Two-dimensional simulation of dust clouds in a plasma
In this article has been carried numerical simulations of the interaction of the partically ionized argon plasma and a dust cloud, which is situated near the wall in a cylindrical vessel. The plasma and dust dynamics studied in the frame of two-dimensional hydrodynamics model, the charge of dust par...
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| Zitieren: | Two-dimensional simulation of dust clouds in a plasma / Yu.I. Chutov, A.Yu. Kravchenko, M.M. Yurchuk, S.M. Lysyuk // Вопросы атомной науки и техники. — 2005. — № 2. — С. 73-75. — Бібліогр.: 6 назв. — англ. |
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irk-123456789-793842015-04-01T03:02:27Z Two-dimensional simulation of dust clouds in a plasma Chutov, Yu.I. Kravchenko, A.Yu. Yurchuk, M.M. Lysyuk, S.M. Basic plasma physics In this article has been carried numerical simulations of the interaction of the partically ionized argon plasma and a dust cloud, which is situated near the wall in a cylindrical vessel. The plasma and dust dynamics studied in the frame of two-dimensional hydrodynamics model, the charge of dust particles is determined acording to the orbit-limited probe model, the potential of the self-consistent electric field is described by Poisson equation. As a result simulations the spatial distributions of dust cloud parameters are obtained at different times. Проведено числовий розрахунок взаємодії частково іонізованої аргонової плазми з пиловим згустком, що утворюється біля стінки в циліндричній камері. Для описання динаміки плазми і пилових частинок використовувалась двовимірна гідродинамічна модель, заряд пилових частинок визначався за допомогою моделі обмежених орбіт, а потенціал самоузгодженого електричного поля описувався рівнянням Пуассона. При аналізі динаміки пилових частинок враховувались електричні сили, а також сили, обумовлені іонною в’язкістю та тертям з нейтральними частинками. В результаті проведеного моделювання одержані просторові розподіли параметрів пилового згустку в різні моменти часу. Проведен численный расчет взаимодействия частично ионизированной аргоновой плазмы с пылевым сгустком, который образуется возле стенки в цилиндрической камере. Для описания динамики плазмы и пылевых частиц использовалась двухмерная гидродинамическая модель, заряд пылевых частиц определялся при помощи модели ограниченных орбит, а потенциал самосогласованного электрического поля описывался уравнением Пуассона. При анализе динамики пылевых частиц учитывались электрические силы, а также силы, обусловленные ионной вязкостью и трением с нейтральными частицами. В результате проведенного моделирования получены пространственные распределения параметров пылевого сгустка в различные моменты времени. 2005 Article Two-dimensional simulation of dust clouds in a plasma / Yu.I. Chutov, A.Yu. Kravchenko, M.M. Yurchuk, S.M. Lysyuk // Вопросы атомной науки и техники. — 2005. — № 2. — С. 73-75. — Бібліогр.: 6 назв. — англ. 1562-6016 PACS: 52.27.Lw http://dspace.nbuv.gov.ua/handle/123456789/79384 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Basic plasma physics Basic plasma physics |
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Basic plasma physics Basic plasma physics Chutov, Yu.I. Kravchenko, A.Yu. Yurchuk, M.M. Lysyuk, S.M. Two-dimensional simulation of dust clouds in a plasma Вопросы атомной науки и техники |
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In this article has been carried numerical simulations of the interaction of the partically ionized argon plasma and a dust cloud, which is situated near the wall in a cylindrical vessel. The plasma and dust dynamics studied in the frame of two-dimensional hydrodynamics model, the charge of dust particles is determined acording to the orbit-limited probe model, the potential of the self-consistent electric field is described by Poisson equation. As a result simulations the spatial distributions of dust cloud parameters are obtained at different times. |
| format |
Article |
| author |
Chutov, Yu.I. Kravchenko, A.Yu. Yurchuk, M.M. Lysyuk, S.M. |
| author_facet |
Chutov, Yu.I. Kravchenko, A.Yu. Yurchuk, M.M. Lysyuk, S.M. |
| author_sort |
Chutov, Yu.I. |
| title |
Two-dimensional simulation of dust clouds in a plasma |
| title_short |
Two-dimensional simulation of dust clouds in a plasma |
| title_full |
Two-dimensional simulation of dust clouds in a plasma |
| title_fullStr |
Two-dimensional simulation of dust clouds in a plasma |
| title_full_unstemmed |
Two-dimensional simulation of dust clouds in a plasma |
| title_sort |
two-dimensional simulation of dust clouds in a plasma |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2005 |
| topic_facet |
Basic plasma physics |
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http://dspace.nbuv.gov.ua/handle/123456789/79384 |
| citation_txt |
Two-dimensional simulation of dust clouds in a plasma / Yu.I. Chutov, A.Yu. Kravchenko, M.M. Yurchuk, S.M. Lysyuk // Вопросы атомной науки и техники. — 2005. — № 2. — С. 73-75. — Бібліогр.: 6 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT chutovyui twodimensionalsimulationofdustcloudsinaplasma AT kravchenkoayu twodimensionalsimulationofdustcloudsinaplasma AT yurchukmm twodimensionalsimulationofdustcloudsinaplasma AT lysyuksm twodimensionalsimulationofdustcloudsinaplasma |
| first_indexed |
2025-07-06T03:27:02Z |
| last_indexed |
2025-07-06T03:27:02Z |
| _version_ |
1836866520694652928 |
| fulltext |
TWO-DIMENSIONAL SIMULATION OF DUST CLOUDS IN A PLASMA
Yu.I. Chutov, A.Yu. Kravchenko, M.M. Yurchuk, S.M. Lysyuk
Taras Shevchenko Kiev University, Kiev, Ukraine
In this article has been carried numerical simulations of the interaction of the partically ionized argon plasma and a
dust cloud, which is situated near the wall in a cylindrical vessel. The plasma and dust dynamics studied in the frame of
two-dimensional hydrodynamics model, the charge of dust particles is determined acording to the orbit-limited probe
model, the potential of the self-consistent electric field is described by Poisson equation. As a result simulations the
spatial distributions of dust cloud parameters are obtained at different times.
PACS: 52.27.Lw
1. INTRODUCTION
The physics of dusty plasmas has been extensively
studied in the last decade in view of practical applications in
space, as well as laboratory situations. Particular attention
has been paid to the study of collective processes, such as the
formation of nonlinear structures like solitons, double layers,
voids, vortexes and dust clouds with sharp boundary. These
phenomena are observed in many capacitively coupled rf
devices [1], dc glow discharged devices [2] and recently
have been discovered in microgravity experiments [3]. A
characteristic feature of bounded dusty plasmas with free
boundaries is the expansion process. The one-dimensional
expansion of an unmagnetized dusty plasma was examined
by [4], [5]. It is necessary note that experimental results
shown that dust clouds are not one-dimensional [3] and this
feature may causes new phenomena.
In this article we investigate the temporal behavior of dust
clouds in plasma near a solid wall using two-dimensional
hydrodynamic model and a computer simulation.
2. MODEL
We consider partially ionized argon plasma in a
cylindrical vessel (fig.1). The cloud of dust particles
immersed into the plasma near the solid wall. The form of
the dust cloud at initial time is a disk. In our model dust
grains acquire a charge and influence the potential of the
electric field ϕ , which is described by Poisson equation:
( )
0
1 .i e d den en q nϕ
ε
∆ = − − +
The wall potential 0ϕ at the bottom of the vessel (Fig.1)
is floating. The other walls of the vessel are grounded (
0ϕ = ).
Fig.1
Electrons are assumed to be in a thermal equilibrium;
therefore their density satisfies the Boltzmann distribution
ne=neo⋅exp ej
kT e ,
where 0en is the electron density far away from the
charged wall.
Ions and dust particles are treated as a cold fluid,
governed by the continuity and the momentum
conservation equations
( )i i
i i d
n Idiv n w n
t e
∂
∂
+ = −r
,
¶ ni
¶ t
div n i wh=-Y i nd ,
i
i i i i i id
wm n w w en F
t
∂ ϕ
∂
й щ+ = − +С Ск ъл ы
r rr r
,
d
d d d d d d id n
wm n w w q n F F
t
∂ ϕ
∂
й щ+ = − − +С Ск ъл ы
r r rr r
.
The dust charge dq is determined by the charging
currents
( )d
d d i e
q w q I I
t
∂
∂
+ = −Сr
.
Here in , dn are ion and dust densities, iwr , dwr are drift
velocities of ion and dust fluids.
According to the orbit-limited probe model, the electron
and ion charging currents eI and iI are determined by
local electron and ion densities, as well as the potential
difference between the grain surface and the local plasma.
They are given by
2 8 ( )e
e d e e d
e
kTI r e n K q
m
π
π
= − ,
I i=πrd
2 e 8 kT i
πmi
n i1 −
eqd
r d kT i ,
Problems of Atomic Science and Technology. Series: Plasma Physics (11). 2005. № 2. P. 73-75 73
plasma
0ϕ ϕ=
0ϕ = dust cloud
sheath
where ( ) exp d
e d
d e
eqK q
r kT
ж ц
= з ч
и ш
when 0dq < and
( ) 1 /e d d d eK q eq r T= + when 0dq > .
We assume that the forces on the dust consist of
electrostatic force, ion drug forces, and neutral collision
force. The ion-drag force idF
r
consists of the collection
c
idF
r
and orbit o
idF
r
components. The collection force is a
result of the momentum transfer from the ions collected
by the particle, so that 2 ,c
i i i i i cF n m w w bπ= r r
and the
orbit force is conditioned by momentum transfer from the
ions of orbital motion around the grain
2
/ 24o
i i i i iF n m w w bππ= Γ
r r r
,
where 2
/ 2 /d i ib eq m wπ = is the orbital impact parameter
and 2 2 2 2 1/ 2
/ 2 / 2ln[( ) /( )]d cb b bπ πλΓ = + + is the Coulomb
logarithm integrated over the interval from collection
impact parameter to Debye radius dλ . The neutral gas
collision force nF
r
is given by:
216 1
3 8
n n
n n
th
r n TF w
w
π πж ц= +з чи ш
r r
,
where nwr is neutral gas velocity, thw is neutral gas mean
thermal velocity, ,n nn T , and nm are the neutral gas
density, temperature, and mass, respectively.
The modified method of big particles [6] is used
for the computer modeling of this problem. In this method
the complex set of equations is separated on simpler
components which describes separated physical
processes. The general solution consists of additive
members of time influences of each process on spatial
parameter distributions. Each process is simulated with
the corresponded minimum characteristic time what
allows to obtain higher simulation precision.
3. RESULTS
We simulated the evolution of the two-dimensional
dust cloud using the large particles method [5].
Calculations were carried out for following plasma
parameters: nio=neo=1012cm-3, 1eT eV= , 0.1dr mµ= ,
nd=108cm-3, nn=1016cm-3. The length and the radius of
the vessel are L=10cm and R0=2.5cm corresponding.
Figure 2a shows the spatial distribution of dust
density at 300pitω = after the beginning of the dust cloud
expansion. The dust density is normalized on the ion
density in the unperturbed plasma; the spatial coordinate
is normalized on Debye radius.
We can see that the density of dust particles is not
uniform along radius. Its maximum is at axis of symmetry
( 0r = ). Expansion of dust cloud is carried out radially.
The dust cloud doesn’t expand along axial axis in
consequence of the balance of electrical and viscosity
forces. It is confirmed by fig.2b, where distributions of
dust density along axial axis are shown. These
distributions are invariable during the long time interval.
60 80 100
0
1
2
3
4
5 twpi=200
500
700
x
nd*104
Fig. 2. The spatial distributions of dust density (a) and
electrical potential (b) at tωpi=300
The electrical potential ϕ is shown in figure 1b as a
function of radius r and axial coordinate x . Here the
potential is normalized on the characteristic potential ekT
e
. We can see that at the boundary of dust cloud double
74
a
b
c
layers are formed. These double layers cause the capture
of dust particles in some region near the wall.
REFERENCES
1. H.Thomas, G.E. Morfill, V. Demmel, J.Goree,
B.Feuerbacher, D. Mohlman // Phys. Rev. Lett. 1994,
v.73, N5, p.652-655.
2. V.E. Fortov, A.P. Nefedov, V.M. Torchinskii,
V.I.Molotkov at al. // JETP Lett. 1996, v.64, N2, p.92-98.
3. V.N. Tsytovich, S.V. Vladimirov, G.E. Morfill,
J. Goree // Phys. Rev. E63. 56609 (2001).
4. R. Bharuthram, N.N.Rao // Planet Space Sci. 1995,
v.43, p.1079.
5. R.Bharuthram, N.N.Rao, S.R.Pillay // IEEE
Transactions on Plasma Sci. 2001, v.29, N2, p.164-174.
6. O.M.Belozerkovsky, Yu.M.Davydov. Method of big
particles in the gas dynamic. M.: “Atomizdat”. 1982.
ДВУХМЕРНОЕ МОДЕЛИРОВАНИЕ ПЫЛЕВЫХ СГУСТКОВ В ПЛАЗМЕ
Ю.И. Чутов, А.Ю. Кравченко, Н.М. Юрчук, С.Н. Лысюк
Проведен численный расчет взаимодействия частично ионизированной аргоновой плазмы с пылевым сгустком,
который образуется возле стенки в цилиндрической камере. Для описания динамики плазмы и пылевых частиц
использовалась двухмерная гидродинамическая модель, заряд пылевых частиц определялся при помощи
модели ограниченных орбит, а потенциал самосогласованного электрического поля описывался уравнением
Пуассона. При анализе динамики пылевых частиц учитывались электрические силы, а также силы,
обусловленные ионной вязкостью и трением с нейтральными частицами. В результате проведенного
моделирования получены пространственные распределения параметров пылевого сгустка в различные моменты
времени.
ДВУХВИМІРНЕ МОДЕЛЮВАННЯ ПИЛОВИХ ЗГУСТКІВ У ПЛАЗМІ
Ю.І. Чутов, О.Ю. Кравченко, М.М. Юрчук, С.М. Лисюк
Проведено числовий розрахунок взаємодії частково іонізованої аргонової плазми з пиловим згустком, що
утворюється біля стінки в циліндричній камері. Для описання динаміки плазми і пилових частинок
використовувалась двовимірна гідродинамічна модель, заряд пилових частинок визначався за допомогою
моделі обмежених орбіт, а потенціал самоузгодженого електричного поля описувався рівнянням Пуассона. При
аналізі динаміки пилових частинок враховувались електричні сили, а також сили, обумовлені іонною в’язкістю
та тертям з нейтральними частинками. В результаті проведеного моделювання одержані просторові розподіли
параметрів пилового згустку в різні моменти часу.
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