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
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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
Confining RingConfining RingElectrodeElectrode
ParticleParticleDispenserDispenser
Top GroundTop GroundElectrodeElectrode
Oil DiffusionOil DiffusionPumpPump
Argon Gas Argon Gas InletInlet
Probe InletProbe Inlet
ObservationObservationWindowWindow
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
Confining RingConfining RingElectrodeElectrode
ParticleParticleDispenserDispenser
Top GroundTop GroundElectrodeElectrode
Oil DiffusionOil DiffusionPumpPump
Argon Gas Argon Gas InletInlet
Probe InletProbe Inlet
ObservationObservationWindowWindow
LaserLaser
Confining RingConfining RingElectrodeElectrode
ParticleParticleDispenserDispenser
Top GroundTop GroundElectrodeElectrode
Oil DiffusionOil DiffusionPumpPump
Argon Gas Argon Gas InletInlet
Probe InletProbe Inlet
ObservationObservationWindowWindow
5
Experimental Setup for Vertical Vortex Motion
Dust vortex in discharge plasma (superposition of 4 frames)
Melamine formaldehyde –2.67 μm(Side view)
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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
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Vortex Movie
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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
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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)
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Vertical Cross Section
P= 120W
P= 80W
P= 60W
P= 30W
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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
The Effect of Power on z-component of the Velocity of Particle
The Effect of Power on z-component of the Velocity of Particle
P= 120W
P= 80W
P= 60W
P= 30W
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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
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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
+=
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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 −=
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Results from Simulation
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Results from Simulation
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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
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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).
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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
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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
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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