A. Samarian and O. Vaulina · 2004. 6. 18. · A. Samarian and O. Vaulina School of Physics,...

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

2

Outlines

The experimental setThe experimental set--upupVertical and horizontal vortices Vertical and horizontal vortices Velocity distributionVelocity distributionSimulation resultsSimulation resultsConclusionConclusion

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 --6.216.21µµmm±±0.090.09µµmm

Argon plasma TArgon plasma Tee~ 2eV &~ 2eV & nnee ~ ~ 101088cmcm--33

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

SelfSelf--bias voltage from 5 to 80Vbias voltage from 5 to 80V

Melamine formaldehyde Melamine formaldehyde -- 2.79 2.79 μμm m ±± 0.06 0.06 μμm m

Argon plasma TArgon plasma Te e ~ 2 eV, V~ 2 eV, Vp p =50V &=50V & nne e ~ 10~ 1099 cmcm--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 chargedcloud 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: 5camcorder (focal length: 5--50 mm). 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 framecomputer via a frame--grabber cardgrabber 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 were trajectory of the individual particles were traced out frame by frametraced out frame by frame

The laser beam enters the discharge chamber The laser beam enters the discharge chamber through a 40through a 40--mm diameter window. mm diameter window. We use the topWe use the top--view window to view the view window to view the horizontal dusthorizontal dust--structure. 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 crossthe vertical cross--section of the dust structure. section of the dust structure.

The experiments were carried out in a The experiments were carried out in a 4040--cm inner diameter cylindrical 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 Heliumare illuminated using a Helium--Neon 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

Num

ber

of p

artic

les

The 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.

)()(),( rEjyEiyrErrr

+=

drdyeZrF Dφρ ),()(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 FFbrbr into account, we get: into account, we get:

where where ll is the is the interparticleinterparticle distancedistance, , mmpp is the particle mass and is the particle mass and ννfrfr is the is the friction frequencyfriction frequency..

NowNow is the is the interparticleinterparticle potential with screening length potential with screening length DD, , and and ee is the electron chargeis the electron charge..

AlsoAlso is the total external forceis the total external force..

extbrk

frp

jk

jk

jlll

kp FF

dtldm

ll

lllF

dtldm

jk

rrr

rr

rrr

rrr ++−−

−= ∑ −=

ν)(int2

2

),()(),()( yreZrEjgmyreZyEiF pext

rrr−−=

)exp(),(Dl

lyreZ

D =φ

)()(),( rEjyEiyrErrr

+=

14

Equation of Motion

Total external force Total external force and and

interparticleinterparticle interactioninteraction areare dependent on the dependent on the

particleparticle’’s coordinate. 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 infincompensate the dissipative losses of energy. It means that infinitesimal itesimal

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

),()(),()( yreZrEjgmyreZyEiF pext

rrr−−=

drdyeZrF Dφρ ),()(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, TTii≈≈0.03eV and0.03eV and nnee≈≈nnii, 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 is the equilibrium dust charge at the point of plasma with the some eleequilibrium dust charge at the point of plasma with the some electron temperatures ctron temperatures TTee, , and and ∆∆TTZZ((r,yr,y) is the variation of dust charge due to the ) is the variation of dust charge due to the ∆∆TTee, then:, then:

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

andand ββyy//<Z><Z>==((∂∂TTee//∂∂yy))TTee--11, , ββρρ//<Z> <Z> = = ((∂∂TTee//∂∂ρρ))TTee

--11

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(ie(i)) in plasma surrounding dust cloud, assuming that conditions in tin plasma surrounding dust cloud, assuming that conditions in the he plasma are close to plasma are close to electroneutralelectroneutral ((δδnn==nnii--nnee««nnee≈≈nnii≈≈nn and and ∆∆nnZZ((r,yr,y))««<Z>)<Z>), where , where ∆∆nnZ(r,yZ(r,y))is the equilibrium dust charge where is the equilibrium dust charge where nnee==nnii, then , then ∆∆nnZZ((r,yr,y) ) is determined is determined by equating the by equating the orbitorbit--limited electrons (ions) currents for an isolated spherical partlimited electrons (ions) currents for an isolated spherical particle with equilibrium icle with equilibrium surface potential < 0, that is.surface potential < 0, that is.

∆∆n n ZZ((ρρ,y,y)) ≈≈ ≈≈where <where <ZZ>>≈≈20002000aaTTee

)/1( 2eaTZen

nZ+

δ

nnZ δ26.0−

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 presenDissipative instability for systems, where dissipation is present (Type 1); t (Type 1); Dispersion instability, when the dissipation is negligibly smallDispersion instability, when the dissipation is negligibly small (Type 2)(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 )=mpg2ξ2/8νfr

2where ξ=Аβr/Zoo determines relative changes of Z(r) within limits of particle trajectory

When a=5µm, ρ=2g/cm3 and νfr≅12P (P~0.2Torr), К( i ) is one order higher than thermal dust energy To≈0.02eV at room temperature for ξ >10-3 (βr/Zoo>0.002cm-1, A=0.5cm)

Increasing gas pressure up to P=5Torr or decreasing particle radius to a=2µm, К( i )/To>10 for ξ>10-2 (βr/Zoo>0.02cm-1, A=0.5cm).

19

Kinetic Energy

For Type 2 instability, К(ii) can be estimated with known ωc

ωр≅(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 ωc of the steady-stated particle oscillations is close to ωр. Then kinetic energy К(ii) can be written in the form:

К(ii)≈5.76 103 (aTe) 2χ2cn/lpwhere cn=exp(-k)1+k+k2/2 and χ=А/lp (~0.5 for dust cloud close to solid structure)

When a=5µm, χ=0.1, k≈1-2, lp=500µm, and Te~1eV, the К(ii)≈3eV. The maximum kinetic energy (which is not destroying the crystalline dust structure) is reached at χ=0.5. And К(ii)

lim=cne2<Z>2/4lp

20

ω-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

ω ω=πβpg/Zovfr β=12 mm-1

0

10

20

30

40

50

60

0 20 40 60 80 100 120 140 160 180 200

Pressure, mTorr

ω

U=40 V

ω=2πFtβp/2mdZovfr β=320 mm-1

a) b)

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

wс = ⎜Ω ⎜/2= F⎜βρ ⎜/2mpZoνfr

21

Conclusion

The results of experimental observation of twoThe results of experimental observation of two types of types of selfself--excited dust vortex motions (vertical and horizontal) in excited dust vortex motions (vertical and horizontal) in planar planar RF RF discharge are presenteddischarge are presentedThe fThe firstirst type type is the vertical rotations of is the vertical rotations of dust dust particles in particles in bulk dust cloudsbulk dust cloudsThe 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 particlesWe attribute the We attribute the inducinductiontion 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 · 2004. 6. 18. · A. Samarian and O. Vaulina School of Physics,...

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