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

What is Dust Plasma Clusters?Rotational Motion of Dust Plasma ClustersInformation provided by the Dust Cluster’s Rotation Theoretical Model for the Dust Cluster’s RotationConclusion

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

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

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

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

What is Dust Plasma Clusters?Rotational Motion of Dust Plasma ClustersInformation provided by the Dust Cluster’s Rotation Theoretical Model for the Dust Cluster’s RotationConclusion

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 Dust Plasma CrystalDust Plasma Cluster

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 Voltage Confinement = +10.5V Magnetic Field Strength = 0 to 90G Electron Temperature = few eV Electron Density = m -3

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. Cluster Configuration & Stability Number of Particles Stability Factor (SF)  =199±4  m  =406±4  m  =495±2  m  =242±2  m  =418±4  m  =487±1  m  =289±3  m  =451±3  m  =492±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) Planar-12 (3,9)  =454±4  m Planar-9 (2,7) Stability Factor (SF) is: Standard Deviation of Cluster Radius Mean Cluster Radius   Pentagonal (Planar-6) structure is most stable or B x

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

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)

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

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

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

Total Angular Momentum Total angular momentum L remains approximately constant with increasing N L is summed over all particles, that is: L=  m  r 2 R (  m)  (  rad/s) L (  Nms) Planar-8 where r is the distance of the particles away from the cluster geometrical center N i = 1

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

Calculated values of F D and F I Assuming ion drag force is responsible for cluster rotation, then: F I +F F = F I –F D = 0 F I =F D The calculated value of the driven force F D (using the equation for the neutral friction force F N ) is ~ 2 x N The calculated value of the azimuthal ion drag force F I is ~ 5 x 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.

Radial Electric Field Profile Assuming ion drag model, we can equate F I and F F and obtain that: E Confinement ~ 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

We attempted to model the previously shown  vs B plot by assuming:  =  B k where  and k are constants However, both  and k were discovered to be dependent on N Taking threshold magnetic field into account, the final derivation became:  = e (-22.83/N) x B -4/N 4 (8.27/N 3/2 ) Theoretical Model of  vs B The above  vs B plot shows how the graph change as the number of particles in the cluster N increases  =  B k

Data Verification of  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

Theoretical Model of  vs N Using our approximation model again but from a different point of view, we can plot  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

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

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 B Threshold decreases as N increases and can be expressed by B Threshold =200/N 2  increases while  decreases as the magnetic field strength increases. L is conserved when the magnetic field strength increases. From experimental data, we obtained the relationship We were able to measure the radial electric field from the linear velocity of the cluster rotation  = e (-22.83/N) x B -4/N 4 (8.27/N 3/2 )