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A. Samarian and O. Vaulina School of Physics, University of Sydney, NSW 2006, Australia Outlines The experimental set-up Vertical and horizontal vortices Velocity distribution Simulation results Conclusion 2 Vortex in ICP 1mm RF discharge 17.5 MHz Pressure from 560 mTorr Input voltage from 500 mV 3 Melamine formaldehyde 6.21m±0.09m Argon plasma Te~ 2eV & ne ~ 108cm-3 Experimental Setup The experiments carried out dust in a Images of thewere illuminated 40-cm diameter cloud areinner obtained using acylindrical chargedstainless steel vacuum vessel with with coupled device (CCD) camera many ports micro for diagnostic access. a 60mm lens and a digital The chamber height is 305-50 cm.mm). The camcorder (focal length: diameters of electrodes are 10atcm The camcorder is operated 25for to the disk and 11.5 cm for the ring The 100 frames/sec. dust particles suspended in the plasma are illuminated using a Helium-Neon Observation laser. Observation Window Top Ground Electrode Particle Dispenser Laser Probe Inlet Argon Gas Inlet Confining Ring Electrode Window RF discharge 15 MHz Oil Diffusion Pump Top Ground Electrode Pressure from 10 to 400 mTorr Input power from 15 to 200 W Probe Inlet Self-bias voltage from 5 to 80V Melamine formaldehyde - 2.79 μm ± 0.06 μm Argon plasma Te ~ 2 eV, Confining Ring Electrode Vp =50V & ne ~ Oil Diffusion Pump 4 109 cm-3 Particle Dispenser The laser video stored on The beam signals enters the are discharge chamber Laser through a 40-mm window. videotapes or diameter are transferred to a computer a frame-grabber We use theviaArgon top-view window card. to view the Gas Inlet horizontal dust-structure. The coordinates of particles were In addition a in window a side the port measured eachmounted frameon and in a perpendicular direction provides a view trajectory of the individual particles wereof the vertical of the dust structure. traced out cross-section frame by frame Experimental Setup for Vertical Vortex Motion Dust vortex in discharge plasma (superposition of 4 frames) Melamine formaldehyde –2.67 μm (Side view) 5 Experimental Setup for Horizontal Vortex Motion Grounded electrode Grounded electrode Pin electrode Dust Vortex Grounded Grounded electrode electrode Dust Vortex Dust Vortex Dust Vortex Powered electrode Side View electrode PinPin electrode Top View Video Images of Dust Vortices in Plasma Discharge 6 Vortex Movie 7 Velocity distribution Spatial Velocity Distribution 15cm/s Velocity Distribution Function 8cm/s 3cm/s P= 70W 0cm/s P= 100W P= 30W 8 Velocity Distribution Number of particles The Effect of Power on Velocity Distribution in Horizontal Plane 70W P= 30W 100W P= velocity (cm/sec) 9 Vertical Cross Section P= 120W P= 80W P= 60W P= 30W 10 Vertical Component of Particles’ Velocity The Effect of Power on z-component of the Velocity of Particle P= 30W P= 60W P= 80W P= 120W 11 Equation of Motion Lets consider the motion of Np particles with charge Z=Z(r,y)=Zoo+Z(r,y), in an electric field E (r , y) i E ( y) j E (r ) , where r=(x2+z2)1/2 is the horizontal coordinates in a cylindrically symmetric system. y y0 Z00 r0 r d Fint (r ) eZ ( , y ) D dr Z00+Z(r,y) 12 Equation of Motion Lets consider the motion of Np particles with charge Z=Z(r,y)=Zoo+Z(r,y), in an electric field E (r , y) i E ( y) j E (r ) , where r=(x2+z2)1/2 is the horizontal coordinates in a cylindrically symmetric system. Taking the pair interaction force Fint, the gravitational force mpg, and the Brownian forces Fbr into account, we get: d l m p 2k Fint (l )l l l k j dt j 2 lk l j dlk m F F p fr br ext dt lk l j where l is the interparticle distance, mp is the particle mass and fr is the friction frequency. Now D eZ (r , y ) exp( l ) is the interparticle potential with screening length D, l D and e is the electron charge. Also F i {E ( y)eZ (r , y) m g} j E (r )eZ (r , y) is the total external force. ext p 13 Equation of Motion Total external force interparticle interaction Fext i {E ( y)eZ (r , y) m p g} j E (r )eZ (r , y) Fint (r ) eZ ( , y ) dD dr and are dependent on the particle’s coordinate. When the curl of these forces 0, the system can do positive work to compensate the dissipative losses of energy. It means that infinitesimal perturbations due to thermal or other fluctuations in the system can grow. 14 Results from Simulation 15 Results from Simulation 16 Dust Charge Spatial Variation ne/ni=f ni(e) Te (r) and Te=f (r) Assuming that drift electron (ion) currents < thermal current, Ti0.03eV and neni, then: <Z> = CzaTe Here Cz is 2x103 (Ar). Thus in the case of Z(r,y)=<Z>+TZ(r,y), where TZ is the equilibrium dust charge at the point of plasma with the some electron temperatures Te, and TZ(r,y) is the variation of dust charge due to the Te, then: T Z(r,y)/<Z> = Te(r,y)/Te and y/<Z>=(Te/y)Te-1, /<Z> = (Te/)Te-1 If spatial variations n Z(r,y) of equilibrium dust charge occur due to gradients of concentrations ne(i) in plasma surrounding dust cloud, assuming that conditions in the plasma are close to electroneutral (n=ni-ne«nenin and nZ(r,y)«<Z>), where nZ(r,y) is the equilibrium dust charge where ne=ni, then nZ(r,y) is determined by equating the orbit-limited electrons (ions) currents for an isolated spherical particle with equilibrium surface potential < 0, that is. 0.26 Z n Z n n Z(,y) n(1 e 2 Z / aT ) n e where <Z>2000aTe 17 Kinetic Energy Energy gain for two basic types of instabilities: Dissipative instability for systems, where dissipation is present (Type 1); 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/{8fr2} 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). 18 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 19 -Dependency on Pressure wс = /2= F /{2mpZofr} Dependency of the rotation frequency on pressure for vertical (a) and horizontal (b) vortices a) 10 U=40 V b) 60 9 8 50 7 pg/{Zov fr } 6 =12 mm-1 5 40 Ftp/{2mdZov fr } 30 =320 mm-1 4 20 3 2 10 1 0 0 0 20 40 60 80 100 120 Pressure, mTorr 20 140 160 180 200 0 20 40 60 80 100 120 Pressure, mTorr 140 160 180 200 Conclusion The results of experimental observation of two types of self-excited dust vortex motions (vertical and horizontal) in planar RF discharge are presented The first type is the vertical rotations of dust particles in bulk dust clouds The second type of dust vortex is formed in the horizontal plane for monolayer structure of particles We attribute the induction of these vortices with the development of dissipative instability in the dust cloud with the dust charge gradient, which have been provided by extra electrode. The presence of additional electrode also produces the additional force which, along with the electric forces, will lead to the rotation of dust structure in horizontal plane 21