22P073-P
Biased-Modulation of Dust Velocity Shear Flow in RF Plasma
RFプラズマ中における微粒子速度シア流へのバイアス変調
Takuma Gohda and Satoru Iizuka
合田 巧真, 飯塚 哲
Graduate School of Engineering, Tohoku University
Aoba 6-6-05, Aoba-ku, Sendai 980-8579, Japan東北大学大学院工学研究科 〒980-8597 仙台市青葉区荒巻字青葉6-6-05
Dynamic behavior of a dust flow with velocity shear was investigated in RF plasmas. Here, neutral dragforce was employed to drive the dust flow. The neutral gas ejected from small nozzles gave momentum tothe particles to generate a directional dust flow with velocity shear. The strength of the velocity shear could
be controlled over a wide range by adjusting the direction of the nozzles and the flow rate of the neutral gas.
The dust shear flow was modulated by applying a sinusoidal voltage to a point electrode, which was placed
just under the dust flow channel plate. The modulation gave rise to a periodic flow motion that waschanged by the flow direction and flow velocity. Wave-like phenomenon was also observed in the dust
shear flow.

1. Introduction
Fine particles introduced in the plasma wereknown to have negative charges, trapped at thesheath edge of a powered RF electrode. The propertyof the dust cloud in a strongly coupled state can becharacterized by the Coulomb coupling parameterΓ,i.e. Γ = ( q d 2 4πε 0 aκTd ) exp(− a λ D ) , where qd isdust charge, Td is dust temperature, a is inter-particle
distance andλD is the Debye length. It is well known
that a phase transition from fluid to solid happens
when Γ >Γcri ～172 in a one-component plasma(OCP). Therefore, the dust cloud behaves as aproperty of Coulomb fluid when Γ < Γcri. In thiscase, the dust cloud may change its shape and ancollective motion will be generated, when theexternal forces, such as the electrostatic force, the ion
drag force, the gravity, and so on, act on the dust
fluid. Note that the viscosity due to the Coulombinteraction depends both on the values of Γ and a/λD.
In our previous experiments, we demonstrated a
dynamic behavior of a dust shear flow, which wasdriven by neutral drag force [1]. Extremely
disordered structure and convection of particles wereobserved experimentally. We had also observed
several chaotic behaviors of the dust shear flow. The
external force drove a convective vortex motion,accompanied with velocity shear flow as a result of
the Coulomb interaction.
There have been many unknown subjects about
physical phenomena of the shear fluid which has
the viscosity caused by the Coulomb collision,
which is intrinsically different from the collision
between molecules in neutral fluids. We intend toinvestigate dynamic behavior of the dust flow thatis considered as the Coulomb fluid in plasmas. Here,
we investigate how the velocity shear flow evolves
when the modulation bias is applied to the dustflow.
2. Experimental apparatus and method
Figure 1 shows a schematic of the experimental
apparatus. Argon plasma was produced by acapacitively coupled RF discharge. We used RFpower of 1 - 20 W at 13.56 MHz, and Ar pressure PAr
was in a range of 20 - 60 Pa. Typical plasma density
was ne ~ 1×109 cm-3 and electron temperature was
Te ~2 eV. The experiment was carried out with a useof special shape of a levitation electrode plate of 1

Fig. 1. Experimental apparatus.

mm in thickness, as shown in Fig. 1. The levitation
plate has a hole at the center with a dumbbell shape,
consisting of a straight part of 7 - 23 mm in lengthand 20 mm in width, combined with two circularparts of 30 mm in diameter. The straight part is used
for a straight channel for counter dust streams. The
dust particles of 10μm in diameter were introduced
externally into the plasma by a dust dropper and canbe trapped mainly above the circular parts.
Increasing the number of the particles injected, theparticles were also trapped above the straight channelregion.
The dust shear flow was modulated by giving asinusoidal voltage to a point electrode that wasplaced just under the dust flow channel plate.

point electrode, the dust particles started to movewith back and forth motions by the electrostatic
potential evolved in the sheath region around theelectrode. Here, although the distribution ofelectrostatic potential formed by the electrodepotential was almost point-symmetric, the responseof the dust flow was dependent on the direction of
the flow. For the particles incoming toward theelectrode the potential modulation seemed to act as
deceleration and for the particles escaping from thepoint electrode region it seemed to act asacceleration.
The applied voltage could also excite a dust
wave propagating in the dust shear flow. The wave
propagation against the dust flow seemed to be

3. Experimental results and discussion
Figure 2(b) shows the streamline of the dust
shear flow, when the modulation bias is turned off.
The point electrode was situated at the center of thedust flow channel as schematically shown in Fig.
2(a). The data was obtained by integrating 30
frames taken by a high-speed camera with 125
frames per second. In this experiment, the dust
particles were driven by a neutral drag force of argon

Fig. 3 Stream lines of dust shear flow
with modulation

heavily damped. However, the wave propagating inthe same direction of the dust flow seemed to be
weakly damped.

Fig. 2 (a) Schematic of dust flow channel
with X-point of flow separatrix at the center.
(b) Stream lines of dust shear flow without
modulation.

gas ejected from two nozzles of 0.8 mm in innerdiameter. Since the experimental position was far
away from the nozzles placed at the outer edge of thecircular parts of the levitation electrode (see Fig. 1),
the flow dynamics ware considered as a result ofelectrostatic interaction between the dust particles inthe shear flow region. The counter flows meet near
the point electrode and form an X-point withseparatrix in the flow pattern.
When the sinusoidal voltage was applied to the4. Conclusion
Dynamic behavior of the dust flow with velocity
shear was investigated in RF plasmas. In this study,
the dust shear flow was modulated by applying asinusoidal voltage to a point electrode placed justunder the dust flow channel plate. The modulation
evolved a periodic flow motion that was changedby the flow direction and flow velocity. Wavephenomenon was also excited by the modulation.
The propagation properties were changed by theflow direction.
References[1] T. Gohda et al., 14th International Conference on
Plasma Physics,, Fukuoka, Japan, Sep 8-12, (2008)
p. 259.