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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
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
~
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.