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

1. Dust Vortex in Complex Plasma A. Samarian and O. Vaulina School of Physics, University of Sydney, NSW 2006, Australia

2. Outlines • The experimental set-up • Vertical and horizontal vortices • Velocity distribution • Simulation results • Conclusion

3. Vortex in ICP RF discharge 17.5 MHz Pressure from 560 mTorr Input voltage from 500 mV Melamine formaldehyde - 6.21m±0.09m Argon plasma Te~ 2eV &ne ~ 108cm-3

4. Experimental Setup The experiments were carried out in a 40-cm inner diameter cylindrical stainless steel vacuum vessel with many ports for diagnostic access. The chamber height is 30 cm. The diameters of electrodes are 10 cm for the disk and 11.5 cm for the ringThe dust particles suspended in the plasma are illuminated using a Helium-Neon laser. The laser beam enters the discharge chamber through a 40-mm diameter window. We use the top-view window to view the horizontal dust-structure. In addition a window mounted on a side port in a perpendicular direction provides a view of the vertical cross-section of the dust structure. Images of the illuminated dust cloud are obtained using a charged-coupled device (CCD) camera with a 60mm micro lens and a digital camcorder (focal length: 5-50 mm). The camcorder is operated at 25 to 100 frames/sec. RF discharge 15 MHz Pressure from 10 to 400 mTorr Input power from 15 to 200 W Self-bias voltage from 5 to 80V Melamine formaldehyde - 2.79 μm ± 0.06 μm Argon plasma Te ~ 2 eV, Vp =50V &ne ~ 109 cm-3 The video signals are stored on videotapes or are transferred to a computer via a frame-grabber card. The coordinates of particles were measured in each frame and the trajectory of the individual particles were traced out frame by frame

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 Top View Side View Video Images of Dust Vortices in Plasma Discharge Grounded Grounded electrode electrode Pin electrode Dust Dust Vortex Vortex Powered electrode Grounded Grounded electrode electrode Dust Vortex Dust Vortex Pin electrode Pin electrode

7. Vortex Movie

8. Velocity distribution

9. Velocity Distribution P= 100W P= 70W P= 30W The Effect of Power on Velocity Distribution in Horizontal Plane Number of particles velocity (cm/sec)

10. Vertical Cross Section P= 120W P= 80W P= 60W P= 30W

11. Vertical Component of Particles’ Velocity

12. Equation of Motion y Z00 y0 r0 r Z00+Z(r,y) Lets consider the motion of Np particles with charge Z=Z(r,y)=Zoo+Z(r,y), in an electric field , where r=(x2+z2)1/2is the horizontal coordinates in a cylindrically symmetric system.

13. Equation of Motion Lets consider the motion of Np particles with charge Z=Z(r,y)=Zoo+Z(r,y), in an electric field , where r=(x2+z2)1/2is 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: where lis the interparticle distance, mp is the particle mass and fr is the friction frequency. Now is the interparticle potential with screening length D, and e is the electron charge. Also is the total external force.

14. Equation of Motion • Total external force and interparticle interactionaredependent 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.

15. Results from Simulation

16. Results from Simulation

17. Dust Charge Spatial Variation 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«neninand 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. n Z(,y)  where <Z>2000aTe ni(e) Te ne/ni=f (r) and Te=f (r) Assuming that drift electron (ion) currents < thermal current, Ti0.03eV and neni, then: <Z>= CzaTe HereCz is 2x103 (Ar). Thus in the case of Z(r,y)=<Z>+TZ(r,y), where TZis 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

18. 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 )=mpg22/{8fr2} where ={Аr/Zoo} determines relative changes of Z(r) within limits of particle trajectory • When a=5m, =2g/cm3andfr12P(P~0.2Torr),К( i ) is one order higher than thermal dust energy To0.02eV 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=2m, 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)22cn/lp where cn=exp(-k){1+k+k2/2} and =А/lp (~0.5 for dust cloud close to solid structure) • When a=5m, =0.1, k1-2, lp=500m, 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

20. w-Dependency on Pressure wс=/2= F/{2mpZofr} Dependency of the rotation frequency w on pressure for vertical (a) and horizontal (b) vortices

21. 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 vortexis 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