Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
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