Dust Plasma Clusters in an Axial Magnetic Field

1. Dust Plasma Clusters in an Axial Magnetic Field F. Cheung, A. Samarian, W. Tsang, B. James School of Physics, University of Sydney, NSW 2006, Australia

2. What is Dust Plasma Clusters? Rotational Motion of Dust Plasma Clusters Information provided by the Dust Cluster’s Rotation Theoretical Model for the Dust Cluster’s Rotation Conclusion

3. What is Dust Plasma Clusters? Difference between Crystal/ Clusters Experimental Apparatus Structural Configuration Stability Factor

4. What is Dust Plasma Clusters? Rotational Motion of Dust Plasma Clusters Angular Velocity Cluster Radius Angular Momentum

5. What is Dust Plasma Clusters? Rotational Motion of Dust Plasma Clusters Information provided by the Dust Cluster’s Rotation w vs B Radial Electric Field Profile Change of Confining Potential due to Magnetized Plasma

6. What is Dust Plasma Clusters? Rotational Motion of Dust Plasma Clusters Information provided by the Dust Cluster’s Rotation Theoretical Model for the Dust Cluster’s Rotation Neutral Friction Force Ion Drag

7. What is Dust Plasma Clusters? Rotational Motion of Dust Plasma Clusters Information provided by the Dust Cluster’s Rotation Theoretical Model for the Dust Cluster’s Rotation Conclusion

8. Dust Plasma Crystal Dust Plasma Cluster Introduction • Dust Plasma Crystal is a well ordered and stable array of highly negatively charged dust particles suspended in a plasma • Dust Plasma Crystal consisted of one to several number of particles is called a Dust Plasma Cluster

9. Experimental Apparatus • Argon Plasma • Melamine Formaldehyde Polymer Spheres • Dust Diameter = 6.21±0.9m • Pressure = 100mTorr • Voltage RF p-p = 500mV at 17.5MHz • VoltageConfinement = +10.5V • Magnetic Field Strength = 0 to 90G • Electron Temperature = few eV • Electron Density = 1015m-3

10. Clusters of 2 to 16 particles, with both single ring and double ring were studied • Interparticle distance  0.4mm • Rotation is in the left-handed direction with respect to the magnetic field. • Stability Factor (SF) is: • Standard Deviation of Cluster Radius • Mean Cluster Radius •  •  • Pentagonal (Planar-6) structure is most stable or Cluster Configuration & Stability B x Planar-2 Planar-3 Planar-4  =199±4m =242±2m =289±3m Planar-6 (1,5) Planar-7 (1,6) Planar-8 (1,7) =406±4m =418±4m =451±3m Planar-9 (2,7) Planar-10 (3,7) Planar-11 (3,8) Planar-12 (3,9) =454±4m =495±2m =487±1m =492±3m

11. Circular Trajectory of Clusters • 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) • Particles in the cluster traced out circular path during rotation

12. Periodic Pause/ Uniform Motion • Planar-2 is the most difficult to rotate with small B field and momentarily pauses at a particular angle during rotation. Other clusters, such as planar-10, rotate with uniform angular velocity (indicated by the constant slope) • Cluster maintains their stable structure during rotation (shown by constant phase in angular position)

13. 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 N2 • Planar-2 is the most resistant to rotation

14. Angular Velocity • w increases with increasing magnetic field strength • w increase linearly for one ring clusters • For double ring clusters, the rate of change in w increases quickly and then saturate

15. Cluster Radius • The mean cluster radius , decreases as magnetic field strength increases • The mean cluster radius is generally larger as the number of particles increases in the cluster

16. Total Angular Momentum • Total angular momentum L remains approximately constant with increasing N • L is summed over all particles, that is: L= mr2 L (10-20Nms) N i = 1 Planar-8 where r is the distance of the particles away from the cluster geometrical center R (10-4m) (10-1rad/s)

17. Friction Force & Ion Drag • The driven force FD for the rotation must be equal but opposite to the friction force FF due to neutrals in the azimuthal direction (FD = -FF) • FF is given by the formula: • Ion drag force FI in the azimuthal direction is a possible mechanism for rotation* • FI is given by the formula: * Source: Morfill et al. Phys. Rev. E, 61(2), Feb 2000

18. Calculated values of FD and FI • Assuming ion drag force is responsible for cluster rotation, then: FI+FF = FI –FD = 0 FI =FD • The calculated value of the driven force FD(using the equation for the neutral friction force FN) is ~ 2 x 10-16 N • The calculated value of the azimuthal ion drag force FI is ~ 5 x 10-20 N • So the magnitude of the ion drag is 4 order less than the actual driven force of rotation • So there must be some other mechanism which drives the cluster rotation other than ion drag.

19. Radial Electric Field Profile • Assuming ion drag model, we can equate FI and FF and obtain that: EConfinement ~ v • So the linear velocity of the cluster v, with different cluster radius  (i.e. at different radial position r) can inform us about the radial electric field profile. • Electric field increases as the magnetic field strength increases

20. Taking threshold magnetic field into account, the final derivation became: (8.27/N3/2) w = e(-22.83/N) x B -4/N4 Theoretical Model of w vs B • The above w vs B plot shows how the graph change as the number of particles in the cluster N increases • We attempted to model the previously shown w vs B plot by assuming: • w = Bk • where  and k are constants • However, both  and k were discovered to be dependent on N w = Bk

21. Data Verification of w vs B • Our approximation model shows the linear variation for planar-3, 4 and 5, yet logarithmic nature for planar-6 up to planar-12 • Our approximation model also fits quite accurately to the actual experimental data

22. Theoretical Model of w vs N • Using our approximation model again but from a different point of view, we can plot w vs N with increasing magnetic field strength • The plot seems to behave differently for single ring and double ring clusters • This is probably because • multiple rings clusters have a bigger cluster radius hence the particles experience different electric field at different region

23. Experimental Trend of w vs N • Our approximation model also agrees with our experimental data from the w vs N plot • From the plot, in general, w increases as the number of particle N increases. And the rate of change becomes constant for double ring clusters.

24. From experimental data, we obtained the relationship • We were able to measure the radial electric field from the linear velocity of the cluster rotation (8.27/N3/2) w = e(-22.83/N) x B -4/N4 Conclusion • It was demonstrated that rotation of small dust coulomb clusters is possible with the application of an axial magnetic field • Clusters maintain their stable structure during rotation. And the direction of the rotation is left-handed to the direction of the magnetic field • The cluster rotation is dependent on N and its structural configuration . It is easier to initiate the rotation of the clusters with larger N than smaller N at very low magnetic field strength • Thus BThresholddecreases as N increases and can be expressed by BThreshold =200/N2 • w increases while r decreases as the magnetic field strength increases. L is conserved when the magnetic field strength increases.