Dynamics of dust clouds in plasmas
We study a dynamics of dust clouds embedded in the infinite uniform initially plasma using computer simulation. In the one dimension, the movement of dust particles and ions is governed by cold hydrodynamics equations, electrons are assumed to be in thermal equilibrium. It is assumed that the forces...
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| Zitieren: | Dynamics of dust clouds in plasmas / O.Yu. Kravchenko, M.M. Yurchuk, O.M. Radchenko // Вопросы атомной науки и техники. — 2007. — № 1. — С. 90-92. — Бібліогр.: 5 назв. — англ. |
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irk-123456789-1104062017-01-05T03:02:33Z Dynamics of dust clouds in plasmas Kravchenko, O.Yu. Yurchuk, M.M. Radchenko, O.M. Plasma dynamics and plasma wall interaction We study a dynamics of dust clouds embedded in the infinite uniform initially plasma using computer simulation. In the one dimension, the movement of dust particles and ions is governed by cold hydrodynamics equations, electrons are assumed to be in thermal equilibrium. It is assumed that the forces on the dust consist of electrostatic force and ion drag forces. The spatial distributions of parameters were obtained at various initial densities of dust grains at different times. Results show the expansion of dust clouds at low initial dust grain density, which is evidence of exceeding the electrostatic force over the ion drag force. At the increasing of dust density oscillations of the central part of dust cloud are observed. За допомогою комп’ютерного моделювання досліджується динаміка пилових згустків в необмеженій плазмі. Рух пилових частинок та іонів описується одновимірними рівняннями холодної гідродинаміки, електрони вважаються рівноважними. В моделі припускається, що на пилові частинки діють електростатична сила та сила іонного тертя. Одержані просторові розподіли параметрів в різні моменти часу при різних значеннях початкової концентрації пилинок. Показано, що пилові згустки розширюються при малих концентраціях пилових частинок, оскільки в цьому випадку електростатична сила переважає силу іонного тертя. При збільшенні концентрації пилових частинок спостерігаються осциляції центральної частини пилових згустків. При помощи компьютерного моделирования исследуется динамика пылевых сгустков в неограниченной плазме. Движение пылевых частиц и ионов описывается одномерными уравнениями холодной гидродинамики, электроны предполагаются равновесными. В модели предполагается, что на пылевые частицы действуют электростатическая сила и сила ионного трения. Получены пространственные распределения параметров в различные моменты времени при различных значениях начальной концентрации пылинок. Показано, что пылевые сгустки расширяются при малых концентрациях пылевых частиц, поскольку в этом случае электростатическая сила превышает силу ионного трения. При увеличении концентрации пылевых частиц наблюдаются осцилляции центральной части пылевых сгустков. 2007 Article Dynamics of dust clouds in plasmas / O.Yu. Kravchenko, M.M. Yurchuk, O.M. Radchenko // Вопросы атомной науки и техники. — 2007. — № 1. — С. 90-92. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.27.Lw http://dspace.nbuv.gov.ua/handle/123456789/110406 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Plasma dynamics and plasma wall interaction Plasma dynamics and plasma wall interaction |
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Plasma dynamics and plasma wall interaction Plasma dynamics and plasma wall interaction Kravchenko, O.Yu. Yurchuk, M.M. Radchenko, O.M. Dynamics of dust clouds in plasmas Вопросы атомной науки и техники |
| description |
We study a dynamics of dust clouds embedded in the infinite uniform initially plasma using computer simulation. In the one dimension, the movement of dust particles and ions is governed by cold hydrodynamics equations, electrons are assumed to be in thermal equilibrium. It is assumed that the forces on the dust consist of electrostatic force and ion drag forces. The spatial distributions of parameters were obtained at various initial densities of dust grains at different times. Results show the expansion of dust clouds at low initial dust grain density, which is evidence of exceeding the electrostatic force over the ion drag force. At the increasing of dust density oscillations of the central part of dust cloud are observed. |
| format |
Article |
| author |
Kravchenko, O.Yu. Yurchuk, M.M. Radchenko, O.M. |
| author_facet |
Kravchenko, O.Yu. Yurchuk, M.M. Radchenko, O.M. |
| author_sort |
Kravchenko, O.Yu. |
| title |
Dynamics of dust clouds in plasmas |
| title_short |
Dynamics of dust clouds in plasmas |
| title_full |
Dynamics of dust clouds in plasmas |
| title_fullStr |
Dynamics of dust clouds in plasmas |
| title_full_unstemmed |
Dynamics of dust clouds in plasmas |
| title_sort |
dynamics of dust clouds in plasmas |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2007 |
| topic_facet |
Plasma dynamics and plasma wall interaction |
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http://dspace.nbuv.gov.ua/handle/123456789/110406 |
| citation_txt |
Dynamics of dust clouds in plasmas / O.Yu. Kravchenko, M.M. Yurchuk, O.M. Radchenko // Вопросы атомной науки и техники. — 2007. — № 1. — С. 90-92. — Бібліогр.: 5 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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AT kravchenkooyu dynamicsofdustcloudsinplasmas AT yurchukmm dynamicsofdustcloudsinplasmas AT radchenkoom dynamicsofdustcloudsinplasmas |
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2025-07-08T00:34:36Z |
| last_indexed |
2025-07-08T00:34:36Z |
| _version_ |
1837036865926987776 |
| fulltext |
PLASMA DYNAMICS AND PLASMA WALL INTERACTION
90 Problems of Atomic Science and Technology. 2007, 1. Series: Plasma Physics (13), p. 90-92
DYNAMICS OF DUST CLOUDS IN PLASMAS
O.Yu. Kravchenko, M.M. Yurchuk, O.M. Radchenko
Taras Shevchenko National Kyiv University, Faculty of Radio Physics, Kyiv, Ukraine,
e-mail: kay@univ.kiev.ua
We study a dynamics of dust clouds embedded in the infinite uniform initially plasma using computer simulation. In the
one dimension, the movement of dust particles and ions is governed by cold hydrodynamics equations, electrons are
assumed to be in thermal equilibrium. It is assumed that the forces on the dust consist of electrostatic force and ion drag
forces. The spatial distributions of parameters were obtained at various initial densities of dust grains at different times.
Results show the expansion of dust clouds at low initial dust grain density, which is evidence of exceeding the
electrostatic force over the ion drag force. At the increasing of dust density oscillations of the central part of dust cloud
are observed.
PACS: 52.27.Lw
1. INTRODUCTION
Ionized gases with dispersed dust grains occur in a
wide variety of cosmic and terrestrial environment, as
well as in laboratory experiments [1, 2]. Dust grains often
form clouds and there is interest to study their interaction
with plasmas. In particular, the expansion of dust clouds
is a fundamental process which is important in many
practical situations. For example, in laboratory devices
dust particles produced in source region can subsequently
expand into the central plasma region [3].
Earlier it was studied the interaction of dust clouds
with plasmas at conditions immobile dust particles [4].
Results show an initiation of soliton-like structures in
distributions of the electrostatic potential and the ion
density. Because of this the interest was appeared to the
investigation of the influence these structures on the dust
grains expansion.
In this paper we study a dynamics of dust clouds
embedded in the infinite uniform initially plasma.
2. MODEL
We consider one-dimensional layer of dust particles
immersed into uniform initially plasma.
In our model dust grains acquire a charge and
influence the potential of the electric field ϕ , which is
described by Poisson equation
[ ]
2
2
0
,i e d d
e n n q n
x
ϕ
ε
∂
= − − +
∂
where , ,i e dn n n are the ion, electron and dust densities,
dq is a dust particle charge.
The change of the dust charge is described by
equation
,d d
d e i
q q
v I I
t x
∂ ∂
+ = +
∂ ∂
where electron and ion currents eI and iI flowing into
dust particle are defined by OML theory [5]:
1 2
2 8
exp ,e d
e d e
e e
kT eq
I r e n
m akT
π
π
= −
1 2
2 2
2
8
1 .
( / 2)
i d
i d i i
i i i i
kT eq
I r en v
m a kT m v
π
π
= + − +
Here eT and iT are electron and ion temperatures, dr is
the radius of dust particle.
The electrons are assumed to be in thermal
equilibrium; therefore the density en satisfies the
Boltzmann relation
0 expe e
e
en n
kT
ϕ
=
,
where 0en is the electron concentration at the unperturbed
plasma.
The ions and dust particles are described by the fluid
equations:
1 ,i i i i
i id
i i i
v v T nev F
t x m x n m x
ϕ∂ ∂ ∂∂
+ = − − +
∂ ∂ ∂ ∂
( )
,i i i
i d
n v n
I n
t x
∂ ∂
+ = −
∂ ∂
,d d d
d di
d
v v q
v F
t x m x
ϕ∂ ∂ ∂
+ = − +
∂ ∂ ∂
( )
0,d d dn v n
t x
∂ ∂
+ =
∂ ∂
where , ,i iv e m are a drift ion velocity, ion charge and
ion mass , ,d dM v are a dust mass and a drift dust
velocity. The member in the right part of the continuity
equation expresses an ion deposition on dust particles.
The ion drag force diF is determined according to [5],
where
2
02 lncoul bσ π= Λ is a section of ion-dust Coulomb
collisions, 0 2
04
d
i i
eq
b
m vπε
= , 2
2
21 d
coll d
d i i
eqr
r m v
σ π
= −
is a
section of an ion deposition on dust particle.
3. RESULTS AND DISCUSSION
We have modeled the time evolution of the one-
dimensional dust layer located in electron-ion plasma. It
is considered the case when an ion and electron densities
in the unperturbed plasma are 18 3
0 10n m−= , an electron
temperature 2eT eV= , an ion temperature is 0.03iT eV= ,
and a dust particle radius is 2dr mµ= . The ratio of the
mailto:kay@univ.kiev.ua
91
ion mass to the dust mass is 0.001idm = . Note, that the
dust particle mass is chosen smaller in our simulations in
comparison with experimental data in order to reduce the
time of computations. As a result of numerical
calculations we have obtained spatial distributions of
plasma parameters at different initial dust densities
0 0 0/d dN n n= .
Results have revealed that the dust cloud dynamics
have essential distinctions at different 0dN . It is occurred
monotonous expansion of the dust cloud at low values
0dN and oscillations of dust particles at large values 0dN .
It is have seen from Fig. 1a and Fig. 2 where spatial
distributions of dust density at different times are
depictured. Here the dust density is normalized on the ion
density in the unperturbed plasma; the spatial coordinate
is normalized on Debye radius, time is normalized on the
inverse ion-plasma frequency.
500 550 600 650
0,00000
0,00005
0,00010
t=0
500
1000
1500
x
Nd
a
500 550 600 650
0,000
0,005
0,010
500 550 600 650
-450
-425
-400
VdQd
X
b
Fig.1. The spatial distributions of dust density at different
times and spatial distributions of the dust particle charge
(solid curve) and the dust drift velocity (dotted curve) at
time 1500t = for case 0 0.0001dN =
One can see that the dust density is decreased and the
drift velocity of dust particles is increased monotonically
at the increasing of the spatial coordinate x from the
centre toward the periphery of the dust cloud. The
normalized dust particle charge /d dQ q e= is increased
at the decreasing of the dust density (Fig.1b). The sharp
boundary of dust cloud is not forming in this case.
The Fig. 2 shows the spatial distributions of dust
density at different times for case with 0 0.003dN = . We
can see that dust particles perform the oscillations.
Therefore the central part of dust cloud is compressed at
first and the pick of the dust density is formed in this
location. At the same time peripheral dust particles are
expanded forming a sharp front of dust cloud. Then, the
front is stopped at time 700pitω = and starts to move
back while the central region of the cloud starts to expand.
Fig.2. The spatial distributions of dust density at different
times for 0 0.003dN =
So, counter propagating flows of dust particles occur.
As a consequence they are generated two peaks of dust
density which are moved toward the centre of the dust
cloud and embodied together. This process is
accompanied by the increasing of a dust density peak in
the centre of the cloud. In some time peaks of dust density
are formed at the periphery again.
Fig.3. Profiles of the dust density near the dust
cloud front (a) and profiles of dust drift velocity
(b) for the case with 0 0.003dN =
92
Profiles of the dust density in the region of the dust cloud
periphery are pictured in Fig. 3a for the case
with 0 0.003dN = . We can see the forming of the dust
cloud front where the dust density is decreased abruptly.
After the dust front oscillations of dust density are
appeared and at 650x ≈ the peak of the dust density is
formed. Profiles of the dust drift velocity are shown in
Fig. 3b. They are evidence of dust particles oscillations. It
is seen alternate regions with the positive and negative
dust drift velocity. Note, that the dust drift velocity is zero
at the dust cloud front and the peak location.
REFERENCES
1. M. Mikikian, L. Boufendi, H.M. Thomas, G.E.Morfill,
A.P. Nefedov, V.E. Fortov et al. // New Journal of
Physics. 2003, p.19.1-19.12.
2. D. Wang, D. Liu, J. Liu // Journal of Applied Physics.
2000, v. 88, p.1276-1280.
3 G.E. Morfill, H.M. Thomas, U. Konopka,
H. Rothermel, M. Zuzic, A. Ivlev, J. Goree // Phys.
Rev. Letters. 1999, v.83, p.1598-1601.
4. A.Yu. Kravchenko, M.M. Yurchuk // Proceedings of
International Conference on Physics of Low
Temperature Plasma, Kyiv, 2004, p. 9.14.113.
5. P.K. Shukla, A.A. Mamun. Introduction to Dusty
Plasma Physics. Bristol and Philadelphia: “IoP
Publishing Ltd.”, 2001, p.36-49.
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