F.M.H. Cheung School of Physics, University of Sydney, NSW 2006, Australia

Rotation of Fine Plasma Crystal in Axial Magnetic Field 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 Electric Field B

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 Dust Plasma CrystalFine Plasma Crystal

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 ~ 3eV Electron Density = m -3

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. Crystal 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 Crystal Radius Mean Crystal Radius   Pentagonal (Planar-6) structure is most stable or B x

Circular Trajectory of Crystals AD Video is running at 5x actual speed 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)

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

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)

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

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 N 2 Planar-2 is the most resistant to rotation

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 ) Approximation Model of  vs B The above  vs B plot shows how the graph change as the number of particles in the crystal N increases  =  B k

Driving Force & Ion Drag The driving 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: Estimation value of the driving force for such rotation is 1.7 x N for driving force (ion drag force ~ 9.6 x N)

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)  2 V = -  /  o  ~ n i + n e 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

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

Experimental Setup Melamine formaldehyde – 6.13 μm ± 0.06 μm Argon plasma T e ~ 2 eV, V p =50V & n e ~ 10 9 cm -3 Confining Ring Electrode ParticleDispenser Top Ground Electrode Diffusion Pump Gas Inlet Probe Inlet Laser ObservationWindow rf discharge 15 MHz Pressure ~ mTorr Input power ~ W Self-bias voltage ~ V

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

Rotational Motion AD

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 B Threshold decreases as N increases: B Threshold =200/N 2 From experimental data: Estimation value of the driving force for such rotation is 1.7x N for driving force (ion drag force ~ 9.6x N) 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.  = e (-22.83/N) x B -4/N 4 (8.27/N 3/2 )