Dusty RF discharges with non-uniform distributions of dust particles
PIC/MC computer simulations of dusty RF discharges in argon with various profiles of the dust particle density in the interelectrode gap shows a slow influence of the profiles on a dust particle charge in the quasi-neutral region of the discharges. However the profile influence spatial distributions...
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| Опубліковано в: : | Вопросы атомной науки и техники |
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| Дата: | 2003 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2003
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| Цитувати: | Dusty RF discharges with non-uniform distributions of dust particles / Yu. I. Chutov, W. Goedheer, O.Yu. Kravchenko, G.I. Levada, T.E. Lisitchenko, R.O. Romanenko, R.D. Smirnov // Вопросы атомной науки и техники. — 2003. — № 4. — С. 226-229. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860252012956876800 |
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| author | Chutov, Yu.I. Goedheer, W. Kravchenko, O.Yu. Levada, G.I. Lisitchenko, T.E. Romanenko, R.O. Smirnov, R.D. |
| author_facet | Chutov, Yu.I. Goedheer, W. Kravchenko, O.Yu. Levada, G.I. Lisitchenko, T.E. Romanenko, R.O. Smirnov, R.D. |
| citation_txt | Dusty RF discharges with non-uniform distributions of dust particles / Yu. I. Chutov, W. Goedheer, O.Yu. Kravchenko, G.I. Levada, T.E. Lisitchenko, R.O. Romanenko, R.D. Smirnov // Вопросы атомной науки и техники. — 2003. — № 4. — С. 226-229. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | PIC/MC computer simulations of dusty RF discharges in argon with various profiles of the dust particle density in the interelectrode gap shows a slow influence of the profiles on a dust particle charge in the quasi-neutral region of the discharges. However the profile influence spatial distributions of electrons and ions in the interelectrode gap as well as the dust particle charge in sheaths.
|
| first_indexed | 2025-12-07T18:44:34Z |
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UDK 533.9
DUSTY RF DISCHARGES WITH NON-UNIFORM DISTRIBUTIONS
OF DUST PARTICLES
Yu. I. Chutov1, W. Goedheer2, O.Yu. Kravchenko1, G.I. Levada1, T.E. Lisitchenko1,
R.O. Romanenko1, R.D. Smirnov1
1Faculty of Radio Physics, Taras Shevchenko Kiev University, 01017 Kiev, Ukraine,
yuch@univ.kiev.ua
2FOM-Institute for Plasma Physics "Rijnhuizen", P.O. Box 1207, 3430 BE Nieuwegein,
The Netherlands
PIC/MC computer simulations of dusty RF discharges in argon with various profiles of the dust particle density
in the interelectrode gap shows a slow influence of the profiles on a dust particle charge in the quasi-neutral region
of the discharges. However the profile influence spatial distributions of electrons and ions in the interelectrode gap as well as
the dust particle charge in sheaths.
1. INTRODUCTION
It is well known for a long time [1-4] that dust
particles can be distributed very non-uniformly in dusty
RF discharges concentrating close to the sheath edge.
Recent experiments [5-8] show the formation of stable
dust-free regions (voids) with sharp boundaries inside a
dust cloud in the dusty RF discharges. The voids are
observed both in laboratory experiments [5-7] and under
microgravity conditions [8]. There are several attempts
[9-12] to consider physical mechanisms for non-
uniform distributions of dust particles in dusty RF
discharges including the void creation. The
consideration includes computer simulations of an
evolution of dust clouds in the dusty RF discharges [9].
However the huge difference in the time scale of the
dust motion and other processes (an ionization and an
excitation of neutral atoms, a collection and a scattering
of electrons and ion by dust particles) in RF discharges
causes a necessary to use very complex hybrid
simulation schemes. The schemes consist of several
linked computer models, which can be solved by time
splitting and an iterative procedure. Note that the
processes indicated above can cause a strong non-
equilibrium of electron and ion energy distribution
functions that influence strongly in turn the non-elastic
processes and dust particle charging [13,14].
The complex hybrid schemes need the very large
computer resources complicating their use. Besides, the
simultaneous account of many processes complicates
understanding physical mechanisms of the void
development. Therefore it is expediently to use simple
simulation schemes allowing investigations of separated
elements of the mechanisms.
The aim of the work is computer simulation of dusty
RF discharges in argon with given various profiles of
the dust particle density to investigate an influence of
the profile on dusty RF discharges and to simplify the
complex hybrid schemes of their simulations.
2. MODEL
A one-dimensional RF discharge between two plane
electrodes separated by the gap of d = 0.02 m, filled
with Ar at pressure of 0.1 Torr, is simulated. Immobile
spherical dust particles with a radius Rd = 1 µm are
distributed in the interelectrode gap according to a given
parabolic distribution nd = ndo + a(x-xo)2 where nd and
ndo is the dust density and a minimum density of dust
particles, respectively. Note that the minimum density
can be located in any point of the interelectrode gap.
The distribution can be changed at the condition of a
conservation of the total number Nd of dust particles in
the interelectrode gap so that the ratio α = ndm / ndo ,
where ndm is a maximum density of dust particles, is
changed. Of course, the case α = 1 corresponds to the
uniform distribution of dust particles with the density
nda = Nd / Sd where S is the area of an electrode. The
dust particles collect and scatter electrons and ions
distributed in the discharge with density ne and ni,
respectively. A harmonic external voltage V(t)=Vosin(ω
t) with a frequency of 13,56 MHz and various
amplitudes Vo sustains the RF discharge. The right
electrode at x=d is grounded.
The PIC/MCC method (PDP1D3v code) described
in detail in [15] for discharges without dust particles is
developed for computer simulations of the RF discharge
with a non-uniform distribution of dust particles. An
electrode collects a "superparticle" if its center reaches
an electrode surface. Each superparticle represents
4*107 real electrons or ions, for the charge distribution it
is a cylinder with an end area S=0.04 m2 and a hight
equal to the size of the simulation cell.
The Monte Carlo technique [15] is used to describe
electron and ion collisions. The collisions include
elastic collisions of electrons and ions with atoms, an
ionization and excitation of atoms by electrons, the
charge exchange between ions and atoms, Coulomb's
collisions of electrons and ions with dust particles, as
well as the electron and ion collection by dust particles.
Electron-electron collisions are not taken into
account due to the low argon ionization degree β = ne/na
where ne and na is electron and atom density,
respectively. The degree is equal about to 10-6 for our
conditions (see below Fig. 2). Indeed, electron-electron
collisions are essential with respect to electron-atom
collisions if the electron-electron energy exchange is
essential in comparison with the electron-atom energy
exchange. The boundary condition corresponding to the
energy exchanges is γeeqeene
2ve ~ γeaqeanenave where γ and
q are the energy accommodation coefficient, and the
effective cross-section, respectively for electron-
electron (ee) and electron-atom (ea) collisions, ve is the
electron velocity. Simple estimations show that an
argon ionization degree β = ne/na corresponding to the
last condition exceeds the value of 10-6 at least for fast
electrons determining the excitation and the ionization
of atoms as well as the dust particle charge.
The cross-sections of electron collection by
immobile dust particles is taken according to the Orbit
Motion Limited (OML) theory [16]. The Coulomb
cross-section for electron and ion scattering by
immobile dust particles is taken from [17].
The simulation starts with an initial uniform
distribution of electrons and ions with densities equal to
1015 m-3 and is prolonged in time using a leap-frog
scheme up to the moment when the change of the
discharge parameters during 10 periods of the applied
voltage is less 0.1 %. The simulations show that no
more than 500 cycles are needed to obtain the periodic
steady state of RF discharges. Note that the simulation
time can be strongly different from relaxation times of
various collisions due to an initial electron density.
3. RESULTS
Spatial distributions of the dust particle density nd
used in the simulations are shown in Fig. 1 for various
ratios α = ndm / ndo of a maximum ndm and minimum ndo
density of dust particles, as well as for various positions
xo of the minimum density of dust particles. Curves in
Fig. 1 are chosen at a conservation of the total number
Nd of dust particles in the interelectrode gap of the RF
discharge. The case of α = 1 corresponds to uniform
distributions of dust particles with nd = 1*1012 m-3.
Spatial distributions of the electron ne (straight lines)
and ion ni (dashed lines) density across the
interelectrode gap are shown in Fig. 2 (cases a, b, c) for
the cases of Fig. 1 at Vo = 300 V and p= 0.1 Torr. In
addition, the distributions are shown also in Fig. 2 (case
d) for the RF discharge without dust particles. The
distributions are obtained for the phase ϕ =ω t = 0 of
the harmonic external voltage V (t). As simulation
results show [14], spatial distributions of the ion density
ni does not change during the period of the sustaining
external harmonic voltage but the electron density ne
changes in oscillating non-neutral RF sheaths close to
both electrodes according to a phase ϕ =ω t of the
sustaining voltage.
As can be seen in Fig. 2, there is the central quasi-
neutral region where the electron density ne is about
equal to ni and does not change like to the ion density ni.
It means a space charge of dust particles is small with
respect to ni and ne, so that dust particles do not
influence essentially a total space electric charge in
simulated regimes.
As can be seen comparing various regimes in Fig. 2,
a change of the dust density profile causes a change of
the spatial distributions of the electron and ion density.
First of all, dust particles expand RF sheaths (cases
a,b,c in Fig. 2) with respect to the RF discharge without
dust particles (case d in Fig. 2) and consequently
0.0 0.5 1.0
0
1
2
3 α =1
α =10, x0/d = 0.50
α =10, x0/d = 0.25
nd*10-12, m-3
x/d
Fig. 1. Spatial distributions of the
dust particle density N
d
0.0 0.5 1.0
0
5
10
0.0 0.5 1.0
0
5
10
a
n*10-15 m-3
x/d
ne
ni
α = 1
b
n*10-15 m-3
α = 10,
xo/d = 0.5
0.0 0.5 1.0
0
5
10
0 . 0 0 . 5 1. 00
5
10
d
n/1015, m-3
x/d
Nd = 0
c
α =10,
xo/d = 0.25
Fig. 2. Spatial distributions of the
electron n
e
and ion n
i
density
constrict the central quasi-neutral region of the
discharge. The indicated influence of dust particles is
caused by an additional space negative electric charge
of dust particles in the sheaths discussed earlier in [14].
Besides, as can be seen comparing Fig. 1 (straight and
dashed lines) and Fig. 2 (cases b and c), the maximum
of the electron and ion densities shifts towards the
minimum of the dust density in a case of non-symmetric
spatial distributions of dust particles. The effect can be
essential for mechanisms of a void creation in dusty RF
discharges.
Spatial distributions of the dust particle charge qd
divided by the negative electron charge e are shown in
Fig. 3 for the cases of Fig. 1. As can be seen in Fig. 3,
the negative charge qd is practically constant in the
quasi-neutral central part of the RF discharge. The
charge is equal about to 7.5*10 2 e that correspond to the
surface potential Vs ~ 1.5 eV. The dust particle charge qd
does not change practically in the quasi-neutral region
of the RF discharge at a change of a dust density
profiles. Therefore it is possible to use the charge qd,
obtained for the quasi-neutral region in the case of
uniform distribution of dust particles, at a simulation of
a dust cloud evolution in RF discharges including a void
creation.
As can be seen in Fig. 4, in which spatial
distributions of the total space electric charge ρ are
shown for cases of Fig. 2, the charge ρ is not changing
also in the quasi-neutral region of the interelectrode gap.
However, the dust particle charge qd is strongly
changing in sheaths and even can change the sign. As
can be seen in Fig. 3, the charge is positive close to the
electrodes of the RF discharge and depends on the
profile of dust particle density. The positive charge of
dust particles is caused by a strong decrease of an
electron density in sheaths close to the electrodes (see
Fig. 2).
Comparing curves in Fig. 3, it can be seen that the
charge qd has a maximum close to the sheath edge, the
maximum shifts together with the sheath edge at
changing a dust particle density profile. The charge
maximum is equal about to 1.3*10 3 e and the maximum
is practically not depending on the profile of the dust
particle density. Therefore the maximum charge
obtained for corresponding uniform distributions of dust
particles can be used also for simulations of a dust cloud
evolution in RF discharges including a void creation.
In the case of a non-symmetric distribution of dust
particles (case c in Fig. 3), the spatial distribution of the
dust particle charge qd is also non-symmetric in sheaths.
Comparing fig. 1 (dashed line) and Fig. 3 (case c), it can
be seen that the dust particle charge is a few lower in
the right region of the interelectrode gap, where the
density of dust particles is higher. The decrease is
caused by the higher ion density in the region (case c in
Fig. 2).
The non-monotonic distributions of the dust particle
charge qd shown in Fig. 3, are caused by the
peculiarities of dust particle charging in RF discharges.
It is well known that the dust particle charge qd is
determined by a balance of electron and ion charging
currents into a dust particle [18]. In the case of
equilibrium uniform plasma without any emission from
dust particles, a negative charge of an isolated dust
particle depends strongly only on the electron
temperature and the size of a dust particle. Furthermore,
the negative dust particle charge can be diminished in
plasmas with non-neutral dust particles due to a
difference between electron and ion densities.
In our case of non-uniform plasma with negative
charged dust particles, the ion charging current is
proportional to the ion density and therefore has to
decrease monotonically at a removal from the maximum
of the ion density due to the monotonic decrease of the
ion density shown in Fig. 1. The electron charging
current is depending on the surface potential of dust
particles and the averaged electron energy distribution
function Fe.
0.0 0.5 1.0
0
1
2
3
ρ *104, C/m-3
x/d
α = 10, x/d = 0.50
α = 10, x/d = 0.25
α = 1
Nd = 0
Fig. 4. Spatial distributions of the
total electric space charge ρ
0.0 0.5 1.0
-1
0
1
2
-1
0
1
2
-1
0
1
2
c
x/d
b
a
α = 10, xo/d = 0.25
α = 10, xo/d = 0.50
α = 1
(qd / e)*10-3
Fig. 3. Spatial distributions of
the dust particle charge q
d
As simulation results show [14], the distribution
functions Fe coincide practically in the energy region ε
>2eV in the quasi-neutral center region of the
interelectrode gap, due to a free mixing of fast electrons
in the almost equipotential center region. Therefore, the
electron charging current into a dust particle is the same
for various points in the center region. The constancy of
the electron charging current and the decrease of the ion
charging current in the center region of the
interelectrode gap towards the sheath edge, cause the
change of the dust particle charge qd shown in Fig. 3.
Other situation takes place in sheaths where a free
mixing of electrons is not possible due to a strong
voltage drop in sheaths. Therefore the number of fast
electrons is not constant in various sheath points
decreasing towards electrodes so that the electron
charging current decreases also in sheaths at a removal
from the sheath edge towards electrodes. Besides, the
mean electron density <ne> is less than the
approximately constant ion density ni in positive
charged sheaths. As can be seen from simulation results,
the density ratio <ne>/ ni decreases here towards
electrodes. As a result, the dust particles charge qd
decreases towards electrodes creating a maximum close
to the sheath edge (Fig. 3).
4. CONCLUSION
The PIC/MCC computer simulation of dusty RF
discharges in argon with various profiles of the dust
particle density in the interelectrode gap shows a slow
influence of the profiles on a dust particle charge in the
quasi-neutral region of the discharges at low densities of
dust particles. Therefore computer simulations of an
evolution of dust clouds can be carried out using the
dust particle charge in the quasi-neutral region of RF
discharges (including the maximum value of the charge)
obtained for a uniform distribution of dust particles in
RF discharges. The change of the profile influence
spatial distributions of electrons and ions in the
interelectrode gap as well as the dust particle charge in
sheaths.
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|
| id | nasplib_isofts_kiev_ua-123456789-111155 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:44:34Z |
| publishDate | 2003 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Chutov, Yu.I. Goedheer, W. Kravchenko, O.Yu. Levada, G.I. Lisitchenko, T.E. Romanenko, R.O. Smirnov, R.D. 2017-01-08T16:38:41Z 2017-01-08T16:38:41Z 2003 Dusty RF discharges with non-uniform distributions of dust particles / Yu. I. Chutov, W. Goedheer, O.Yu. Kravchenko, G.I. Levada, T.E. Lisitchenko, R.O. Romanenko, R.D. Smirnov // Вопросы атомной науки и техники. — 2003. — № 4. — С. 226-229. — Бібліогр.: 18 назв. — англ. 1562-6016 https://nasplib.isofts.kiev.ua/handle/123456789/111155 533.9 PIC/MC computer simulations of dusty RF discharges in argon with various profiles of the dust particle density in the interelectrode gap shows a slow influence of the profiles on a dust particle charge in the quasi-neutral region of the discharges. However the profile influence spatial distributions of electrons and ions in the interelectrode gap as well as the dust particle charge in sheaths. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Газовый разряд, ППР и их применения Dusty RF discharges with non-uniform distributions of dust particles Article published earlier |
| spellingShingle | Dusty RF discharges with non-uniform distributions of dust particles Chutov, Yu.I. Goedheer, W. Kravchenko, O.Yu. Levada, G.I. Lisitchenko, T.E. Romanenko, R.O. Smirnov, R.D. Газовый разряд, ППР и их применения |
| title | Dusty RF discharges with non-uniform distributions of dust particles |
| title_full | Dusty RF discharges with non-uniform distributions of dust particles |
| title_fullStr | Dusty RF discharges with non-uniform distributions of dust particles |
| title_full_unstemmed | Dusty RF discharges with non-uniform distributions of dust particles |
| title_short | Dusty RF discharges with non-uniform distributions of dust particles |
| title_sort | dusty rf discharges with non-uniform distributions of dust particles |
| topic | Газовый разряд, ППР и их применения |
| topic_facet | Газовый разряд, ППР и их применения |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/111155 |
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