F. Cheung, A. Samarian, B. JamesSchool of Physics, University of Sydney, NSW 2006, Australia

Comparison of forces

Multi-ring saturation effectThreshold magnetic field

Explanation for various cluster rotation properties

Experimental results

B

Periodic pause in rotation

Experimental Apparatus

Argon PlasmaMelamine Formaldehyde Polymer SpheresDust Diameter = 6.21±0.9mPressure = 100mTorr

VoltageConfinement = +10.5VMagnetic Field Strength = 0 to 90GElectron Temperature ~ 3eVElectron Density = 1015m-3

RF Coil setin Araldite Argon

Gas InletParticle Shaker

To magnetically coupled manipulator

Magnetic Coil

To diffusionpump

Camera

PCB Electrode

ObservationWindow

Laser

5cm

Dust Crystal

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

Cluster Configuration

=199±4m

=406±4 m

=495±2 m

=242±2 m

=418±4 m

=487±1 m

=289±3 m

=451±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)

=454±4 mPlanar-9 (2,7)

B x

Circular Trajectory of Clusters

Video is running at 5x actual speed

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)

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

Periodic Pause of Planar-2

Video is running at 5x actual speed

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

increases with increasing magnetic field strength

increases linearly for planar-6, -7 and -8

For planar-10, -11 and -12, the rate of change in increases quickly and then saturate

Angular Velocity

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 (2.71m).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

2222/1 ipiiiIonDrag vmeZvnmF

rvnmFnTnngNeutralDra 2

3

4

))/(1(

)/(1

0

20

S

Ci Ep

BEp

c

NeutralDriving FF

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

EC

Bz

BES

Br

FLi~ECxBz FL

i~ESxBr

Magnetic Coil

EConfinement

ESheath

Multi-ring Saturation Effect

Inner ring attempts to rotate in opposite direction as the outer ring.

B

FF

vi

ErEr

vi

Ar+

Ar+Fint

Fint

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

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

Multi-ring Saturation Effect

mr elarmor

51014.6~

mr ilarmor

21066.1~

VV

rrB field off

B field one-

Ar+

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.

Er = eZ/40{ 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

/6/6

2/6

/6

For single ring cluster,Er = eZ/160r2

{ k=1n-1 [sin(k/n)]-1 } where n is the number of particles in the outer ring

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.

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.

t

t

When F >> F When F ~ F

F1 F2

OscillationRotation

M = F1 rcos + F2 rcos(+)

x

y

r

x

FF

~

Oscillatory Motion of Planar-2

Video is running at 6x actual speed

Rim Orbital Motion

Video is running at 1/3x actual speed

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.