as a result of
inelastic collisions (excitation and shock ionization ac
cordingly).
We enter a threshold of inelastic processes - po
tential of excitation on the lowest allowed power level
ε1 . In the energy range εε1 inelastic processes are
insignificant, therefore it is possible to put the right part
of the KE (2) equal to zero. The solution of the received
equation is determined by the following ratio:
66 Problems of Atomic Science and Technology. 2005. № 1. Series: Plasma Physics (10). P. 66-68
f 0 ε =C1∫
ε
ε0
exp[∫
ε
ε'
dε ''
V ε ε
''
Dε ε
''
] dε '
Dε ε '
(3)
where constants of integration are defined at the solutions
sew together.
But here it is necessary to insert one more energy
range 0ε kT 1 , where kT 1 is a small power
scale of wane EEDF. This scale of wane is numerically
equal to the energy which remaining at the electron after
inelastic impact. Therefore it is necessary to take into ac
count the first and the third composed in the right part (2).
The solution of the received equation:
f 0 ε =∫
ε
ε0 dε '
D ε ε
'
∫
0
ε '
dε '' ε ''ε 1
ε ''
ν¿ ε ''ε 1׿
¿
¿ f 0 ε
''ε1 (4)
With the account of (4) the EEDF (3) it is valid in the
energy range kT 1 εε1 . The following power
range- ε1εε2 , where ε2=−eΦwall -is a wall po
tential of the chamber. In this energy range it is neglected
by elastic collisions (the second composed in the left part
(2)) and the electrons returning in the area of small ener
gy after inelastic processes (the first and the third com
posed in the right part (2)). But also in this case we re
ceive the equation with variable coefficients. For possibil
ity of its solution we shall simulate dependence of fre
quency of inelastic processes on energy as degree func
tion: ν inel ε =ν0[
ε−eΦs x
ε
−1 ]p−1 . Then with
the account of (1) the solution of KE in this energy range
is determined by the following ratio:
f 0 ε ={B1 K μ σ
2
μ B2 I μ σ
2
μ } ε
ε 1
−1
(5)
where K μ x , I μ x - McDonald's and Bessel cylin
drical functions of the second kind about μ accordingly;
μ= 1
p2 ; σ=
ε−ε 1
kT 1
; the power scale of wane of
the EEDF in inelastic area is defined by the following ra
tio: kT 1 =[ 4
μν1
ε 1
p Dε ε1 ]
μ
. It is necessary to no
tice, that the EEDF as (5) coincides with subintegral dis
tribution function in (4).
At the energies εε2 nonlocal approach is not ap
plicable, since it is limited on the field value by the condi
tion eE λε1 . In this energy range it is necessary to
solve not KE (2), and to solve the kinetic equation in view
of spatial gradients. But the electrons energy should ex
ceed potential of a wall on small size for an opportunity
sew together received solutions with received by means
of nonlocal approach. For the same reason it is possible to
neglect dependence of the coefficients in KE from energy
and to take their values at ε=ε2 . The solution for EEDF
in the energy range εε2 has the following kind:
f 0 ε , x =Cn exp {−nπ
ε−ε 2
kT 2
}cos nπ x
d
(6)
where: kT 2 =d D ε ε2
D x ε 2
(the coefficient of spatial
diffusion is determined by the following ratio-
D x=
2e
3m
ε−eΦs x
3
2
νen ε−eΦ s x
) - small power scale of
the wane EEDF in tail area. Carrying out the sew
together of the solutions (4) - (7) in the points ε=ε1
also ε=ε2 we find values of the constants of integra
tion:
B2=−B1
π
2
exp {−2σ
2
μ} ;
Cn=B1
2
μ
kT 2
kT 1
4 1
σ π
2
kT 1
ε1
exp {−σ
2
μ} ;
B1=C1
ε1
Χ 1
V ε ε1
Dε ε1
exp {−∫
0
ε1 V ε ε
Dε ε
dε } ,
And value of a constant C1 is defined by the value of the
plasma density on the axis of a layer. Having de
fined ratio for EEDF, we can [6] define in the standard
image distributions of the discharge characteristics. So
with the help of a ratio:
n x =4 2π
m
3
2
∫
−eΦ s x
∞
ε−eΦ s x
3
2 f 0 ε dε
(7)
it is possible to find spatial distribution of the plasma den
sity. By means of a ratio:
D x x = 8π
3m2 ∫
=eΦ s x
∞
ε−eΦ s x 2
f 0 ε
νen ε
dε
(8)
coefficient of spatial diffusion. By means of a ratio:
ν inel x =
8πN a
m2 ∫
−eΦs x
∞
ε−eΦs x ׿
¿
¿σ inel ε f 0 ε dε (9)
distributions of the frequency of inelastic processes. And
a ratio:
W={4πV2 D ε ε
∂ f 0 ε
∂V
}∣V =V inel
(10)
Where N a - concentration of neutral atoms; σ inel -
sections of inelastic processes (excitation, shock ioniza
tion, etc.). And included in the ratio (8) - (11) EEDF are
defined according to (4) - (7). EEDF is determined
through the coefficient of power diffusion, and in plasma
of the low pressure there is a contribution from anoma
lous skin-effect on the bounce electrons. As shown in [1]
in the collisionless limit the contribution from the bounce
electrons at least is not less, than the contribution from the
quasylinear diffusion. It means that in the field of low
pressure vary EEDF. And it conducts to change of all dis
charge characteristics.
3. CONCLUSIONS
The non self-consistent theory of the discharge sus
tained by SW is constructed. Solutions for EEDF in ap
proximation of the set field various power ranges of ener
gy are received. With the help of this ratio discharge char
acteristics are found. From them the contribution given by
the bounce electrons follows, that under certain conditions
can become dominating.
REFERENCES
1. N.A.Azarenkov et al, submitted to Quest. of Atom.
Sci. and Tech. 2004.
2. V.I.Kolobov, V.A.Godyak // IEEE Trans. Plasma
Sci.(23). 1995, p.503-531.
3. U.Kortshagen, C.Busch et al.// Plasma Sources Sci.
Techn. (5). 1996,p.1-17.
4. U.Kortshagen //Phys.Rew.E (49). 1994, p.4369-4379.
5. Yu.M.Aliev, A.V.Maximov et al. // Phys.Rew.E (51).
1995, p.6091-6103.
6. L.D.Tsendin, Y.B.Golubovskii // Sov. J. Tech. Phys.
(22), 1977, p.1066-1075.
ВЛИЯНИЕ АНОМАЛЬНОГО СКИН-ЭФФЕКТА НА РАЗРЯД ПОДДЕР
ЖИВАЕМЫЙ ПОВЕРХНОСТНЫМИ ВОЛНАМИ
Н.А.Азаренков, Владимир В. Гущин, Валерий В.Гущин
В данной работе построена несамосогласованная теория разряда, поддерживаемого ПВ. В приближе
нии заданного поля найдены аналитические решения для ФРЭЭ. Получены приближенные распределения раз
рядных характеристик, таких как плотность плазмы, коэффициент пространственной диффузии, частоты эле
ментарных процессов (возбуждения, ионизации и т.п.) и количество неупругих процессов. Показано, что при
определенных условиях вклад от bounce электронов может стать определяющим.
ВПЛИВ АНОМАЛЬНОГО СКІН-ЕФЕКТУ НА РОЗРЯД, ЩО ПІДТРИМУ
ЄТЬСЯ ПОВЕРХНЕВИМИ ХВИЛЯМИ
М.О.Азарєнков, Володимир В. Гущин, Валерій В. Гущин
В даній роботі побудовано самоузгоджену теорію розряду, що підтримується ПХ. У наближенні за
даного поля знайдено аналітичні рішення для ФРЕЕ. Отримано наближені розподіли характеристик розряду, та
ких як густина плазми, коефіцієнт просторової дифузії, частоти елементарних процесів (збудження, іонізації та
ін.) та кількості процесів. Показано, що за певних умов bounce електрони можуть відігравати визначну роль.
68
|
| id | nasplib_isofts_kiev_ua-123456789-78656 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:47:46Z |
| publishDate | 2005 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Azarenkov, N.A. Gushchin, Vladimir V. Gushchin, Valery V. 2015-03-19T18:01:33Z 2015-03-19T18:01:33Z 2005 The influence of anomalous skin-effect no the discharge sustained by surface wave / N.A. Azarenkov, Vladimir V. Gushchin, Valery V. Gushchin // Вопросы атомной науки и техники. — 2005. — № 1. — С. 66-68. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.50-b; 52.80 Pi; Dg.52.25. Fi https://nasplib.isofts.kiev.ua/handle/123456789/78656 In the present work the non self-consistent theory of the discharge sustained by SW. In the approximation of the set field analytical ratio for EEDF are found. The approached distributions of discharge parameters, such as plasma density, spatial diffusion coefficient, frequencies of elementary processes (excitation, ionization, etc.), and quantities of inelastic processes are received. It is shown, that under certain conditions the contribution to them from bounce electrons can become determining. В даній роботі побудовано самоузгоджену теорію розряду, що підтримується ПХ. У наближенні заданого поля знайдено аналітичні рішення для ФРЕЕ. Отримано наближені розподіли характеристик розряду, таких як густина плазми, коефіцієнт просторової дифузії, частоти елементарних процесів (збудження, іонізації та ін.) та кількості процесів. Показано, що за певних умов bounce електрони можуть відігравати визначну роль. В данной работе построена несамосогласованная теория разряда, поддерживаемого ПВ. В приближении заданного поля найдены аналитические решения для ФРЭЭ. Получены приближенные распределения разрядных характеристик, таких как плотность плазмы, коэффициент пространственной диффузии, частоты элементарных процессов (возбуждения, ионизации и т.п.) и количество неупругих процессов. Показано, что при определенных условиях вклад от bounce электронов может стать определяющим. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Basic plasma physics The influence of anomalous skin-effect no the discharge sustained by surface wave Вплив аномального скін-ефекту на розряд, що підтримується поверхневими хвилями Влияние аномального скин-эффекта на разряд поддерживаемый поверхностными волнами Article published earlier |
| spellingShingle | The influence of anomalous skin-effect no the discharge sustained by surface wave Azarenkov, N.A. Gushchin, Vladimir V. Gushchin, Valery V. Basic plasma physics |
| title | The influence of anomalous skin-effect no the discharge sustained by surface wave |
| title_alt | Вплив аномального скін-ефекту на розряд, що підтримується поверхневими хвилями Влияние аномального скин-эффекта на разряд поддерживаемый поверхностными волнами |
| title_full | The influence of anomalous skin-effect no the discharge sustained by surface wave |
| title_fullStr | The influence of anomalous skin-effect no the discharge sustained by surface wave |
| title_full_unstemmed | The influence of anomalous skin-effect no the discharge sustained by surface wave |
| title_short | The influence of anomalous skin-effect no the discharge sustained by surface wave |
| title_sort | influence of anomalous skin-effect no the discharge sustained by surface wave |
| topic | Basic plasma physics |
| topic_facet | Basic plasma physics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/78656 |
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