Dynamics of dust clouds in plasmas
Kravchenko O.Yu., Yurchuk M.M.
Taras Shevchenko National Kyiv University, Volodymirs’ka str. 64, 01033 Kyiv, Ukraine
Abstract. In this paper 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, and therefore the number density satisfied the Boltzmann
relation. 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. It is expanded
and compressed periodically. This process is accompanied by an appearance of a dust density peak at the cloud periphery,
which is increased and decreased periodically too. The oscillations of dust grains are caused by an increasing of the ion
flow towards the dust cloud that produces the forming of double layers at the boundary of cloud and increases an ion drag
Keywords: Dusty plasma, computer simulation, dust clouds.
Dust particles are frequently observed in space and laboratory plasmas. In the past several years, much attention
has been paid to collective effects in dusty plasmas, as well as the formation of nonlinear structures like double
layers, voids and dust clouds. These phenomena are consequence of self-organization in dusty plasmas. The system
forms dust clouds and voids with sharp stable boundaries, which can be stationary or oscillate in time. They were
observed in many capacitively coupled rf devices , dc glow discharged devices  and recently have been
discovered in microgravity experiments . There are several attempts at finding theoretical explanation of this
effect, but it is still not understood. In some articles it was investigated the interaction of motionless dust clouds with
plasma and studied a forming of waves in this system . It is shown that a dust density increasing causes the
increasing of the ion flow toward the dust cloud and rising of instabilities. It is of interest to determine the influence
of these instabilities on dust particles dynamics. In this connection we investigate the temporal behavior of dust
clouds in a plasma using a computer simulation in this article.
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 fieldϕ , which is described
by Poisson equation
RESULTS AND DISCUSSION
We have modeled the time evolution of the one-dimensional dust layer located in electron-ion plasma. It is
considered case when an ion and electron densities in the unperturbed plasma are 18 3
0 n =10 m− , an electron
temperatureTe = 2eV , an ion temperature is 0.03 iT = eV , and a dust particle radius is 2 dr = μm. The ratio of
the ion mass to the dust mass is 0.001 id m = . 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 d N = n n .
Results have revealed that the dust cloud dynamics have essential distinctions at different d 0 N . It is occurred
monotonous expansion of the dust cloud at low values d 0 N and oscillations of dust particles at large values d 0 N . It
is have seen from figure 1a and figure 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.
FIGURE 1. The spatial distributions of dust density at different times (a) and spatial distributions of the dust particle charge
(solid curve) and the dust drift velocity (dotted curve) at time t =1500 for case 0 0.0001 d N = .
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 d Q = 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 figure 2 shows the spatial distributions of dust density at different times for case with 0 0.003 d N = . 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 700 pi tω = and starts to move back while the
central region of the cloud starts to expand. 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.
Profiles of the dust density in the region of the dust cloud periphery are pictured in figure 3a for the case
with 0 0.003 d N = . We can see the forming of the dust cloud front where the dust density is decreased abruptly.
FIGURE 3. Profiles of the dust density near the dust cloud front (a) and profiles of dust drift velocity (b) for the case
with 0 0.003 d N = .
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