Surface wave attenuation caused by secondary electron emission
This study aims to contribute to the analysis of the mechanisms of surface-wave-energy absorption. The discussion is based on a consideration of emissive processes from dielectric surface, which is in contact with collisional nonisothermal plasma, and on an analysis of secondary electron motion in t...
Gespeichert in:
| Veröffentlicht in: | Вопросы атомной науки и техники |
|---|---|
| Datum: | 2005 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
|
| Schlagworte: | |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/79345 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Surface wave attenuation caused by secondary electron emission/ Yu.A. Akimov, V.P. Olefir // Вопросы атомной науки и техники. — 2005. — № 2. — С. 64-66. — Бібліогр.: 6 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859824653209436160 |
|---|---|
| author | Akimov, Yu.A. Olefir, V.P. |
| author_facet | Akimov, Yu.A. Olefir, V.P. |
| citation_txt | Surface wave attenuation caused by secondary electron emission/ Yu.A. Akimov, V.P. Olefir // Вопросы атомной науки и техники. — 2005. — № 2. — С. 64-66. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | This study aims to contribute to the analysis of the mechanisms of surface-wave-energy absorption. The discussion is based on a consideration of emissive processes from dielectric surface, which is in contact with collisional nonisothermal plasma, and on an analysis of secondary electron motion in the wave-fields. Through electron acceleration due to the action of ponderomotive force, the secondary emission affects the wave behavior. The role of secondary emission in maintenance of wave-produced gas discharges is discussed as well.
В роботі проведено аналіз механізмів поглинання енергії поверхневих хвиль. Розглянуто процеси емісії з поверхні діелектрика, що знаходиться у контакті з низькотемпературною плазмою. Проведено аналіз руху вторинних електронів в полі хвилі. Показано, що вторинна електронна емісія приводить до додаткового загасання хвилі, обумовленого прискоренням вторинних електронів в полі хвилі, унаслідок дії сили високочастотного тиску. Проведено аналіз впливу вторинної емісії на підтримку розряду на поверхневих хвилях.
Проведен анализ механизмов поглощения энергии поверхностных волн. Рассмотрены эмиссионные процессы с поверхности диэлектрика, находящегося в контакте с низкотемпературной плазмой. Проведен анализ движения вторичных электронов в поле волны. Показано, что вторичная электронная эмиссия приводит к дополнительному затуханию волны, обусловленному ускорением вторичных электронов в поле волны, вследствие действия силы высокочастотного давления. Проведен анализ влияния вторичной эмиссии на поддержание разряда на поверхностных волнах.
|
| first_indexed | 2025-12-07T15:27:36Z |
| format | Article |
| fulltext |
SURFACE WAVE ATTENUATION CAUSED BY
SECONDARY ELECTRON EMISSION
Yu.A. Akimov, V.P. Olefir
Department of Physics and Technology, Institute of High Technologies,
V.N. Karazin Kharkov National University, Kharkov, Ukraine,
E-mail: olefir@pht.univer.kharkov.ua
This study aims to contribute to the analysis of the mechanisms of surface-wave-energy absorption. The discussion
is based on a consideration of emissive processes from dielectric surface, which is in contact with collisional non-
isothermal plasma, and on an analysis of secondary electron motion in the wave-fields. Through electron acceleration
due to the action of ponderomotive force, the secondary emission affects the wave behavior. The role of secondary
emission in maintenance of wave-produced gas discharges is discussed as well.
PACS: 52.25.Tx, 52.35.Mw
1. INTRODUCTION
It is well known that the efficiency of power transfer
from a guided wave to a plasma depends on the
dissipation mechanisms, the most important of which are
collisions and absorption of wave power by local wave-
plasma resonance [1-4]. Depending on the operating gas-
pressure and other discharge parameters, some of them
can dominate over the other [4]. Here we will consider
another mechanism of wave-energy dissipation caused by
secondary electron emission (SEE) from dielectric
surface. It can be important, e.g. to maintain surface-
wave-produced gas discharges.
2. SURFACE WAVES
This study concerns the behavior of surface wave
(SW) of frequency with wavenumber , propagating
in planar plasma waveguides. The waveguide
configuration considered here consists of an
inhomogeneous non-isothermal ( , and are
the electron and ion temperatures) collisional plasma
occupying the half-space and surrounded by
dielectric situated in . The inhomogeneous plasma
forms a uniform core of the plasma in and a
transition layer of the width d in the region
ω zk
ie TT >> eT iT
0>x
0<x
dx >
dx <<0
close to the plasma-dielectric interface. In the non-
uniform transition layer the plasma density drops rapidly
from the uniform value in the core to some finite
value at the plasma-dielectric interface. We will consider
the strong plasma-density inhomogeneity, when
or what is equivalent to
0n
1−κ<< pd ppp dxd εκ>>ε / .
Here characterizes penetration depths of
the wave-fields into plasma; is the vacuum
wavenumber, and is the speed of light in vacuum. The
dielectric permittivities of the mediums are denoted by
for the dielectric and by for
the plasma. In the expression for plasma permittivity,
and are the plasma and electron collision frequencies,
respectively.
pzp kk ε−=κ 222
ck
64 Problems of Atomic Science and Technology. Series: Plasma Physics (11). 2005. № 2. P. 64-66
/ω=
c
dε )](/[1 2 ν+ωωω−=ε ipp
pω
ν
In such waveguides, SWs are well known to be slow
E-waves with the phase velocities less than the speed
of light in dielectric [3].
phV
The continuity of the tangential wave-field
components at the interfaces and 0=x dx =
(expressions for the wave-fields under the above-
mentioned condition can be found, e.g. in [3]) yields the
well-known results for the wavenumber : )(ωzk
)/( dpdpz kk ε+εεε= (1)
and the damping rate: rescoll γ+γ=γ , caused by both
electron collisions:
dp
pdcol
ε+ε
ε−ε
ω
ν
=
ω
γ
2
)1(
2
, (2)
and excitation of the Langmuir wave near the resonant
point , where : 0x 0)( 0 =ε xp
)1(32
222
pdppd
dp
dp
pres k
ε−εε−ε−ε
εε
ε+ε
ε
−πη−=
ω
γ
. (3)
In (1)-(3), is respective value in the region of
uniform plasma core; with
being the unit step function, equal to 0 for
)(dpp ε≡ε
1
0
)/))(0(( −
=εε=η xxpp dxdP
)(yP 0<y ,
and 1 for . 0≥y
To mark, in these relations it has been taken into
account that the electron collision frequency is less than
the wave frequency ( ω<<ν ), and therefore, with the
accuracy of the order of , . 0)/( ων 22 /1 ωω−=ε pp
Later we will use the total wave-energy stored up in
the plasma and dielectric per unit of the area:
)2exp(
)1(
16 2
p
3
p
2
d
2
2
0 t
k
E
W pdp
d
dp
s γ−
ε
ε−εε−ε−ε
ε
ε+ε
−
π
= ,
where being the amplitude value of -field at the
plasma-dielectric interface ( ). According to this
expression, the energy of SWs dissipates, that the power
transferred to a plasma per unit of the area is equal to
0E zE
0=x
sWγ2 . The part scollWγ2 of this power is liberated to a
plasma layer of the width of about the wave-field
penetration depth into the plasma. The remaining
power
1−κ p
sresWγ2 is transferred to the Langmuir wave and
goes to a narrow resonant layer, the width of which is of
the order
of [3]. Thus, spatial distribution of the wave-
power input to the plasma is determined by factor
2dpκ
rescoll γγ / and contracts, under a low gas-pressure, when
1/ <<γγ rescoll , to the narrow resonant layer.
To note, both these attenuations (collisional and
resonant) are reputed to be most important for SWs. But,
among of a variety of dissipative mechanisms, there is
another one, whose effect on SWs is surprisingly high
and can dominate, under certain conditions, over those of
the collisions and resonance. This mechanism is
connected with secondary electron emission.
3. SECONDARY ELECTRON EMISSION
First, let us briefly consider main features of the
secondary emission. As it is well known [5], when a
dielectric surface is bombarded by plasma particles, it is
charged negatively, building up that electric field, which
brakes plasma electrons and accelerates plasma ions to
the surface. At the same time there is a SEE from the
dielectric. In dynamic equilibrium, the dielectric potential
can be found from equation: ϕ
ieTeee meTeV /4)/exp()1( ϕπ−=ϕσ− . (4)
It should be noted that in (4) the SEE yield eeσ is
determined by energy of the incident electrons [6].
Usually, this dependence is characterized by a maximum
, which is attained under the incident electron energy
(for fused silica
mσ
me EE = 1.2≅σm , eV [5]).
For low energies, , this dependence is linear.
For gas-discharge plasmas, the latter condition is fulfilled
inside a wide range of the electron temperature .
Therefore we will use a linear approximation of the very
beginning of this curve, where it can be represented as the
following [5]:
400≅mE
me EE <<
eT
memee EE /4σ=σ (5)
For the Maxwellian distribution of the incident electrons,
the mean energy is given by
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
ϕ−−
ϕϕ−
π
+=
e
eee
e Teerf
TeTeT
E
/1
)/exp(/21
2
(6)
with the error function erf.
Solving equation (4) with (5) and (6), one can get the
dielectric potential and SEE coefficient ϕ eeσ as
functions of the electron temperature , sort of gas and
dielectric characteristics. To mark, the mean velocity ,
with which secondary electrons arrive at the plasma core,
after their acceleration in the electric field of the
transition layer, is of the order of the thermal velocity
, and, because the SWs considered have phase
velocities much more than [3], . This
fact will be used later, in the secondary electron motion
computation.
eT
0V
TeV
TeV 1/0 <<phVV
65
4. RESULTS AND DISCUSSION
The secondary electron flux can lead to the
significant, especially under a low gas-pressure , wave
attenuation. It is connected with the fact that the wave-
fields decrease exponentially deep into the plasma. It
leads to acceleration of the secondary electrons in the
wave-fields due to the action of ponderomotive force,
which pushes them out to the region of weaker fields.
Damping rate of this attenuation
p
seeγ one can find from
the energy balance equation. Introducing the
dimensionless wave-field amplitude )/(~ 2
00 ω= ez mkeEE
and electron velocity phVVV /~ = , the normalized
damping rate can be written as
.
)1(
)1(
2
)/exp(
)~,~(
32
00
pdppd
pdp
d
p
ph
Tee
ee
see
V
VTe
EVF
ε−εε−ε−ε
ε−εε
ε
ε
−⋅
π
ϕ
σ−=
ω
γ
(7)
Thus, the total damping rate is seerescoll γ+γ+γ=γ . The
parameter >−=< 2
0
22
00
~/)~~()~,~( EVVEVF in (7) can be
found from the equation of electron motion in the wave-
fields:
,~
~
~
,~
~
~
),~~exp(]~sin~~[cos~
~
~
),~~exp(~sin)]1~(1[~
~
~
~
0
0
zx
pz
z
pz
p
x
V
td
zdV
td
xd
xzVAzE
td
Vd
xzVA
E
td
Vd
==
ε−−−−=
ε−−++−
ε−
−=
(8)
where ω= tt~ , xkx z=~ , )(~ tVzkz phz −= , phxx VVV /~ = ,
1/~ −= phzz VVV , ppA ε−ε+= ~/)~1( , dpp εε=ε /~ .
The system (8) has been solved numerically with the
following initial conditions for the secondary electrons:
0~0 =x , 1~
0 <<xV , 1~
0 −=zV . The initial electron positions
0
~z has been varied from 0 till . After averaging of the
coefficient
π2
2
0
22 ~/)~~( EVV − over the initial positions 0
~z ,
the parameter )~,~( 00 EVF has been calculated. The
maximum max 0.2)~,~( 00 ≈EVF is achieved under
1~ −=εp (the quasistatic surface waves), whereas the
minimum min 5.0)~,~( 00 ≈EVF is reached under
−∞→εp
~ .
In that way one can get dependence of the normalized
damping rate (7) on the plasma parameters and wave-
0.00 0.05 0.10 0.15
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
ωγ /see
pωω /
eVTe 5=
eVTe 2=
eVTe 1=
Dimensionless SEE-induced damping rate
frequency (see Figure). The analysis of the dependence
reveals, the SEE mechanism of wave-energy dissipation
is especially effective for low-frequency SW propagating
in dense plasmas with high electron temperature.
Let us compare the SEE-induced damping rate (7)
with the resonant one (3). To note, contribution of SEE to
the SW attenuation increases with a growth of plasma
permittivity (or with a wave-frequency drop). However,
in the high-frequency range, where , the
resonant attenuation predominates over the SEE-induced
damping, that the latter can be neglected.
0)0( ≥ε p
66
For the low-frequency waves, when , the
plasma resonance is absent, and wave attenuation is
determined by plasma electron collisions and SEE only.
Thus, under a low gas-pressure, contribution of SEE to
the wave-energy dissipation becomes comparable with
that of electron collisions. The numerical estimates
carried out for the argon plasma under the gas-pressure
, electron temperature , plasma
density , and the collision frequency
, reveal that a wave with the frequency
damps with the
normalized rate
0)0( <ε p
mTorrp 5= eVTe 2≈
311
0 107.1 −⋅≈ cmn
MHz9.2≈ν
MHz360)2/( =πω )100( −=ε p
=ωγ+γ=ωγ /)(/ seecoll
5100.3 −⋅ . To
note, for this conditions the contributions of both
mechanisms are equal: 0.1/ =γγ collsee . Investigation of
the electron temperature effect on dependence of
on the normalized wave-frequency
for argon plasma bounded by fused silica has shown that
the SEE-induced damping is especially essential for low-
frequency SWs with .
)/)(/( pcollsee ωνγγ
pω<<ω
Below we will apply the results obtained to planar
waveguide discharges maintained by SWs. No doubt, this
model is too simple to describe surface-wave-produced
discharges, but it allows to better understand the
processes lying on the basis of this phenomenon.
First of all, SEE from dielectric surface leads to an
additional wave-energy dissipation channel and, as a
result, to an increase of the wave-power transferred into a
plasma. Secondly, besides the main energy source (by
surface wave) for discharge maintenance, an additional
source (by SEE) arises. The power of surface wave and
that of SEE transferred for plasma sustention can be of
the same order:
2
0
2
000
2
000
~2~)~,~(
~)~,~(
VEEVF
EEVF
P
P
seeSEE
SW
+γ
γ
= , (9)
especially under a low gas-pressure of a dense plasma
( ), when
p
1/ >>ωω p seeγ≈γ . That situation is also
typical of near a discharge end, where the wave-field
amplitude decreases that 00
~~ VE ≤ . In those discharge
regions, plasma is sustained, mainly, by SEE. At the same
time, not only amount of the power transferred to a
plasma but also its spatial distribution, which determines
that of plasma parameters, are relevant. So, in contrast to
the surface wave power maintaining plasma in a layer
with the width of λ<<εε−≈κ −− 11 / zpdp k , the SEE can
sustain it within a layer of several wavelengths λ .
REFERENCES
1. Y.A. Romanov // Sov. Phys.-Techn. Phys. (47). 1964,
p. 2119.
2. K.N. Stepanov // Sov. Phys.-Techn. Phys. (10). 1965,
p.773.
3. A.N. Kondratenko. Plasma Waveguides. Moscow:
“Atomizdat”, 1976.
4. A. Shivarova, K. Tarnev // Plasma Sources Sci.
Technol. (10). 2001, p. 260.
5. I.M. Bronshtein, B.S. Friman. Secondary Electron
Emission. Moscow: “Nauka”, 1969.
6. E.J. Sternglass. Theory of Secondary Electron
Emission under Electron Bombardment.
Westinghouse Research Laboratories, Pittsburgh,
Scientific Paper 6-94410-2-P9, Jul. 1957.
ЗАТУХАНИЕ ПОВЕРХНОСТНЫХ ВОЛН ВСЛЕДСТВИЕ ВТОРИЧНОЙ ЭЛЕКТРОННОЙ ЭМИССИИ
Ю.А. Акимов, В.П. Олефир
Проведен анализ механизмов поглощения энергии поверхностных волн. Рассмотрены эмиссионные
процессы с поверхности диэлектрика, находящегося в контакте с низкотемпературной плазмой. Проведен
анализ движения вторичных электронов в поле волны. Показано, что вторичная электронная эмиссия приводит
к дополнительному затуханию волны, обусловленному ускорением вторичных электронов в поле волны,
вследствие действия силы высокочастотного давления. Проведен анализ влияния вторичной эмиссии на
поддержание разряда на поверхностных волнах.
ЗАГАСАННЯ ПОВЕРХНЕВИХ ХВИЛЬ УНАСЛІДОК ВТОРИННОЇ ЕЛЕКТРОННОЇ ЕМІСІЇ
Ю.О. Акімов, В.П. Олефір
В роботі проведено аналіз механізмів поглинання енергії поверхневих хвиль. Розглянуто процеси емісії з
поверхні діелектрика, що знаходиться у контакті з низькотемпературною плазмою. Проведено аналіз руху
вторинних електронів в полі хвилі. Показано, що вторинна електронна емісія приводить до додаткового
загасання хвилі, обумовленого прискоренням вторинних електронів в полі хвилі, унаслідок дії сили
67
високочастотного тиску. Проведено аналіз впливу вторинної емісії на підтримку розряду на поверхневих
хвилях.
4. RESULTS AND DISCUSSION
REFERENCES
|
| id | nasplib_isofts_kiev_ua-123456789-79345 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T15:27:36Z |
| publishDate | 2005 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Akimov, Yu.A. Olefir, V.P. 2015-03-31T13:52:54Z 2015-03-31T13:52:54Z 2005 Surface wave attenuation caused by secondary electron emission/ Yu.A. Akimov, V.P. Olefir // Вопросы атомной науки и техники. — 2005. — № 2. — С. 64-66. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.25.Tx, 52.35.Mw https://nasplib.isofts.kiev.ua/handle/123456789/79345 This study aims to contribute to the analysis of the mechanisms of surface-wave-energy absorption. The discussion is based on a consideration of emissive processes from dielectric surface, which is in contact with collisional nonisothermal plasma, and on an analysis of secondary electron motion in the wave-fields. Through electron acceleration due to the action of ponderomotive force, the secondary emission affects the wave behavior. The role of secondary emission in maintenance of wave-produced gas discharges is discussed as well. В роботі проведено аналіз механізмів поглинання енергії поверхневих хвиль. Розглянуто процеси емісії з поверхні діелектрика, що знаходиться у контакті з низькотемпературною плазмою. Проведено аналіз руху вторинних електронів в полі хвилі. Показано, що вторинна електронна емісія приводить до додаткового загасання хвилі, обумовленого прискоренням вторинних електронів в полі хвилі, унаслідок дії сили високочастотного тиску. Проведено аналіз впливу вторинної емісії на підтримку розряду на поверхневих хвилях. Проведен анализ механизмов поглощения энергии поверхностных волн. Рассмотрены эмиссионные процессы с поверхности диэлектрика, находящегося в контакте с низкотемпературной плазмой. Проведен анализ движения вторичных электронов в поле волны. Показано, что вторичная электронная эмиссия приводит к дополнительному затуханию волны, обусловленному ускорением вторичных электронов в поле волны, вследствие действия силы высокочастотного давления. Проведен анализ влияния вторичной эмиссии на поддержание разряда на поверхностных волнах. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Basic plasma physics Surface wave attenuation caused by secondary electron emission Загасання поверхневих хвиль унаслідок вторинної електронної емісії Затухание поверхностных волн вследствие вторичной электронной эмиссии Article published earlier |
| spellingShingle | Surface wave attenuation caused by secondary electron emission Akimov, Yu.A. Olefir, V.P. Basic plasma physics |
| title | Surface wave attenuation caused by secondary electron emission |
| title_alt | Загасання поверхневих хвиль унаслідок вторинної електронної емісії Затухание поверхностных волн вследствие вторичной электронной эмиссии |
| title_full | Surface wave attenuation caused by secondary electron emission |
| title_fullStr | Surface wave attenuation caused by secondary electron emission |
| title_full_unstemmed | Surface wave attenuation caused by secondary electron emission |
| title_short | Surface wave attenuation caused by secondary electron emission |
| title_sort | surface wave attenuation caused by secondary electron emission |
| topic | Basic plasma physics |
| topic_facet | Basic plasma physics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79345 |
| work_keys_str_mv | AT akimovyua surfacewaveattenuationcausedbysecondaryelectronemission AT olefirvp surfacewaveattenuationcausedbysecondaryelectronemission AT akimovyua zagasannâpoverhnevihhvilʹunaslídokvtorinnoíelektronnoíemísíí AT olefirvp zagasannâpoverhnevihhvilʹunaslídokvtorinnoíelektronnoíemísíí AT akimovyua zatuhaniepoverhnostnyhvolnvsledstvievtoričnoiélektronnoiémissii AT olefirvp zatuhaniepoverhnostnyhvolnvsledstvievtoričnoiélektronnoiémissii |