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A. Samarian and O. Vaulina
School of Physics, University of Sydney, NSW 2006, Australia
Outlines
The experimental set-up
Vertical and horizontal vortices
Velocity distribution
Simulation results
Conclusion
2
Vortex in ICP
1mm
RF discharge 17.5 MHz
Pressure from 560 mTorr
Input voltage from 500 mV
3
Melamine formaldehyde 6.21m±0.09m
Argon plasma Te~ 2eV & ne ~
108cm-3
Experimental Setup
The
experiments
carried out dust
in a
Images
of thewere
illuminated
40-cm
diameter
cloud areinner
obtained
using acylindrical
chargedstainless
steel vacuum
vessel with
with
coupled device
(CCD) camera
many
ports micro
for diagnostic
access.
a 60mm
lens and
a digital
The
chamber
height
is 305-50
cm.mm).
The
camcorder
(focal
length:
diameters
of electrodes
are 10atcm
The camcorder
is operated
25for
to
the
disk
and
11.5
cm
for
the
ring
The
100 frames/sec.
dust particles suspended in the plasma
are illuminated using a Helium-Neon
Observation
laser.
Observation
Window
Top Ground
Electrode
Particle
Dispenser
Laser
Probe Inlet
Argon Gas
Inlet
Confining Ring
Electrode
Window
RF discharge 15 MHz
Oil Diffusion
Pump
Top Ground
Electrode
Pressure from 10 to 400 mTorr
Input power from 15 to 200 W
Probe Inlet
Self-bias voltage from 5 to 80V
Melamine formaldehyde - 2.79 μm ± 0.06 μm
Argon plasma Te ~ 2 eV,
Confining Ring
Electrode
Vp =50V
& ne ~
Oil Diffusion
Pump
4
109 cm-3
Particle
Dispenser
The laser
video
stored
on
The
beam signals
enters the are
discharge
chamber
Laser
through
a 40-mm
window.
videotapes
or diameter
are transferred
to a
computer
a frame-grabber
We
use theviaArgon
top-view
window card.
to view the
Gas
Inlet
horizontal
dust-structure.
The coordinates
of particles were
In
addition a in
window
a side the
port
measured
eachmounted
frameon and
in
a perpendicular
direction provides
a view
trajectory
of the individual
particles
wereof
the
vertical
of the dust structure.
traced
out cross-section
frame by frame
Experimental Setup for Vertical Vortex Motion
Dust vortex in discharge plasma
(superposition of 4 frames)
Melamine formaldehyde –2.67 μm
(Side view)
5
Experimental Setup for Horizontal Vortex Motion
Grounded
electrode
Grounded
electrode
Pin electrode
Dust
Vortex
Grounded
Grounded
electrode
electrode
Dust
Vortex
Dust
Vortex
Dust
Vortex
Powered electrode
Side View
electrode
PinPin
electrode
Top View
Video Images of Dust Vortices in Plasma Discharge
6
Vortex Movie
7
Velocity distribution
Spatial Velocity Distribution
15cm/s
Velocity Distribution Function
8cm/s
3cm/s
P= 70W
0cm/s
P= 100W
P= 30W
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Velocity Distribution
Number of particles
The Effect of Power on Velocity
Distribution in Horizontal Plane
70W
P= 30W
100W
P=
velocity (cm/sec)
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Vertical Cross Section
P= 120W
P= 80W
P= 60W
P= 30W
10
Vertical Component of Particles’ Velocity
The Effect of Power on z-component of
the Velocity of Particle
P= 30W
P= 60W
P= 80W
P= 120W
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Equation of Motion
Lets consider the motion of Np particles with charge Z=Z(r,y)=Zoo+Z(r,y), in



an electric field E (r , y)  i E ( y)  j E (r ) , where r=(x2+z2)1/2 is the horizontal
coordinates in a cylindrically symmetric system.
y
y0
Z00
r0
r
d
Fint (r )  eZ (  , y ) D
dr
Z00+Z(r,y)
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Equation of Motion
Lets consider the motion of Np particles with charge Z=Z(r,y)=Zoo+Z(r,y), in



an electric field E (r , y)  i E ( y)  j E (r ) , where r=(x2+z2)1/2 is the horizontal
coordinates in a cylindrically symmetric system.
Taking the pair interaction force Fint, the gravitational force mpg, and the
Brownian forces Fbr into account, we get:

d l
m p 2k   Fint (l )l  l l
k
j
dt
j
2
 


lk  l j
dlk 

m


F

F
 
p fr
br
ext
dt
lk  l j
where l is the interparticle distance, mp is the particle mass and fr is the
friction frequency.
Now D  eZ (r , y ) exp( l ) is the interparticle potential with screening length D,
l
D
and e is the electron charge.



Also F  i {E ( y)eZ (r , y)  m g}  j E (r )eZ (r , y) is the total external force.
ext
p
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Equation of Motion
 Total external force
interparticle interaction



Fext  i {E ( y)eZ (r , y)  m p g}  j E (r )eZ (r , y)
Fint (r )  eZ (  , y )
dD
dr
and
are dependent on the
particle’s coordinate.
 When the curl of these forces  0, the system can do positive work to
compensate the dissipative losses of energy. It means that infinitesimal
perturbations due to thermal or other fluctuations in the system can grow.
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Results from Simulation
15
Results from Simulation
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Dust Charge Spatial Variation
ne/ni=f
ni(e)
Te
(r) and Te=f (r)
Assuming that drift electron (ion) currents < thermal current, Ti0.03eV and neni, then:
<Z> = CzaTe
Here Cz is 2x103 (Ar). Thus in the case of Z(r,y)=<Z>+TZ(r,y), where TZ is the
equilibrium dust charge at the point of plasma with the some electron temperatures Te,
and TZ(r,y) is the variation of dust charge due to the Te, then:
T Z(r,y)/<Z> = Te(r,y)/Te
and
y/<Z>=(Te/y)Te-1, /<Z> = (Te/)Te-1
If spatial variations n Z(r,y) of equilibrium dust charge occur due to gradients of
concentrations ne(i) in plasma surrounding dust cloud, assuming that conditions in the
plasma are close to electroneutral (n=ni-ne«nenin and nZ(r,y)«<Z>), where nZ(r,y) is
the equilibrium dust charge where ne=ni, then nZ(r,y) is determined by equating the
orbit-limited electrons (ions) currents for an isolated spherical particle with equilibrium
surface potential < 0, that is.
 0.26 Z n
Z n
n Z(,y)  n(1  e 2 Z / aT ) 
n
e
where <Z>2000aTe
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Kinetic Energy
Energy gain for two basic types of instabilities:
Dissipative instability for systems, where dissipation is present (Type 1);
Dispersion instability, when the dissipation is negligibly small (Type 2)
1. O. S. Vaulina, A. P. Nefedov, O. F. Petrov, and V. E. Fortov, JETP 91, 1063 (2000).
2. O. S. Vaulina, A. A. Samarian, A. P. Nefedov, V. E. Fortov, Phys. Lett. A 289, 240(2001)
3. O. S. Vaulina, A. A. Samarian, O. F. Petrov, B. W. James ,V. E. Fortov, Phys. Rev. E (to be published)
4. O. S. Vaulina, A. A. Samarian, A. P. Nefedov, V. E. Fortov, Phys. Lett. A 289, 240(2001)
The kinetic energy К(i), gained by dust particle after Type 1 instability is:
К( i )=mpg22/{8fr2}
where ={Аr/Zoo} determines relative changes of Z(r) within limits of particle
trajectory
When a=5m, =2g/cm3 and fr12P (P~0.2Torr), К( i ) is one order higher than
thermal dust energy To0.02eV at room temperature for  >10-3 (r/Zoo>0.002cm-1,
A=0.5cm)
Increasing gas pressure up to P=5Torr or decreasing particle radius to a=2m, К( i )/To
>10 for >10-2 (r/Zoo>0.02cm-1, A=0.5cm).
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Kinetic Energy
For Type 2 instability, К(ii) can be estimated with known c
р(2e2Z(r,y)2npexp(-k){1+k+k2/2}/mp)1/2
where k=lp/D and Z(r,y)<Z> for small charge variations
Assume that resonance frequency c of the steady-stated particle oscillations
is close to р. Then kinetic energy К(ii) can be written in the form:
К(ii)5.76 103 (aTe) 22cn/lp
where cn=exp(-k){1+k+k2/2} and =А/lp (~0.5 for dust cloud close to solid
structure)
When a=5m, =0.1, k1-2, lp=500m, and Te~1eV, the К(ii)3eV. The
maximum kinetic energy (which is not destroying the crystalline dust
structure) is reached at =0.5. And К(ii)lim=cne2<Z>2/4lp
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-Dependency on Pressure
wс =  /2= F /{2mpZofr}
Dependency of the rotation frequency  on pressure
for vertical (a) and horizontal (b) vortices
a)
10
U=40 V
b)
60
9
8

50
7

pg/{Zov fr }
6
=12 mm-1
5
40
Ftp/{2mdZov fr }
30
=320 mm-1
4
20
3
2
10
1
0
0
0
20
40
60
80
100
120
Pressure, mTorr
20
140
160
180
200
0
20
40
60
80
100
120
Pressure, mTorr
140
160
180
200
Conclusion
The results of experimental observation of two types of
self-excited dust vortex motions (vertical and horizontal) in
planar RF discharge are presented
The first type is the vertical rotations of dust particles in
bulk dust clouds
The second type of dust vortex is formed in the horizontal
plane for monolayer structure of particles
We attribute the induction of these vortices with the
development of dissipative instability in the dust cloud
with the dust charge gradient, which have been provided
by extra electrode. The presence of additional electrode
also produces the additional force which, along with the
electric forces, will lead to the rotation of dust structure in
horizontal plane
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