Effect of secondary emission on the afterglow of argon with negatively charged dust particles
A theoretical model for an argon/dusty plasma afterglow in presence of nano-sized dust particles with large density is developed. According to the model, in the plasma afterglow the electrons are generated in metastable collisions and in the secondary emission by collisions of ions with electrodes....
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| Cite this: | Effect of secondary emission on the afterglow of argon with negatively charged dust particles / I.B. Denysenko, I. Stefanović, N.A. Azarenkov, G.P. Burmaka // Вопросы атомной науки и техники. — 2014. — № 6. — С. 157-159. — Бібліогр.: 11 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-819522025-02-09T16:52:15Z Effect of secondary emission on the afterglow of argon with negatively charged dust particles Влияние вторичной эмиссии на распад аргоновой плазмы, которая содержит негативно заряженные пылевые частицы Вплив вторинної емісії на розпад аргонової плазми, що містить негативно заряджені пильові частинки Denysenko, I.B. Stefanović, I. Azarenkov, N.A. Burmaka, G.P. Низкотемпературная плазма и плазменные технологии A theoretical model for an argon/dusty plasma afterglow in presence of nano-sized dust particles with large density is developed. According to the model, in the plasma afterglow the electrons are generated in metastable collisions and in the secondary emission by collisions of ions with electrodes. By using the model and experimental time-dependencies for metastable density and electrode bias, the time-dependencies for electron density in argon/dusty plasma afterglow are calculated. The effect of secondary emission on electron generation in argon/dusty plasma afterglow is analyzed. Разработана теоретическая модель распадающейся пылевой аргоновой плазмы, которая имеет высокую плотность наноразмерных пылинок. Данная модель учитывает генерацию электронов при столкновениях метастабильных атомов между собой и благодаря вторичной эмиссии при столкновениях ионов с электродами. Используя эту модель и экспериментальные временные зависимости для плотности метастабильных атомов и потенциала электродов, рассчитаны временные зависимости для плотности электронов в пылевой распадающейся аргоновой плазме. Проанализировано влияние вторичной эмиссии на генерацию электронов в этой среде. Розроблено теоретичну модель пилової аргонової плазми, що розпадається, та має високу густину порошинок нанорозміру. Дана модель враховує генерацію електронів при зіткнені метастабільних атомів між собою та завдяки вторинній емісії при зіткнені іонів з електродами. Використовуючи цю модель та експериментальні часові залежності для густини метастабільних атомів та потенціалу електродів, розраховано часові залежності для густини електронів у запорошеній аргоновій плазмі, що розпадається. Проаналізовано вплив вторинної емісії на генерацію електронів у цьому середовищі. 2014 Article Effect of secondary emission on the afterglow of argon with negatively charged dust particles / I.B. Denysenko, I. Stefanović, N.A. Azarenkov, G.P. Burmaka // Вопросы атомной науки и техники. — 2014. — № 6. — С. 157-159. — Бібліогр.: 11 назв. — англ. 1562-6016 PACS: 52.25.Vy, 52.27.Lw, 51.50.+v, 52.80.Pi https://nasplib.isofts.kiev.ua/handle/123456789/81952 en Вопросы атомной науки и техники application/pdf Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии |
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Низкотемпературная плазма и плазменные технологии Низкотемпературная плазма и плазменные технологии Denysenko, I.B. Stefanović, I. Azarenkov, N.A. Burmaka, G.P. Effect of secondary emission on the afterglow of argon with negatively charged dust particles Вопросы атомной науки и техники |
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A theoretical model for an argon/dusty plasma afterglow in presence of nano-sized dust particles with large density is developed. According to the model, in the plasma afterglow the electrons are generated in metastable collisions and in the secondary emission by collisions of ions with electrodes. By using the model and experimental time-dependencies for metastable density and electrode bias, the time-dependencies for electron density in argon/dusty plasma afterglow are calculated. The effect of secondary emission on electron generation in argon/dusty plasma afterglow is analyzed. |
| format |
Article |
| author |
Denysenko, I.B. Stefanović, I. Azarenkov, N.A. Burmaka, G.P. |
| author_facet |
Denysenko, I.B. Stefanović, I. Azarenkov, N.A. Burmaka, G.P. |
| author_sort |
Denysenko, I.B. |
| title |
Effect of secondary emission on the afterglow of argon with negatively charged dust particles |
| title_short |
Effect of secondary emission on the afterglow of argon with negatively charged dust particles |
| title_full |
Effect of secondary emission on the afterglow of argon with negatively charged dust particles |
| title_fullStr |
Effect of secondary emission on the afterglow of argon with negatively charged dust particles |
| title_full_unstemmed |
Effect of secondary emission on the afterglow of argon with negatively charged dust particles |
| title_sort |
effect of secondary emission on the afterglow of argon with negatively charged dust particles |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2014 |
| topic_facet |
Низкотемпературная плазма и плазменные технологии |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/81952 |
| citation_txt |
Effect of secondary emission on the afterglow of argon with negatively charged dust particles / I.B. Denysenko, I. Stefanović, N.A. Azarenkov, G.P. Burmaka // Вопросы атомной науки и техники. — 2014. — № 6. — С. 157-159. — Бібліогр.: 11 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-11-28T04:54:47Z |
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2025-11-28T04:54:47Z |
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| fulltext |
ISSN 1562-6016. ВАНТ. 2014. №6(94)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2014, №6. Series: Plasma Physics (20), p. 157-159. 157
EFFECT OF SECONDARY EMISSION ON THE AFTERGLOW OF
ARGON WITH NEGATIVELY CHARGED DUST PARTICLES
I.B. Denysenko1, I. Stefanović2, N.A. Azarenkov1, G.P. Burmaka1
1V.N. Karazin Kharkiv National University, Kharkiv, Ukraine;
2Institute of Physics, University of Belgrade, Belgrade, Serbia
E-mail: idenysenko@yahoo.com
A theoretical model for an argon/dusty plasma afterglow in presence of nano-sized dust particles with large
density is developed. According to the model, in the plasma afterglow the electrons are generated in metastable
collisions and in the secondary emission by collisions of ions with electrodes. By using the model and experimental
time-dependencies for metastable density and electrode bias, the time-dependencies for electron density in
argon/dusty plasma afterglow are calculated. The effect of secondary emission on electron generation in argon/dusty
plasma afterglow is analyzed.
PACS: 52.25.Vy, 52.27.Lw, 51.50.+v, 52.80.Pi
INTRODUCTION
In the last two decades plasmas with nano- and
micrometre-sized (dust) particles have been extensively
studied. However, most of the studies are focused on the
steady-state plasma regime [1-3]. In contrast, the
properties of dusty plasmas in the afterglow regime are
still not well studied, especially of the plasmas with
large dust density where negative charge on dust
particles is larger than free electron density edd nZn ≥ .
en , dn and dZ are the electron density, dust density
and dust charge, respectively.
In [4, 5], experimental results on plasma afterglow
with large dust density are presented. It was found that
at the very beginning of the plasma decay the electron
density increased unexpectedly. First, the increase of en
was attributed to the releasing of electrons from dust
particles by secondary emission in collisions of reactive
species with dusts [4, 5]. Later on, it was shown that the
Ar metastable-metastable collisions (metastable
pooling) can be the source of the observed electron
density increase [6, 7]. Recent experiments on plasma
afterglow with large dust density revealed the negative
electrode voltage in the afterglow sufficiently large to
produce secondary electrons by collisions of positive
ions with electrodes. This also can increase en at the
very beginning of the plasma decay [8, 9].
In this paper, we study the effect of the secondary
electron emission from electrodes on the properties of
argon/dusty plasma afterglow with large dust density.
The study is carried out for 0.1 mbar argon plasma
generated by a capacitively coupled symmetrically
driven RF discharge between two 30 cm diameter
electrodes with 7 cm gap, the same as that used in
experiments of Refs. [4, 5]. We will compare: i) the
time-dependencies for density of electrons calculated by
taking into account the secondary emission from
electrodes ii) the time-dependencies of electron density
without secondary emission and iii) electron density
measured in the experiment.
THEORETICAL MODEL AND
ASSUMPTIONS
Let us consider the plasma of radius R=15 cm and
height L= 7 cm, consisting of singly charged positive
ions (Ar+) with density ni, negatively charged dust
particles with density nd, radius ad and mean (averaged
over all particles) charge Zd (in units of electron charge
e), ground-state argon atoms (Ar0) with density na and
metastable argon atoms (Arm) with density nm. It is
assumed that there are three groups of electrons in the
plasma afterglow: i) thermal electrons with Maxwellian
distribution and characterized by electron temperature
Te and density ne, ii) “energetic” electrons generated by
metastable pooling with density nef and energies about
7.3 eV [6], and iii) secondary electrons generated on
electrodes with density nh and energies about the
electrode voltage.
We assume that soon after switching of the RF
power the electron temperature decays exponentialy
according to )/exp()( 0 Tee tTtT τ−= , where t is the time,
0eT is the electron temperature in power-on phase and
sT μτ 50= is the Te´s decay time [5,6]. We assume that
Te can not be smaller than a certain temperature aftT =
0.1 eV [10], i. e. the electron temperature stays constant
after it reaches aftT . The potentials of a cylindrical
metal wall and the electrode potential with respect to
bulk plasma are ew T7.4−=Φ and ,wfel VU Φ+≈
respectively [11]. fV is the electrode potential with
respect to the cylindrical wall [11]. The electrode
potentials as a function of time were measured for dust-
free and dusty plasma afterglows (Fig. 1) [8, 9].
The density of thermal electrons in the plasma
afterglow is governed by the following equation:
./
)(/
*
*
de
e
deweme
i
mefef
hhha
i
ahm
i
mhea
i
ae
nnKτnnnK+n
n+nnKnK+nnK=tn
−−
++∂∂
ν
ν (1)
Here, i
aK is the rate for ionization of ground-state atoms
by Maxwellian electrons, i
mhK and i
ahK are the rates for
ionization of metastable atoms and ground-state atoms
by secondary electrons, respectively. *
hν and *
fν are the
158 ISSN 1562-6016. ВАНТ. 2014. №6(94)
frequencies determining the termalization of electrons
due to inelastic collisions of secondary and energetic
electrons, respectively. i
meK is the rate for ionization of
Ar metastable atoms by thermal electrons. ewτ is the
electron diffusion time constant. e
dK is the rate for
collection of thermal electrons by dust particles, which
is calculated by orbital motion limited (OML) theory.
Fig. 1. The time-dependence of electrode voltages Vf in
the dust-free (curve 1) and dusty (curve 2) plasma
afterglows
The balance equation for energetic electrons is [7]:
,// *2
fwefdef
ef
deffmmef nnnKnnktn τν −−−=∂∂ (2)
where km is the rate for electron production in
metastable pooling. ef
dK is the rate for collection of
energetic electrons by dust particles, and fwτ is the
time characterizing the escape of energetic electrons to
the walls.
The balance equation for secondary electrons is:
hwhdh
h
dhhiwiih nnnKnntn τντγ /// * −−−=∂∂ . (3)
The first term on the right-hand side in (3) describes
generation of secondary electrons on the electrodes.
Here, iγ is the effective secondary emission yield, and
iwτ is the ion diffusion time constant. The second term
accounts for the thermalization of secondary electrons
in inelastic collisions. The third term on the right-hand
side in (3) describes the collection of secondary
electrons by dust particles with the rate h
dK .
To calculate the rates e
dK , ef
dK and h
dK in (1)-(3),
one has to know the dust particle charge. dZ is found
from the balance equation for dust charging:
i
i
dh
h
def
ef
de
e
dd nKnKnKnKtZ −++=∂∂ / , (4)
where i
dK is the rate for collection of ions by dust
particles.
The time-dependence for ion density in the afterglow
is described by the ion balance equation:
./
)(/
2
di
i
diwimm
me
i
meha
i
ahm
i
mhea
i
ai
nnKτnnk
nnK+nnKnK+nnK=tn
−−
++∂∂ (5)
The plasma is assumed to be quasi-neutral, or
ddhefei nZnnnn +++= . (6)
Equations (1) - (6) are solved numerically. The time
dependencies for metastable density and electrode
voltage in the afterglow are taken from the experiment
[7-9], while the dust radius and ion density for the
power-on phase are assumed to be known. In particular,
the time-dependence for the spatially-averaged Ar
metastable density can be approximated as
)/exp()0()( mmm tntn τ−×= , where )0(mn is the
metastable density in the power-on phase and mτ is the
decay time for metastable density [7]. The procedure of
calculation is similar to that used in [6].
RESULTS
Using the analytical expressions (1)-(6), we have
calculated plasma parameters (the densities of thermal,
energetic and secondary electrons, ion density and dust
charge) as a function of time in the dusty plasma
afterglow.
The calculated decay of spatially averaged thermal
electron density and the experimental results of electron
decay are compared in Fig. 2. The time-dependence for
ne is calculated for ad = 50 nm, nd =3.5×107 cm-3, p =
0.1 mbar, Tg= 366 K and 1.0=iγ .
Fig. 2. The time-dependence for ne in dusty plasma
afterglow, measured in the experiment (curve 1) and
calculated using the model (curve 2)
One can see from Fig. 2 that the calculated electron
density follows well the experimental value. However,
the calculated ne(t) dependence has a peak at 1≈t ms,
while the peak for experimental electron density is at
5.0≈t ms. Moreover, for 1>t ms, the decrease of the
calculated electron density with time is faster than that
in the experiment. We belive that our model
underestimates the electron temperature at the begining
of the afterglow (for t < 1 ms) and overestimates the
electron loss in the late afterglow (for t > 1 ms).
Next, we analysed how metastable pooling and
secondary electron emission from the electrodes affect
the electron density in the afterglow. To understand the
role of the electron production processes, we made
calculations with different simplifications. First, we
considered the case when the secondary emission is
absent, while the metastable pooling takes place. In
Fig. 3, the ne(t) dependence calculated for 0=iγ (curve
2) is compared with that for 1.0=iγ (curve 1).
One can see that the secondary emission increases
the electron density. The peak density at 1.0=iγ is
about 15 % larger than that at 0=iγ . In the case when
the metastable pooling is absent (km=0) and the
secondary emission takes place ( 1.0=iγ ), it was
found that the thermal electron density decreases rapidly
with time (see curve 3 in Fig. 3). Thus, the effect of
secondary electron emission is less important than
ISSN 1562-6016. ВАНТ. 2014. №6(94) 159
metastable pooling in argon/dusty plasma afterglow.
Note that nearly the same time-dependence for ne(t)
can be obtained by excluding the secondary electron
emission ( 0=iγ ) but decreasing the dust density down
to nd =3.25×107 cm-3.
Fig. 3. The time-dependences for ne calculated using
different assumptions in the model
In conclusion, we have calculated the time-
dependencies for electron density in argon/dusty plasma
afterglow by using the model and experimental time-
dependencies for metastable density and electrode
voltage. The effect of secondary electron emission from
the electrodes on the electron behaviour in argon/dusty
plasma afterglow has been estimated by varying
secondary emission yields. It has been found that the
secondary electron emission is less important than argon
metastable pooling.
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1. A. Bouchoule. Dusty Plasmas: Physics, Chemistry,
and Technological Impacts in Plasma Processing / Еd
by. New York. ”Wiley”, 1999, p. 418.
2. I. Denysenko, K. Ostrikov, M.Y. Yu,
N.A. Azarenkov // Phys. Rev. E. 2006, v. 74, p. 036402.
3. I. Denysenko, M.Y. Yu, L. Stenflo, S. Xu // Phys.
Rev. E. 2005, v. 72, p. 016405.
4. J. Berndt et. al. Anomalous behaviour of the electron
density in a pulsed complex plasma // Plasma Sources
Sci. Technol. (15). 2006, p. 18.
5. I. Stefanović et al. Secondary electron emission of
carbonaceous dust particles // Phys. Rev. E. 2006,
v. 74, p. 026406.
6. I. Denysenko et al. // J. Phys. D: Appl. Phys. 2011,
v. 44, p. 205204.
7. I.B. Denysenko et al. Discharging of dust particles in
the afterglow of plasma with large dust density // Phys.
Rev. E. 2013, v. 88, p. 023104.
8. B. Sikimić, I. Stefanović, I.B. Denysenko, J. Winter.
A non-invasive technique to determine ion fluxes and
ion densities in reactive and non-reactive pulsed
plasmas // Plasma Sources Sci. Technol. 2013, v. 22,
p. 045009.
9. B. Sikimić et al. Dynamics of pulsed reactive RF
discharges in response to thin film deposition // Plasma
Sources Sci. Technol. 2014, v. 23, p. 025010.
10. V.I. Demidov, C.A. DeJoseph, A.A. Kudryavtsev.
Anomalously high near-wall sheath potential drop in a
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Article received 19.09.2014
ВЛИЯНИЕ ВТОРИЧНОЙ ЭМИССИИ НА РАCПАД АРГОНОВОЙ ПЛАЗМЫ, КОТОРАЯ
СОДЕРЖИТ НЕГАТИВНО ЗАРЯЖЕННЫЕ ПЫЛЕВЫЕ ЧАСТИЦЫ
И.Б. Денисенко, И. Стефанович, Н.А. Азаренков, Г.П. Бурмака
Разработана теоретическая модель распадающейся пылевой аргоновой плазмы, которая имеет высокую
плотность наноразмерных пылинок. Данная модель учитывает генерацию электронов при столкновениях
метастабильных атомов между собой и благодаря вторичной эмиссии при столкновениях ионов с
электродами. Используя эту модель и экспериментальные временные зависимости для плотности
метастабильных атомов и потенциала электродов, рассчитаны временные зависимости для плотности
электронов в пылевой распадающейся аргоновой плазме. Проанализировано влияние вторичной эмиссии на
генерацию электронов в этой среде.
ВПЛИВ ВТОРИННОЇ ЕМІСІЇ НА РОЗПАД АРГОНОВОЇ ПЛАЗМИ, ЩО МІСТИТЬ
НЕГАТИВНО ЗАРЯДЖЕНІ ПИЛЬОВІ ЧАСТИНКИ
І.Б. Денисенко, І. Стефанович, М.О. Азарєнков, Г.П. Бурмака
Розроблено теоретичну модель пилової аргонової плазми, що розпадається, та має високу густину
порошинок нанорозміру. Дана модель враховує генерацію електронів при зіткнені метастабільних атомів
між собою та завдяки вторинній емісії при зіткнені іонів з електродами. Використовуючи цю модель та
експериментальні часові залежності для густини метастабільних атомів та потенціалу електродів,
розраховано часові залежності для густини електронів у запорошеній аргоновій плазмі, що розпадається.
Проаналізовано вплив вторинної емісії на генерацію електронів у цьому середовищі.
|