Transcript Criterion for phase transition

Particle’s Dynamics in Dusty Plasma
with Gradients of Dust Charges
Institute for High Energy Densities, Russian Academy of Sciences, Moscow, Russia,
O. S. Vaulina, O. F. Petrov, V. E. Fortov
School of Physics, University of Sydney, NSW 2006, Australia,
A. A. Samarian, B.W.James2
 Dust Vortices in Gas Discharge Plasma
 Stochastic Dust Motion
 Self-exited Dust Motion in Rf- Discharge
Laboratory Dusty Plasma – weakly ionized gas
with micron-sized dust particles (macroparticles)
Typical conditions of experiments
in gas discharge plasma
Parameters of gas discharge plasma:
Temperature of
ions and electrons: Ti << Te~1-7eV
Gas pressure:
Р ~ 0.03-3 Тorr
Plasma concentration:
~ 108-109 см-3
Neutral’s concentration :
~ 1014-1016 см-3
dc- discharge
rf- discharge
Laboratory Dusty Plasma – weakly ionized gas
with micron-sized dust particles (macroparticles)
Typical conditions of experiments
Parameters of dust particles:
Radius:
ap ~ 1-10 м
Charge:
Z p ~ 102 - 105
Concentration:
np ~ 103 - 105 см –3
Kinetic
TEMPERATURE:
Тp ~ 0.03-100 eV
(«Abnormal dust heating»)
Dust Vortices
Crystal
Fluid
Oscillations of separate particles
Instability of the system with the dust charge
gradients orthogonal to the non-electrostatic force
 =Z(l)/l – due to inhomogeneity of plasma surrounding the dust cloud ne(i),Te(i) ),Ve(i)
 Electron Temperature Gradients (Te/r)
 Variations in regular ion’s velocity (Vi/r)
 Gradients of plasma densities ((ni - ne)/r)
/<Z> ~ (1-100)% см-1
/<Z> ~ (1- 50)% см-1
/<Z> ~ (1- 50)% см-1
Equations of motions for particles with Zр(,y) in an electric field Eext of cylindrically
symmetric trap:





d lk
dl k
mp
  m p v fr
 F  Fnon  Fbr
2
dt
dt


2
F  Fint  Fext, Fext = e Zр(,y) E(,y),


Fint   eZ (  , y )
l
j
  
l  l k l j
 
lk  l j
 
lk  l j
For typical conditions of ground-based experiments in gas discharge plasma
Non-electrostatic forces Fnon - gravity force mpg,
ion drag force Fi  (0.1-0.5) mpg,
thermothoretic force Fт < 0.1 mpg
Conditions for occurrence of dust instabilities
Disperse Instability
when the frictional force does
not damp the dust oscillations
(regular vibrations or random
dust fluctuations similar to the
Brownian motion)
Conditions of Occurrence
for Z >> Z
fr 2< c 2 < o  / fr 
 = rot V  (y) Fnony() / {mpZofr},
o - shift parameter,
c – resonance frequency
Dissipative Instability when a restoring force is absent (dust vortexes)
c 4 < ofr 
Dust vortices under ground-based conditions
in dc- discharge
in rf - discharge
argon, Р ~ 0.02-0.2 Тorr, (aр ~ 1.4 м)
argon,
Р ~ 0.02-0.2 Тоrr,
iron particles
(aр ~ 3.5 м)
Formation of combined
dust oscillations due to
variation of plasma
parameters
1. Direction of dust rotation is in accordance to theoretical estimation
of dust charge gradients
2. Small variations of dust charge < 1-5% см-1 need for formation of
these dust rotations in field of gravity
Dust vortices in microgravity conditions
(International Space Station, PKE - Nefedov)
Scheme of gas discharge camera
Argon
P = 36-98 Pa
W=0.14-1 W
Te = 1-3eV
ni ~ 109 см -3
aр = 1.7 м
Experiment
Numerical Simulation
o~ 0.04 -0.16 c-1
«void»
2o  Fi /mpZpfr,
Fi  0.3 mpg,
/Zp ~ 5 - 20% cм-1
Random fluctuation of dust charge
Two basic reasons:
 random nature of currents charging dust particles
 stochastic dust motions in spatially
inhomogeneous plasma (in presence of dust
charge gradients)
Random fluctuations of dust charges 
 fluctuation of interparticles potential ~ Zp(t)2;
 fluctuation of electric force ~ Zp(t)E in external electric field Е
It leads to stochastic motions of dust particles additionally to their thermal Brownian motions
Influence of discrete charging currents
on kinetic dust temperature
Additional kinetic energy:
fT = e2Zp2E2/(frmp)
Zp = <Zp>1/2 – amplitude and
с=1/ - time of correlations for charge fluctuations in plasma
fT, эВ
 In gas discharge plasma kinetic
energy of macroparticles with radius
ар > 10 м can reach fT ~ 1 eV
, c-1
fT < 0.1 eV для ар < 2 м, Р > 0.02 Тоrr
Influence of spatial variation of dust charge
on kinetic dust temperature
Taking into account of spatial inhomogeneity of bulk plasma in region of stochastic dust motions
Additional kinetic energy:
s T  (Tn   f T ) /(1   1 )
Stochastic dust oscillations near the
electrode of rf- discharge Тр ~ 3 - 30 эВ

y=dZp/dy
Dependence of oscillation amplitude on
pressure for particles : 1– 1 м; 2 – 2.1 м.
100
Ay (P i)/Ay(P o)


y


1 
2
 Z v l 
 р fr p 
2
1
10
2
1
10
30
50
70
90
pressure, [мТоrr]
 Dust charge gradients y can lead to formation of stochastic dust motions with big kinetic energy
CONCLUSIONS
The small dust charge gradients due to
inhomogeneity of plasma surrounding
macroparticles
 can lead to the dust vortex formation, and
 can influence on the stochastic dust motions
in plasma of gas discharges.
Experimental Setup for Vertical Vortex
Motion
Dust vortex in discharge plasma
(superposition of 4 frames)
Melamine formaldehyde –2.67 μm
(Side view)
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
-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
140
160
180
200
0
20
40
60
80
100
120
Pressure, mTorr
140
160
180
200
Self-excited oscillation in
extreme region
Grounded Electrode
4cm
Powered Electrode
8cm
11cm
Equation of Motion
Side Observation
Window
Top View
Top Observation
Window
Particle
Dispenser
Top Ground
Electrode
a
v1
DC Power
AC Power
s1
 
Particle
Driving Pad
ZD 
mas  F (v1 ) s1  F (v2 )s2
Zd
(2f 0 ) 2 m
E'
Where f 0 is the resonant frequency
'
And E is the electric field gradient
where
4
F   mnn vTn a 2 v
3
Gas Inlet
RF Supply
15MHz
  f (r )
v
Radial potential distribution
potencial, [V]
50
/<Z>~(divE)
40
30
20
1,2
10
1,0
0
0,8
0
1
2
3
distance, [cm]
4
5
 r 
0,6
0,4
0,2
r/R
0,0
0,0
0,2
0,4
0,6
0,8
1,0
Dependences of critical amplitude
and charge gradient
140
critical amplitude
critical charge gradient ~ 20 mm-1
120
Input power, W
100
80
60
40
20
0
3.5
3.75
4
4.25
radial distance, mm
4.5
4.75
5
Summary
The overview of experimental and theoretical
investigations of charged gradient induced instabilities
were presented.
We attribute the observed instabilities to inhomogenaties
in the plasma, and show that greater instability of dust
structures can be explained by larger space charge
gradient.
The authors have clearly been developing and promoting
this idea for the few years and are making some progress
on the experimental and theoretical side.
Thanks Everybody!