Vortex Structures in Complex Plasmas

A.A SamarianSchool of Physics, University of Sydney

http://www.usyd.edu.au/

Outlines

IntroductionThe experimental set-upExperimental observation of vorticesVelocity distributionDescription and implementation of modelSimulated and experimental resultsConclusion

IntroductionDust vortices provide an opportunity to study large scale vortex structures on a kinetic level

Tornado Cyclone GalaxyWater Vortex

Experimental Observation of Vortices

1mm1mm

DC Discharge IC RF Discharge

Experimental Observation of Vortices

Vortex ExcitationNon-homogenous plasmaAdditional pin electrodeVortex pair observed in horizontal planeRotation toward probe tip

…..

CCD Camera

Powered Electrode

15MHz Signal Generator

Pin Electrode

Dust Tray

Grounded Electrode

TOP VIEW

SIDE VIEW

Grounded Electrode

Dust Vortices

Pin Electrode

Powered Electrode

Analysis of DataApplied Tracking program

Problems with the “Closest Dust” algorithm Method used

Frame nFrame n + 1

Visualisation of Velocity Map

Real time rendered version

Velocity distribution

Velocity Distribution Function

P= 100W

P= 70W

P= 30W

Velocity Distribution Function

P= 100W

P= 70W

P= 30W

Velocity Distribution

Num

ber

of p

artic

les

The Effect of Power on Velocity Distribution in Horizontal Plane

P= 100WP= 70WP= 30W

velocity (cm/sec)

Vertical Cross Section

P= 120W

P= 80W

P= 60W

P= 30W

Vertical Cross Section

Vertical Component of Particle Velocity

The Effect of Pow er on z-component of the Velocity of Particle

P= 120W

P= 80W

P= 60W

P= 30W

The Effect of Pow er on z-component of the Velocity of Particle

The Effect of Pow er on z-component of the Velocity of Particle

P= 120W

P= 80W

P= 60W

P= 30W

The Effect of Pow er on z-component of the Velocity of Particle

P= 120W

P= 80W

P= 60W

P= 30W

The Effect of Pow er on z-component of the Velocity of Particle

The Effect of Pow er on z-component of the Velocity of Particle

P= 120W

P= 80W

P= 60W

P= 30W

Num

ber

of

part

icle

s

velocity (cm/sec)

P= 100W

P= 70W

P= 30W

The Effect of Power on Velocity Distribution in Horizontal Plane P= 120W

P= 80W

P= 60W

P= 30W

Model Description

Based on standard 2-D MHD equations:Momentum equation:

Introducing Vorticity:Taking the curl of the momentum equationNeglecting B fields and assuming incompressibility

( ) ( ) uBuEuuu fdustmq

nmp

tυ−×++∇−=∇•+

∂∂

u×∇=ω

Governing Equations

Vorticity-Streamfunction form:

Form a closed set assuming q and E are known.

( )ψ,0,0×∇=u

( ) ωυωω fdustmq

t−×∇=∇•+

∂∂ Eu

ωψ −=∇ 2

Vortex Generation

Source term in vorticity equation:

Charge gradient required for vortex excitation!

⎟⎟⎠

⎞⎜⎜⎝

⎛∇×∇−

∂∂

−∂∂

=×∇ φqyqE

xqE

mmq

xy1E

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

−∂∂

=yqE

xqE

m xy1

Plasma Model

E field obtained from Poisson’s equation:

Due to bulk electro-neutrality, approx:

Charge value chosen to approximate experimental potential

( )( )probedustdustei qnqnne ++−=•∇ E0ε

*0 probeq=•∇ Eε

Dust Charge

( )( )yxZZennvTq eiiedust ,),,,( ∆+−=

Charge function:

Simulated Vortices

vf = 100 (s-1), dQ ~ 2%, V = 20V

* Blue is clockwise rotation

Results

Angular velocity distribution obtained from a current loop analysis

2

21

ω=

×∇=Ω u

Results

ω=ωоexp(-σR)

Results

Samarian, A.A, Vaulina, O., Tsang, W., James, B.W (2002). Formation of Vertical and Horizontal Dust Vortexes in an RF-Discharge Plasma. Physica Scripta T98

dQ ~ 2%, V = 20V

Results

vf = 100 (s-1)

dQ = A*Vprobe0

Conclusions

The proposed model is capable of modeling vortex structures in complex plasmas

Vortex generation requires gradient of dust charge

Vortex characteristics independent of charge magnitude, determined by charge gradient

Experimental support for the simulated vortices given for:General angular velocity distributionVariation of angular frequency with frictional frequencyThe dependence of angular frequency on pin electrode potential assuming the dust charge gradient was held constant

Vortex Structures in Complex PlasmasOutlinesIntroductionExperimental Observation of VorticesExperimental Observation of VorticesAnalysis of DataVisualisation of Velocity MapVelocity distributionVelocity DistributionVertical Cross SectionVertical Component of Particle VelocityGoverning EquationsVortex GenerationPlasma ModelDust ChargeSimulated VorticesResultsResultsResultsResultsConclusions