1. 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

2. 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 ~ Тorr
Plasma concentration: ~ см-3
Neutral’s concentration : ~ см-3
dc- discharge
rf- discharge

3. Laboratory Dusty Plasma – weakly ionized gas
with micron-sized dust particles (macroparticles)
Typical conditions of experiments
Parameters of dust particles:
Radius: ap ~ м
Charge: Z p ~
Concentration: np ~ см –3
Kinetic
TEMPERATURE: Тp ~ eV
(«Abnormal dust heating»)
Dust Vortices
Crystal Fluid
Oscillations of separate particles

4. 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) /<Z> ~ (1-100)% см-1
 Variations in regular ion’s velocity (Vi/r) /<Z> ~ (1- 50)% см-1
 Gradients of plasma densities ((ni - ne)/r) /<Z> ~ (1- 50)% см-1
Equations of motions for particles with Zр(,y) in an electric field Eext of cylindrically symmetric trap:
, Fext = e Zр(,y) E(,y),
For typical conditions of ground-based experiments in gas discharge plasma
Non-electrostatic forces Fnon - gravity force mpg,
ion drag force Fi  ( ) mpg,
thermothoretic force Fт < 0.1 mpg

5. 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 

6. Dust vortices under ground-based conditions
in dc- discharge
argon,
Р ~ Тоrr,
iron particles
(aр ~ 3.5 м)
in rf - discharge
argon, Р ~ Тorr, (aр ~ 1.4 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

7. Dust vortices in microgravity conditions
(International Space Station, PKE - Nefedov)
Scheme of gas discharge camera
Argon
P = Pa
W= W
Te = 1-3eV
ni ~ 109 см -3
aр = 1.7 м
Experiment
Numerical Simulation
o~ c-1
2o  Fi /mpZpfr,
Fi  0.3 mpg,
/Zp ~ % cм-1
«void»

8. 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

9. 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 > Тоrr

10. 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:
Dependence of oscillation amplitude on
pressure for particles : 1– 1 м; 2 – 2.1 м.
Stochastic dust oscillations near the electrode of rf- discharge Тр ~ эВ
 y=dZp/dy
Dust charge gradients y can lead to formation of stochastic dust motions with big kinetic energy

11. 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.

12. Experimental Setup for Vertical Vortex Motion
Dust vortex in discharge plasma (superposition of 4 frames) Melamine formaldehyde –2.67 μm (Side view)

13. Experimental Setup for Horizontal Vortex Motion
Grounded
electrode
Dust
Vortex
Powered electrode
Pin electrode
Grounded
Grounded
electrode
electrode
Dust Vortex
Dust Vortex
Side View
Top View
Video Images of Dust Vortices in Plasma Discharge
Pin electrode
Pin electrode

14. w-Dependency on Pressure
wс =  /2= F /{2mpZofr}
Dependency of the rotation frequency w on pressure
for vertical (a) and horizontal (b) vortices

15. Self-excited oscillation in extreme region

16. Equation of Motion Side Observation Window Top View Top Observation
Particle
Driving Pad
Dispenser
Top Ground
Electrode
Gas Inlet
RF Supply
15MHz
AC Power
DC Power
Side Observation
Window
Top Observation
where
Top View
Where is the resonant frequency
And is the electric field gradient

17. Radial potential distribution
/<Z>~(divE)

18. Dependences of critical amplitude and charge gradient

19. 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.

20. Thanks Everybody!