Rotation of Dust Particles in Magnetized

1. Rotation of Dust Particles in Magnetized and Complex Plasma F.M.H. Cheung School of Physics, University of Sydney, NSW 2006, Australia

2. Rotational Motion of Dust Plasma Crystals Information provided by the Crystal’s Rotation Approximation Model for Crystal’s Rotation Rotation of Fine Plasma Crystal in Axial Magnetic Field B Rotation of Fine Plasma Crystal in Electric Field

3. Dust Plasma Crystal Fine Plasma Crystal 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 Fine Plasma Crystal

4. 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 ~ 3eV • Electron Density = 1015m-3

5. Crystals 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 Crystal Radius • Mean Crystal Radius •  •  • Pentagonal (Planar-6) structure is most stable or Crystal 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

6. 02.9.00AD Circular Trajectory of Crystals Trajectory of the crystals 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

7. Circular Trajectory of Crystals • Particles in the crystal traced out circular path during rotation

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

9. Angular Velocity • w increases with increasing magnetic field strength • w increase linearly for planar-6 and -8 • For double ring crystals, the rate of change in w increases quickly and then saturate

10. Threshold Magnetic Field • Ease of rotation increases with number of particles in the crystal, N • Magnetic field strength required to initiate rotation is inversely proportional to N2 • Planar-2 is the most resistant to rotation

11. Taking threshold magnetic field into account, the final derivation became: (8.27/N3/2) w = e(-22.83/N) x B -4/N4 Approximation Model of w vs B • The above w vs B plot shows how the graph change as the number of particles in the crystal 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

12. Driving Force & Ion Drag • The driving 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: • Estimation value of the driving force for such rotation is 1.7 x10-16N for driving force (ion drag force ~ 9.6 x 10-18N)

13. Nonuniform Space Charge Driver • Non-uniformity in charge variation dusty plasma systems might be a possible mechanism for rotation • Electrons confined by magnetic field more than ions because of smaller mass (Bq/m) • 2V = -/o •  ~ ni + ne • Magnetic field modifies the radial profile of electron and ion density, presumably due to the magnetization of the electrons • Magnetic field might affect electric potential • A change in shape of the potential might make particle to rotate V r

14. Change of potential? • Ratio of electron gyrofrequency to frequency of electron-neutral collisions ~1.5 (for ions, this ratio <0.01) • Change of radial distribution of ne (ni) can lead to an increase in dust charge spatial gradient r = Z(r)/r. The angular velocity of rotation can be estimated from where Fnonis the non-electric force, Z is the dust particle charge, and fr is the collisional frequency • Thermophoretic force Fth(r) = where  is the heat conductivity. Estimation value of the charge gradient r/<Z> which would be sufficient to drive the rotation can be found by substituting the above expression for Fth into equation: • Temperature gradient in sheath is about 0.5 K/cm. Therefore r /<Z>= 0.2, 0.14, 0.06 cm-1 for large, annular and small crystals respectively. = Fnonr/2mdZfr

15. Observation Window Particle Dispenser Top Ground Electrode Laser Probe Inlet Confining Ring Electrode Gas Inlet Diffusion Pump Experimental Setup rf discharge 15 MHz Pressure ~10 - 400 mTorr Input power ~ 15 - 200 W Self-bias voltage ~ 5 - 180V Melamine formaldehyde – 6.13 μm ± 0.06 μm Argon plasma Te ~ 2 eV, Vp =50V &ne ~ 109 cm-3

16. Top layer Bottom layer Rotational Motion Electrode shift ~ 3mm  ~ 2rpm Electrode shift ~ 3mm Bottom ~ 3rpm Top ~ 5rpm dp=6.13 mm, P= 80W, p=70 mTorr;

17. 02.9.00AD Rotational Motion

18. Conclusion • Rotation of fine dust crystals is possible with application of axial magnetic field • The crystal rotation is dependent on N and its structural configuration . It is easier to initiate crystal rotation with larger N than smaller N at very low magnetic field strength • Thus BThreshold decreases as N increases: BThreshold =200/N2 • From experimental data: • Estimation value of the driving force for such rotation is 1.7x10-16N for driving force (ion drag force ~ 9.6x10-18N) • Non-uniform charge distribution in plasma crystal can lead to such rotation. • Rotation of unmagnetized complex plasma in rf discharge shifted with electrode was observed. w = e(-22.83/N) x B -4/N4 (8.27/N3/2)