Alex Samarian Complex Plasma Laboratory School of Physics, University of Sydney, NSW 2006, Australia

What is Dust Cluster? Dust Particles Top View Plasma Side View Dusty Cluster Side View = m1m & (As seen in Vacuum Chamber)(As seen under microscope)(As seen above Confinement Electrode) 0.5mm

“Zoom Out” View Experimental Apparatus “Zoom In” View

Applications of Dust Cluster Manipulation of particles individually and collectively Dust control in plasma processing Fabrication of nano- scaled mechanical devices Astrophysical interests such as planetary rings under gravitational field

Clusters of 2 to 16 particles studied 0 to 100G Interparticle distance about 0.4mm Left-handed direction rigid body rotation with respect to B field

Ion Drag Force Prevalent theory in explaining cluster rotation. 1 x N3 x N

Magnetization of Electrons 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 B field off Potential is Parabolic B field on Potential is Caved-in Magnetic Coil B Electrons are highly magnetised

Electric Field Dependence Electric field is modified by the magnetic field, so 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

Angular Velocity Saturation Single ring clusters exhibits B threshold with oscillation at low B and periodic pauses at high B For one and a half ring clusters,  increases linearly with B For double ring clusters,  saturates with increase of B  saturation occurs at 30G

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  F F vivi ErEr ErEr vivi Ar + F int

Conclusion Dust clusters of 2 to 16 particles have been rotated under axial B field Angular velocity increases: Linearly for single ring cluster as B field increases, but require certain threshold magnetic field strength for rotation to initiate Linearly for one and a half ring cluster as B field increases Initially linear for double ring cluster, but then saturates as B field increases Electrons are highly magnetized and ions are partially magnetized Hence B field modifies the electron and ion density profile which leads to a change in the electric field potential Angular velocity saturation might be due to magnetization of electrons