A. Samarian and O. Vaulina School of Physics, University of Sydney, NSW 2006, Australia

A. Samarian and O. VaulinaSchool of Physics, University of Sydney, NSW 2006, Australia

2

Outlines

The experimental set-upThe experimental set-up

Vertical and horizontal vortices Vertical and horizontal vortices

Velocity distributionVelocity distribution

Simulation resultsSimulation results

ConclusionConclusion

3

Vortex in ICP

RFRF discharge 17.5 MHz discharge 17.5 MHz Pressure from 560 mTorr Pressure from 560 mTorr Input voltage from 500 mVInput voltage from 500 mV

Melamine formaldehyde - Melamine formaldehyde - 6.216.21m±0.09m±0.09mm

Argon plasma TArgon plasma Tee~ 2eV &~ 2eV & nne e ~ ~

101088cmcm-3-3

1mm1mm

4

RFRF discharge 15 MHz discharge 15 MHz

Pressure from 10 to 400 mTorr Pressure from 10 to 400 mTorr

Input power from 15 to 200 WInput power from 15 to 200 W

Self-bias voltage from 5 to 80VSelf-bias voltage from 5 to 80V

Melamine formaldehyde - 2.79 μm ± 0.06 μm Melamine formaldehyde - 2.79 μm ± 0.06 μm

Argon plasma TArgon plasma Te e ~ 2 eV, V~ 2 eV, Vp p =50V &=50V & nne e ~ 10~ 1099 cm cm--

3 3

LaserLaser

Confining RingConfining RingElectrodeElectrode

ParticleParticleDispenserDispenser

Top GroundTop GroundElectrodeElectrode

Oil DiffusionOil DiffusionPumpPump

Argon Gas Argon Gas InletInlet

Probe InletProbe Inlet

ObservationObservationWindowWindow

LaserLaser








Images of the illuminated dust Images of the illuminated dust cloud are obtained using a charged-cloud are obtained using a charged-coupled device (CCD) camera with coupled device (CCD) camera with a 60mm micro lens and a digital a 60mm micro lens and a digital camcorder (focal length: 5-50 mm). camcorder (focal length: 5-50 mm). The camcorder is operated at 25 to The camcorder is operated at 25 to 100 frames/sec.100 frames/sec.

The video signals are stored on The video signals are stored on videotapes or are transferred to a videotapes or are transferred to a computer via a frame-grabber cardcomputer via a frame-grabber card..The coordinates of particles were The coordinates of particles were measured in each frame and the measured in each frame and the trajectory of the individual particles trajectory of the individual particles were traced out frame by framewere traced out frame by frame

The laser beam enters the discharge chamber The laser beam enters the discharge chamber through a 40-mm diameter window. through a 40-mm diameter window. We use the top-view window to view the We use the top-view window to view the horizontal dust-structure. horizontal dust-structure. In addition a window mounted on a side port In addition a window mounted on a side port in a perpendicular direction provides a view of in a perpendicular direction provides a view of the vertical cross-section of the dust structure. the vertical cross-section of the dust structure.

The experiments were carried out in a The experiments were carried out in a 40-cm inner diameter cylindrical 40-cm inner diameter cylindrical stainless steel vacuum vessel with stainless steel vacuum vessel with many ports for diagnostic access. many ports for diagnostic access. The chamber height is 30 cm. The The chamber height is 30 cm. The diameters of electrodes are 10 cm for diameters of electrodes are 10 cm for the disk and 11.5 cm for the ringthe disk and 11.5 cm for the ring The The dust particles suspended in the plasma dust particles suspended in the plasma are illuminated using a Helium-Neon are illuminated using a Helium-Neon laser. laser.

Experimental Setup

LaserLaser








LaserLaser








5

Experimental Setup for Vertical Vortex Motion

Dust vortex in discharge plasma (superposition of 4 frames)

Melamine formaldehyde –2.67 μm(Side view)

6

Experimental Setup for Horizontal Vortex Motion

Groundedelectrode

DustVortex

Powered electrode

Groundedelectrode

DustVortex

Pin electrode

Groundedelectrode

Pin electrode

Dust Vortex

Groundedelectrode

Pin electrode

Dust Vortex

Side View Top View

Video Images of Dust Vortices in Plasma Discharge

7

Vortex Movie

8

Velocity distribution

Spatial Velocity Distribution

0cm/s

15cm/s

8cm/s

3cm/s

Spatial Velocity Distribution

0cm/s

15cm/s

8cm/s

3cm/s

0cm/s

15cm/s

8cm/s

3cm/s

Velocity Distribution Function

P= 100W

P= 70W

P= 30W

Velocity Distribution Function

P= 100W

P= 70W

P= 30W

9

Nu

mb

er o

f p

arti

clesThe Effect of Power on Velocity Distribution in Horizontal Plane

P= 100WP= 70WP= 30W

Velocity Distribution

velocity (cm/sec)

10

Vertical Cross Section

P= 120W

P= 80W

P= 60W

P= 30W

11

Vertical Component of Particles’ Velocity

The Effect of Power on z-component of the Velocity of Particle

P= 120W

P= 80W

P= 60W

P= 30W



P= 120W

P= 80W

P= 60W

P= 30W

12

Equation of Motion

Lets consider the motion of Lets consider the motion of NNpp particles with charge particles with charge Z=Z(r,y)=Zoo+Z(r,y), in , in

an electric fieldan electric field , where , where r=(x2+z2)1/2 is the horizontal is the horizontal

coordinates in a cylindrically symmetric system.coordinates in a cylindrically symmetric system.

)()(),( rEjyEiyrE

dr

dyeZrF D ),()(int

y

r

Z00

Z00+Z(r,y)

r0

y0

13

Equation of Motion

Lets consider the motion of Lets consider the motion of NNpp particles with charge particles with charge Z=Z(r,y)=Zoo+Z(r,y), in , in

an electric fieldan electric field , where , where r=(x2+z2)1/2 is the horizontal is the horizontal

coordinates in a cylindrically symmetric system.coordinates in a cylindrically symmetric system.

Taking the pair interaction force Taking the pair interaction force FFintint,, the gravitational force the gravitational force mmppgg, and the , and the

Brownian forces Brownian forces FFbr br into account, we get: into account, we get:

where where ll is the interparticle distanceis the interparticle distance, , mmpp is the particle mass and is the particle mass and frfr is the is the

friction frequencyfriction frequency..

NowNow is the interparticle potential with screening is the interparticle potential with screening

length length DD, , and and ee is the electron charge is the electron charge..

AlsoAlso is the total external is the total external

forceforce..

extbrk

frp

jk

jk

jlll

kp FF

dt

ldm

ll

lllF

dt

ldm

jk

)(int2

2

),()(}),()({ yreZrEjgmyreZyEiF pext

)exp(),(

D

l

l

yreZD

)()(),( rEjyEiyrE

14

Equation of Motion

Total external force and Total external force and

interparticle interactioninterparticle interaction areare dependent on the dependent on the

particle’s coordinate. particle’s coordinate.

When the curl of these forces When the curl of these forces 0, the system can do positive work to 0, the system can do positive work to

compensate the dissipative losses of energy. It means that infinitesimal compensate the dissipative losses of energy. It means that infinitesimal

perturbations due to thermal or other fluctuations in the system can growperturbations due to thermal or other fluctuations in the system can grow..

),()(}),()({ yreZrEjgmyreZyEiF pext

dr

dyeZrF D ),()(int

15

Results from Simulation

16

Results from Simulation

17

Dust Charge Spatial Variation

Assuming that drift electron (ion) currents < thermal current, Assuming that drift electron (ion) currents < thermal current, TTii0.03eV and0.03eV and n neennii, then:, then:

<Z><Z> = = CCzzaaTTee

HereHere CCzz is is 2x102x1033 ( (ArAr). ). Thus in the case of Thus in the case of ZZ((r,yr,y)=<)=<ZZ>+>+TTZZ((r,yr,y), where ), where TTZZ is the equilibrium dust is the equilibrium dust

charge at the point of plasma with the some electron temperatures charge at the point of plasma with the some electron temperatures TTee, and , and TTZZ((r,yr,y) is the variation of ) is the variation of

dust charge due to the dust charge due to the TTee, then:, then:

T T ZZ((r,yr,y)/<)/<ZZ> = > = TTee((r,yr,y)/)/TTee

andand yy//<Z><Z>==((TTee//yy))TTee-1-1, , //<Z> <Z> = = ((TTee//))TTee

-1-1

If spatial variations If spatial variations n n ZZ((r,yr,y) ) of of equilibrium equilibrium dust charge dust charge occur due to gradients of occur due to gradients of

concentrations concentrations nne(i)e(i) in plasma surrounding dust cloud, assuming that conditions in the plasma in plasma surrounding dust cloud, assuming that conditions in the plasma

are close to electroneutral (are close to electroneutral (nn==nnii--nnee«n«neenniinn and and nnZZ((r,yr,y))«<Z>)«<Z>), where , where nnZ(r,y)Z(r,y) is the is the

equilibrium dust charge where equilibrium dust charge where nnee==nnii, then , then nnZZ((r,yr,y) ) is determined is determined by equating the orbit-limited by equating the orbit-limited

electrons (ions) currents for an isolated spherical particle with equilibrium surface potential < 0, electrons (ions) currents for an isolated spherical particle with equilibrium surface potential < 0, that is.that is.

n n ZZ((,y,y))

where <where <ZZ>>20002000aaTTee

)/1( 2eaTZen

nZ

n

nZ 26.0

nnee/n/nii=f (r) and T=f (r) and Tee=f (r)=f (r)ni(e) Te

18

Kinetic Energy

Energy gain for two basic types of instabilities: Dissipative instability for systems, where dissipation is present (Type 1); Dissipative instability for systems, where dissipation is present (Type 1); Dispersion instability, when the dissipation is negligibly small (Type 2)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 )=mpg22/{8fr

2}where ={Аr/Zoo} determines relative changes of Z(r) within limits of particle trajectory

When a=5m, =2g/cm3 and fr12P (P~0.2Torr), К( i ) is one order higher than thermal dust energy To0.02eV 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=2m, К( i )/To

>10 for >10-2 (r/Zoo>0.02cm-1, A=0.5cm).

19

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) 22cn/lp

where cn=exp(-k){1+k+k2/2} and =А/lp (~0.5 for dust cloud close to solid structure)

When a=5m, =0.1, k1-2, lp=500m, 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

0

1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100 120 140 160 180 200

Pressure, mTorr

pg/{Zov fr }

=12 mm-1

0

10

20

30

40

50

60

0 20 40 60 80 100 120 140 160 180 200

Pressure, mTorr

U=40 V

Ft

p/{2mdZov fr }=320 mm-1

a) b)

Dependency of the rotation frequency on pressure for vertical (a) and horizontal (b) vortices

wс = /2= F /{2mpZofr}

21

Conclusion

• The results of experimental observation of twoThe results of experimental observation of two types of types of self-excited dust vortex motions (vertical and horizontal) self-excited dust vortex motions (vertical and horizontal) in planar in planar RF RF discharge are presenteddischarge are presented

• The fThe first irst type type is the vertical rotations of is the vertical rotations of dust dust particles in particles in bulk dust cloudsbulk dust clouds

• The second type of dust The second type of dust vorvorttexex isis formed in the horizontal formed in the horizontal plane for monolayer structure of particlesplane for monolayer structure of particles

• We attribute the inducWe attribute the inductiontion of these vortices with the of these vortices with the developdevelopmentment of dissipative instability in the dust cloud of dissipative instability in the dust cloud with the dust charge gradient, which have been provided with the dust charge gradient, which have been provided by extra electrode. by extra electrode. The presence of additional electrode The presence of additional electrode also produces the additional force which, along with the also produces the additional force which, along with the electric forces, will lead to the rotation of dust structure in electric forces, will lead to the rotation of dust structure in horizontal planehorizontal plane

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A. Samarian and O. Vaulina School of Physics, University of Sydney, NSW 2006, Australia