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Rotation of Dust Coulomb Clusters

Rotation of Dust Coulomb Clusters. in axial magnetic field. F. Cheung, A. Samarian, B. James School of Physics, University of Sydney, NSW 2006, Australia. Multi-ring saturation effect. Threshold magnetic field. Periodic pause in rotation. Experimental results. Comparison of forces.

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Rotation of Dust Coulomb Clusters

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  1. Rotation of Dust Coulomb Clusters in axial magnetic field F. Cheung, A. Samarian, B. James School of Physics, University of Sydney, NSW 2006, Australia

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

  3. Camera RF Coil set in Araldite Argon Gas Inlet Particle Shaker To diffusion pump To magnetically coupled manipulator Laser PCB Electrode Dust Crystal Magnetic Coil Observation Window 5cm Experimental Apparatus • Argon Plasma • Melamine Formaldehyde Polymer Spheres • Dust Diameter = 6.21±0.9m • Pressure = 100mTorr • VoltageConfinement = +10.5V • Magnetic Field Strength = 0 to 90G • Electron Temperature ~ 3eV • Electron Density = 1015m-3

  4. Cluster Configuration • 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 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) =454±4 m =495±2 m =487±1 m

  5. 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) Video is running at 5x actual speed

  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 N2 • Planar-2 is the most resistant to rotation

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

  10. Driving Force & Ion Drag • Driving force FDriving for rotation must be equal but opposite to friction due to neutral drag FNeutral 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. • FF is given by the formula: • Estimation value of the driving force for such rotation is 1.7 x10-16N for driving force • Upper limit of ion drag is given by: where • ion drag force < 10-17N

  11. Divergence of Magnetic Field • For a magnetic field divergence of 11.5 degrees, the ECxBz component and the ESxBr component will be equal. • Only small divergence of the magnetic field is needed to affect the azimuthal ion drift velocity. B B Bz ES EC Br B FLi~ECxBz FLi~ESxBr EConfinement Magnetic Coil ESheath

  12. Multi-ring Saturation Effect B  • Inner ring attempts to rotate in opposite direction as the outer ring. Er Ar+ Fint Er Ar+ vi vi F F Fint

  13. Multi-ring Saturation Effect B  • 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.

  14. B field on B field off Multi-ring Saturation Effect • 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) • 2V = -/0 •  ~ ni + ne V e- Ar+ r

  15. r 2/6 r /6 /6 r /6 Er = 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 For single ring cluster, Er = eZ/160r2{ k=1n-1 [sin(k/n)]-1 } where n is the number of particles in the outer ring 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.

  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. Rotation Oscillation y When F~F When F>>F r  x F2 F1   M = F1 rcos +F2 rcos(+) t t

  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.

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