Ion Drag on Dust Grains in Electronegative Plasmas

I. Denysenko1, M. Y. Yu2, N. A. Azarenkov1, K. Ostrikov3, S. Xu4
1School of Physics and Technology, V. N. Karazin Kharkiv National University, Svobody sq.4, 61077 Kharkiv,
Ukraine; 2Theoretical Physics I, Ruhr University, D-44780 Bochum, Germany; 3School of Physics, The University of
Sydney, Sydney, NSW 2006, Australia; 4Plasma Sources and Applications Center, NIE, Nanyang Technological
University, 1 Nanyang Walk, 637616 Singapore.
Abstract. The electric, and the positive- and negative-ion drag forces on a dust grain in an electronegative complex
plasma are investigated. It is shown that at low neutral gas pressures the number of locations where the drag forces
balance the electric force is considerably larger than that in an electropositive plasma. The balance occurs in the so-called
oscillation regime where the electric field oscillates in space. At large neutral gas pressures among the forces acting on
the dust grain, the negative-ion drag force is found to be important. Our results imply that both dust voids and balls can be
Keywords: complex, plasma, dust particles, gas discharges.
PACS: 52.25.Vy,52.27.Lw,52.77.Dq,52.80.Pi
Consider a steady-state plasma containing singly charged positive and negative ions, electrons, as well as neutral
particles. All the species interact among themselves as well as with each other. The plasma is located in a
cylindrical discharge chamber of large aspect ratio (L << D, here L and D are the height and diameter of the plasma,
respectively), so that all the plasma parameters depend only on the coordinate x perpendicular to the planes bounding
the plasma slab. For simplicity, it is assumed that the electron temperature Te is spatially constant. Therefore, the
plasma is symmetrical with respect of the center of the slab (x=0). It is assumed that there is an isolated dust grain in
the plasma. We shall consider the forces acting on the grain for different grain locations. The effect of the dust drain
on the electron and ion densities as well as the electron temperature is negligible.
We shall consider the two regimes:
a) The neutral gas pressure is sufficiently high ( λ+Te / LT+ ≤ 1) and the ion-ion volume recombination is
b) The neutral gas pressure is sufficiently low ( λ+Te / LT+ >1) and the positive-ion loss is predominantly to
the walls rather than due to volume recombination.
Here, λ+ is the positive-ion mean free path , and T+ is the positive ion temperature.
In the case a) the plasma is quasineutral, or n+ = n__ + ne. In the case b) it is nonquasineutral and we apply the
Poisson’s equation:

One can see that with an increase of the negative ion density the negative ion drag force also increases with
respect to the positive ion drag and electric forces. The increase is attributed to the enhancement of the negative ion
flux which at relatively large n_ is directed towards the center of the discharge. At small α0 the negative ion flux is
significantly smaller than that of the positive ions [Fig. 1 (d)]. At largeα0 , the positive and negative ion fluxes have
almost the same magnitude. As a result, the total ion drag force Fdr+ + Fdr – decreases significantly as compared with
Fdr+ . One can see that at small α0 the total drag force is larger than the electric force |Zd eE | at x < 0.5 cm. At large
α0 due to increase of |Fdr-| the total ion drag force is smaller than |Zd eE| in the entire plasma slab.
The distributions of the forces for the case b) are shown in Fig. 2.

FIGURE 2. The normalized forces for different electron densities at x = 0 ne0. Profiles are for L/2 = 1.5 cm, p0= 20
mTorr, α0 = 5, T+ = 600 K, ad = 100 nm.
One can see that for the parameters considered there are spatial oscillations of the electric field near the
boundary between the electronegative core of the discharge and the electropositive region near the edge x = L/2 of
the discharge. The periodic pattern takes place when the electronegative discharge is in the so-called “oscillation
regime” [5,6]. With increase of ne0 the drag forces grow, consistent with Eq. 4. There are several locations where the
positive-ion drag force equals the electric force |Zd eE |. The first is near the discharge center x = 0, where all the
forces vanish. The other locations are for x > 0.75 cm. It is of interest to note that the number of static-equilibrium
points (where |Zd eE | = Fdr+) for x ≠ 0 can be larger than one. In electropositive plasmas there are usually only one
or two points where the ion drag force can balance the electric force [1]. In an electronegative discharge, because of
the oscillations in the charge density, the number of static-equilibrium points can be considerably larger than 2 (for
example, 3 in Fig. 2 (b) and about 9 in Fig.2 (c). At higher ne0, the number of such points is reduced because of an
increase of the positive-ion drag force [2].
Thus, it is shown that the direction of the negative-ion drag force depends on the negative ion density n__.
At small n_ the force is directed towards the plasma boundary, and at large negative ion density the direction is
reversed. The directions of the electric and positive-ion drag forces do not depend on n_. For a negatively charged
dust grain the electric and positive ion drag forces are directed towards and away from the discharge center,
At high negative ion densities the negative ion drag force is important. The magnitude of the force is near
that of the positive ions if the negative and positive ion fluxes are of similar magnitude. Due to the negative-ion drag
force the total ion drag force acting on a dust particle in an electronegative plasma usually decreases because Fdr- is
directed towards the discharge center at relatively large negative ion densities. As a result, at large n_ the total ion
drag force can be smaller than the electric force in the entire plasma volume. At small n_ the total ion drag force
dominates over |Zd eE | in the central part of the discharge.
If the condition | (Fdr- + Fdr+ )/ Zd eE | > 1 is satisfied at the center of the discharge, appearance of voids in
complex plasmas is possible [7,8]. To develop so-called ball cluster [9] structures a force directed towards the
discharge center is needed. Arp et al. [9] heated a substrate in order to apply the thermothoresis force in the
direction of the discharge center.
The results of our study show that at high negative ion densities the total force acting on a dust particle can
be directed towards the center in the plasma volume. Thus one can have balls in electronegative complex plasmas
even without the thermothoresis force by simply increasing the negative ion density. When the total force is directed
to the discharge center, we can expect that the dust particles will be trapped near the center of the plasma. Such a
configuration can be useful in particle plasma processing, as well as for basic studies of crystal behavior.
One of the authors (I.D.) was supported by the Humboldt Foundation. This work was partially supported by the
Australian Research Council, The University of Sydney, A*STAR (Singapore), and the International Research
Network for Deterministic Plasma-Aided Nanofabrication.
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