1. F. Cheung, A. Samarian, B. James School of Physics, University of Sydney, NSW 2006, Australia

2. Comparison of forces Multi-ring saturation effect Threshold magnetic field Explanation for various cluster rotation properties Experimental results B Periodic pause in rotation

3. Experimental Apparatus Argon Plasma Melamine Formaldehyde Polymer Spheres Dust Diameter = 6.21±0.9  m Pressure = 100mTorr Voltage Confinement = +10.5V Magnetic Field Strength = 0 to 90G Electron Temperature ~ 3eV Electron Density = 10 15 m -3 RF Coil set in Araldite Argon Gas Inlet Particle Shaker To magnetically coupled manipulator Magnetic Coil To diffusion pump Camera PCB Electrode Observation Window Laser 5cm Dust Crystal

4. Clusters illuminated by HeNe laser & video captured by CCD camera Clusters of 2 to 16 particles were studied Interparticle distance  0.4mm Rotation is in the left-handed direction with respect to the magnetic field Cluster Configuration  =199±4  m  =406±4  m  =495±2  m  =242±2  m  =418±4  m  =487±1  m  =289±3  m  =451±3  m Planar-2 Planar-6 (1,5) Planar-10 (3,7) Planar-3 Planar-7 (1,6) Planar-11 (3,8) Planar-4 Planar-8 (1,7)  =454±4  m Planar-9 (2,7) B x

5. Circular Trajectory of Clusters Video is running at 5x actual speed Trajectory of the clusters were tracked for a total time of 6 minutes with magnetic field strength increasing by 15G every minute (up to 90G)

6. Periodic Pause/ Uniform Motion Stable structure during rotation (constant phase in angular position) Planar-2 is most difficult to rotate. Momentarily pauses at particular angle during rotation Planar-10, rotate with uniform angular velocity

7. Periodic Pause of Planar-2 Video is running at 5x actual speed

8. Threshold Magnetic Field Ease of rotation increases with number of particles in the cluster, N Magnetic field strength required to initiate rotation is inversely proportional to N 2 Planar-2 is the most resistant to rotation

9.  increases with increasing magnetic field strength  increases linearly for planar- 6, -7 and -8 For planar-10, -11 and -12, the rate of change in  increases quickly and then saturate Angular Velocity

10. Driving Force & Ion Drag Driving force F Driving for rotation must be equal but opposite to friction due to neutral drag F Neutral in azimuthal direction, that is: Under same experimental conditions, experiment was repeated with smaller sized particles (2.71  m).  small ~ 2rpm (  large ~ 1 rpm) and exhibits complex fluctuation and motion. F F is given by the formula: Estimation value of the driving force for such rotation is 1.7 x10 -16 N for driving force Upper limit of ion drag is given by: where ion drag force < 10 -17 N

11. Divergence of Magnetic Field For a magnetic field divergence of 11.5 degrees, the E C xB z component and the E S xB r component will be equal. Only small divergence of the magnetic field is needed to affect the azimuthal ion drift velocity. B B ECEC BzBz B ESES BrBr FLi~ECxBzFLi~ECxBz F L i ~E S xB r Magnetic Coil E Confinement E Sheath

12. Multi-ring Saturation Effect Inner ring attempts to rotate in opposite direction as the outer ring. B  F F vivi ErEr ErEr vivi Ar + F int

13. Multi-ring Saturation Effect Inner ring attempts to rotate in opposite direction as the outer ring. Due to strong interparticle force, cluster remains rigid body. Hence the net torque decreases. As magnetic field increases, radial electric field at the inner ring increases. Saturation of double ring cluster rotation occurs. B 

14. B field modifies radial profile of electron and ion density due to magnetization of electrons  change in electric potential Ratio of electron gyrofrequency to electron-neutral collisional frequency ~1.5 (for ions, this ratio <0.01)  2 V = -  /  0  ~ n i + n e Multi-ring Saturation Effect V r B field off B field on e-e- Ar +

15. Electric Field Dependence Since electric field is modified by the magnetic field, it must be taken into account in the analysis of the driving force of cluster rotation. E r = eZ/4  0 { sin(  /6)[2rsin(  /6)] -2 + sin(2  /6)[2rsin(2  /6)] -2 + sin(3  /6)[2rsin.(3  /6)] -2 + sin(4  /6)[2rsin(4  /6)] -2 + sin(5  /6)[2rsin(5  /6)] -2 r r r  /6 2  /6  /6 For single ring cluster, E r = eZ/16  0 r 2 {  k=1  n-1 [sin(k  /n)] -1 } where n is the number of particles in the outer ring

16. Electric Field Dependence Experimental data show that angular velocity of the cluster rotation is linearly proportional to the product of the B and E field.

17. Spatial Variation of Linear Force Provided that the linear force and its gradient is strong enough, the rotational motion of the cluster degenerates into an oscillation.  t  t  When F  >>  F When F  ~  F F1F1 F2 F2 OscillationRotation M = F 1 rcos  + F 2 rcos(  +  ) x y r

18. Oscillatory Motion of Planar-2 Video is running at 6x actual speed

19. Rim Orbital Motion Video is running at 1/3x actual speed

20. Conclusion Rotation of dust clusters is possible with application of axial magnetic field The cluster rotation is dependent on N and its structural configuration. Multi-ring Saturation Effect Periodic Pause/ Oscillatory Motion/ Rim Orbital Motion Threshold Magnetic Field The model explaining the observed phenomena proposed.