Two-dimensional simulation of dynamic dust clouds in the plasma boundary near the wall
It is carried a computer simulation of the dynamics of dust clouds near a conducting wall at microgravity conditions and its effect on the sheath. We used two-dimensional axially symmetric hydrodynamic model, which takes into account self-consistent variable charge of dust particles and the mutual i...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
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| Цитувати: | Two-dimensional simulation of dynamic dust clouds in the plasma boundary near the wall / O.Yu. Kravchenko, I.S. Maruschak, G.I. Levada // Вопросы атомной науки и техники. — 2010. — № 6. — С. 100-102. — Бібліогр.: 5 назв. — англ. |
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irk-123456789-174712011-02-27T12:06:58Z Two-dimensional simulation of dynamic dust clouds in the plasma boundary near the wall Kravchenko, O.Yu. Maruschak, I.S. Levada, G.I. Динамика плазмы и взаимодействие плазма – стенка It is carried a computer simulation of the dynamics of dust clouds near a conducting wall at microgravity conditions and its effect on the sheath. We used two-dimensional axially symmetric hydrodynamic model, which takes into account self-consistent variable charge of dust particles and the mutual influence of plasma and dust components. The simulation results show that the dust cloud modifies the potential profile of the plasma so that double layers are formed on its boundaries, which give rise to a flow of ions inside the cloud. In a number of regimes is formed a potential well for dust particles. It is shown that the dust cloud in the sheath under the influence of electrical forces and the ion drag force reciprocates in the direction perpendicular to the wall. Проведено компьютерное моделирование динамики пылевых сгустков возле проводящей стенки в условиях микрогравитации и ее влияния на приэлектродный слой. Использовалась двухмерная аксиально-симметричная гидродинамическая модель, которая учитывает самосогласованный переменный заряд пылевых частиц и взаимное влияние плазмы и пылевой компоненты. Результаты моделирования показывают, что пылевой сгусток изменяет профиль потенциала плазмы так, что на его границах образуются двойные слои, которые приводят к появлению потоков ионов внутрь сгустка. В ряде режимов формируется потенциальная яма для пылевых частиц. Показано, что в приэлектродном слое пылевой сгусток под действием электрической силы и силы ионного трения совершает возвратно-поступательное движение в направлении, перпендикулярном к стенке. 2010 Article Two-dimensional simulation of dynamic dust clouds in the plasma boundary near the wall / O.Yu. Kravchenko, I.S. Maruschak, G.I. Levada // Вопросы атомной науки и техники. — 2010. — № 6. — С. 100-102. — Бібліогр.: 5 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/17471 en Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Динамика плазмы и взаимодействие плазма – стенка Динамика плазмы и взаимодействие плазма – стенка |
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Динамика плазмы и взаимодействие плазма – стенка Динамика плазмы и взаимодействие плазма – стенка Kravchenko, O.Yu. Maruschak, I.S. Levada, G.I. Two-dimensional simulation of dynamic dust clouds in the plasma boundary near the wall |
| description |
It is carried a computer simulation of the dynamics of dust clouds near a conducting wall at microgravity conditions and its effect on the sheath. We used two-dimensional axially symmetric hydrodynamic model, which takes into account self-consistent variable charge of dust particles and the mutual influence of plasma and dust components. The simulation results show that the dust cloud modifies the potential profile of the plasma so that double layers are formed on its boundaries, which give rise to a flow of ions inside the cloud. In a number of regimes is formed a potential well for dust particles. It is shown that the dust cloud in the sheath under the influence of electrical forces and the ion drag force reciprocates in the direction perpendicular to the wall. |
| format |
Article |
| author |
Kravchenko, O.Yu. Maruschak, I.S. Levada, G.I. |
| author_facet |
Kravchenko, O.Yu. Maruschak, I.S. Levada, G.I. |
| author_sort |
Kravchenko, O.Yu. |
| title |
Two-dimensional simulation of dynamic dust clouds in the plasma boundary near the wall |
| title_short |
Two-dimensional simulation of dynamic dust clouds in the plasma boundary near the wall |
| title_full |
Two-dimensional simulation of dynamic dust clouds in the plasma boundary near the wall |
| title_fullStr |
Two-dimensional simulation of dynamic dust clouds in the plasma boundary near the wall |
| title_full_unstemmed |
Two-dimensional simulation of dynamic dust clouds in the plasma boundary near the wall |
| title_sort |
two-dimensional simulation of dynamic dust clouds in the plasma boundary near the wall |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2010 |
| topic_facet |
Динамика плазмы и взаимодействие плазма – стенка |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/17471 |
| citation_txt |
Two-dimensional simulation of dynamic dust clouds in the plasma boundary near the wall / O.Yu. Kravchenko, I.S. Maruschak, G.I. Levada // Вопросы атомной науки и техники. — 2010. — № 6. — С. 100-102. — Бібліогр.: 5 назв. — англ. |
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2025-07-02T18:41:18Z |
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2025-07-02T18:41:18Z |
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| fulltext |
100 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2010. № 6.
Series: Plasma Physics (16), p. 100-102.
TWO-DIMENSIONAL SIMULATION OF DYNAMIC DUST CLOUDS
IN THE PLASMA BOUNDARY NEAR THE WALL
O.Yu. Kravchenko, I.S. Maruschak, G.I. Levada
Taras Shevchenko National University of Kiev, Kiev, Ukraine
E-mail: maruschak@univ.kiev.ua
It is carried a computer simulation of the dynamics of dust clouds near a conducting wall at microgravity conditions
and its effect on the sheath. We used two-dimensional axially symmetric hydrodynamic model, which takes into
account self-consistent variable charge of dust particles and the mutual influence of plasma and dust components. The
simulation results show that the dust cloud modifies the potential profile of the plasma so that double layers are formed
on its boundaries, which give rise to a flow of ions inside the cloud. In a number of regimes is formed a potential well
for dust particles. It is shown that the dust cloud in the sheath under the influence of electrical forces and the ion drag
force reciprocates in the direction perpendicular to the wall.
PACS: 52.27.Lw.
INTRODUCTION
In many practical cases, including etching, deposition
and sputter plasmas, dust particles have been observed at
the plasma-sheath boundary [1]. Charged dust particles
also appear at tokamak edges as natural contaminants
arising from the plasma interaction with divertor plates,
plasma limiters and blankets [2]. These microparticles
result from sputtering of the electrode and wall surfaces,
gas phase nucleation, and polymerization. The
observation of the microparticles has shown that those
particles are trapped inside the sheath region, close to the
plasma-sheath boundary. Dust particles can strongly
influence on sheaths [2,3] due to the selective adsorption
of background electrons and ions (penetrating through
sheaths) by dust particles. In the result, dust particles
create the space electric charge influencing on the sheath
structure.
Due to their heavy masses and tendency to form self-
organized structures the dust particles affect waves,
instabilities and transport processes. Recent laboratory
experiments [4] have conclusively demonstrated the
motions of charged dust clouds near negatively biased
electrodes in low temperature dusty plasma discharges. In
a dusty plasma sheath the dust grains execute bouncing
motions, which are repeatedly away and towards the
electrode
In this paper we use the two-dimensional fluid model
to study the plasma sheath structure and the behavior of a
dust cloud in the field of the plasma sheath in
microgravity conditions.
MODEL
We consider the wall region of two-dimensional dusty
plasma model, wherein the plasma is contaminated by
dust charged grains. Plasma consist of electrons, ions and
dust particles with densities en , in , dn . At initial time
electron and ions are distributed uniformly in space, but
dust particles form a cloud, which is located at the edge
of the sheath. Dust particles are charged after their
appearance in the plasma due to the selective collection
of electrons and ions so that a change of plasma
parameters starts inside the dust layer. This change
propagates into plasma due to the self-consistent electric
field.
An evolution of the sheath with the dust cloud can be
considered in the hydrodynamic approach with the self-
consistent electric potential ϕ described by the following
Poisson equation
2
2
0
1 ( ) ( )i e d d
er n n z n
r r rx
ϕ ϕ
ε
∂ ∂ ∂
+ = − ⋅ − − ⋅
∂ ∂∂
.
The change of the dust charge is described by
equation
d
e i
dq
I I
dt
= + ,
where electron and ion currents eI and iI flowing into
dust particle are defined by relations:
1 2
2 8
exp ,e d
e e
e e
kT eq
I a e n
m akT
π
π
⎛ ⎞ ⎛ ⎞
= − ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠
1 2
2 2
2
8
1
( / 2)
i d
i i i
i i i
kT eq
I a en v
m a kT m w
π
π
⎛ ⎞⎛ ⎞
= + −⎜ ⎟⎜ ⎟ ⎜ ⎟+⎝ ⎠ ⎝ ⎠
.
The electrons are assumed to be in thermal
equilibrium, therefore the density en satisfies the
Boltzmann relation.
The ions are described by the fluid equations
( )i i
i i d
n I
n w n
t e
∂
+∇ ⋅ ⋅ =
∂
uur
,
( ) 0i i
i i i i
i
n u ediv n u w n
dt m r
ϕ∂ ∂
+ ⋅ ⋅ + =
∂
r ,
( ) 0i i
i i i i
i
n v ediv n v w n
dt m z
ϕ∂ ∂
+ ⋅ ⋅ + =
∂
r ,
where , ,i iw e mr are the vector of drift velocity, charge,
mass of the ions, ,i iu v are ion velocity components along
axes r and z .
101
The dust components of plasma are described by the
following equations
( ) 0d
dd
n
n w
t
∂
+∇ ⋅ ⋅ =
∂
ur
,
( ) 0d d d
d d d d idr
d
n u Q
div n u w n F
dt m r
ϕ∂ ∂
+ ⋅ ⋅ + + =
∂
r ,
( ) 0d d d
d d d d idz
d
n v Q
div n v w n F
dt m z
ϕ∂ ∂
+ ⋅ ⋅ + + =
∂
r ,
where idrF and idzF are components of the ion drag force
[5], ( , )d d dw u v= is the drift dust velocity vector.
RESULTS AND DISCUSSION
The influence of dust particles on the sheath illustrates
spatial distributions of the electric potential (Fig. 1). The
potential profiles along a perpendicular direction to the
wall are presented on the Fig.1,a for 0/ 0.01dn n = and
0dn = . Here spatial coordinates r and z are divided by
the initial electron Debye length
d
λ , the dust density dn is
divided by the ion concentration in the undisturbed
plasma 0n , the potential ϕ is divided by the
characteristic value /o ekT eφ = . We can see that potential
is decreased towards the wall monotonically if a dust
cloud is absent. At the dust cloud boundaries potential
jumps are formed that indicate about appearance of
double layers. An electric force in these layers push dust
particles if we took account of their movement. Note, the
potential changes are different at boundaries of the dust
cloud due to an ion flow towards the wall.
0 5 10 15 20 25
-16
-12
-8
-4
0
n d= 0 .01
n d= 0
φ
z
b
0 5 10 15 20 25
-3
-2
-1
0
φ
r
z=10
z=15
z=18
z=21
c
Fig. 1. Potential distributions (a) along the perpendicular
direction to the wall at 00.01dn n= ⋅ , (b) along axe r at
different z at 00.01dn n= ⋅
Consider potential dependences of radius at different
distance from the wall (Fig. 1, b). One can see that the
electric potential is changed in area 0 10r≤ ≤ before and
after the dust cloud, as well as inside the one. It should
be noted that potential distribution has oscillations in the
dust cloud region in radial direction. This means that
there are potential wells for dust particles, which may
prevent from the expansion of particles in radial direction.
Besides, oscillations of the electric potential indicate the
possibility of a plasma-dust crystal formation.
Spatial distributions of the ion velocity are shown in
Fig. 2. We can see that ions are accelerated on all the way
to the wall in the case without a dust cloud. While the ion
drift velocity is changed significantly at the boundaries of
the dust cloud. It is observed an essential acceleration of
ions to dust cloud boundaries which is associated with an
electric field in double layers.
0 5 10 15 20 25
-4
-3
-2
-1
0
1
2 nd=0.005
nd=0.001
nd=0v
z
Fig. 2. Spatial distributions of the ion velocity along
axe z
Note, that the ion flow is formed in radial direction to
the dust cloud. At the cloud boundary an ion velocity
depends of a dust density. The ion flow is subsonic at
0.001dn = and the one is supersonic at 0.005dn = . In
the latter case oscillations are appeared in distributions of
plasma parameters. This may be due to the drift instability
in plasma.
0 10 20 30 40 50
0,0000
0,0006
0,0012
0,0018
0,0024
n
d
z
tωpi=1.8*106
tωpi=2.2*106
tωpi=2.6*106
tωpi=3*106
tωpi=4.3*106
Fig.3. Spatial distributions of the dust density along the
perpendicular direction to the wall at different times
a
b
102
We obtained also spatial distributions of dust density
at different times. Results show that peaks of the dust
density are formed in space of the dust cloud and dust
particles perform the oscillations along axial direction
(Fig.3). Moreover, dust cloud is compressed along axial
and radial axes. It is shown that ion density is increased in
the dust cloud and has peaks on the boundaries of dust
cloud.
CONCLUSIONS
The simulation results show that the dust cloud
modifies the potential profile of the plasma so that double
layers are formed on its boundaries, which give rise to a
flow of ions inside the cloud. In a number of regimes is
formed a potential well for dust particles. It is shown that
the dust cloud in the sheath under the influence of
electrical forces and the ion drag force reciprocates in the
direction perpendicular to the wall.
This work was supported by joint NASU-RFFR grant.
REFERENCES
1. G.M. Jellum, D.B. Graves. Particulates in aluminum
sputtering discharges// J. Appl. Phys. 1990, v. 67,
p. 6490.
2. J. Winter. A new challenge in nuclear fusion research //
Physics of Plasmas. 2000, v. 7, N 10, p. 3862–3866.
3. G.S. Selwyn, J. Singh, R.S. Bennett. In situ laser
diagnostic studies of plasma-generated particulate
contamination//J. Vac. Sci. Technol. A. 1989, v. 7,
p. 2758.
4. S. Takamura, T. Misawa, N. Ohno, S. Nunomura,
M. Sawai, K. Asano, K. Kaw. Dynamic behaviour of
dust particles in the plasma-sheath boundary // Phys.
Plasmas. 2001, v. 8, p. 1886-1892.
5. Jin-Xiu Ma, M. Y.Yu. Electrostatic sheath at the
boundary of a dusty plasma // Phys. Plasmas. 1995,
v. 2, p. 1343-1348.
Article received 16.09.10
ДВУХМЕРНОЕ МОДЕЛИРОВАНИЕ ДИНАМИКИ ПЫЛЕВЫХ СГУСТКОВ
НА ГРАНИЦЕ ПЛАЗМЫ ВОЗЛЕ СТЕНКИ
А.Ю. Кравченко, И.С. Марущак, Г.И. Левада
Проведено компьютерное моделирование динамики пылевых сгустков возле проводящей стенки в условиях
микрогравитации и ее влияния на приэлектродный слой. Использовалась двухмерная аксиально-симметричная
гидродинамическая модель, которая учитывает самосогласованный переменный заряд пылевых частиц и
взаимное влияние плазмы и пылевой компоненты. Результаты моделирования показывают, что пылевой
сгусток изменяет профиль потенциала плазмы так, что на его границах образуются двойные слои, которые
приводят к появлению потоков ионов внутрь сгустка. В ряде режимов формируется потенциальная яма для
пылевых частиц. Показано, что в приэлектродном слое пылевой сгусток под действием электрической силы и
силы ионного трения совершает возвратно-поступательное движение в направлении, перпендикулярном к
стенке.
ДВОВИМІРНЕ МОДЕЛЮВАННЯ ДИНАМІКИ ПИЛОВИХ ЗГУСТКІВ НА ГРАНИЦІ
ПЛАЗМИ БІЛЯ СТІНКИ
О.Ю. Кравченко, І.С. Марущак, Г.І. Левада
Проведено комп’ютерне моделювання динаміки пилових згустків поблизу провідної стінки в умовах
мікрогравітації та її впливу на приелектродний шар. Використовувалась двохвимірна аксіально-симетрична
гідродинамічна модель, яка враховує самоузгоджений змінний заряд пилових частинок та взаємний вплив
плазми і пилової компоненти. Результати моделювання показують, що пиловий згусток змінює профіль
потенціалу плазми так, що на його границях утворюються подвійні шари, які приводять до появи потоків іонів
всередину згустка. В ряді режимів формується потенціальна яма для пилових частинок. Показано, що в
приелектродному шарі пиловий згусток під дією електричної сили та сили іонного тертя здійснює зворотньо-
поступальний рух в напрямку, перпендикулярному до стінки.
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