Dust Plasma Clusters in an Axial Magnetic Field

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

What is Dust Plasma Clusters?

Rotational Motion of Dust Plasma Clusters

Information provided by the Dust Cluster’s Rotation

Theoretical Model for the Dust Cluster’s Rotation

Conclusion


Difference between Crystal/ Clusters

Structural Configuration

Stability Factor

Experimental Apparatus



Angular Velocity

Cluster Radius

Angular Momentum




Radial Electric Field Profile

Change of Confining Potential due toMagnetized Plasma

vs B





Neutral Friction Force

Ion Drag





Conclusion

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 a Dust Plasma Cluster

Dust Plasma Crystal Dust Plasma Cluster

Experimental Apparatus

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

Voltage RF p-p = 500mV at 17.5MHz

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

Clusters 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.

Cluster Configuration & Stability

Number of

Particles

Stability Factor (SF)

2 4.4

3 1.6

4 2.6

5 -

6 1.4

7 2.2

8 5.0

9 1.9

10 1.7

11 1.5

12 1.9

=199±4m

=406±4m

=495±2m

=242±2m

=418±4m

=487±1m

=289±3m

=451±3m

=492±3m

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±4m

Planar-9 (2,7)

Stability Factor (SF) is:Standard Deviation of Cluster Radius

Mean Cluster Radius

Pentagonal (Planar-6) structure is most stable

or

B x

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)Particles in the cluster traced out circular path during rotation

Periodic Pause/ Uniform Motion

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

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

increase linearly for one ring clusters

For double ring clusters, the rate of change in increases quickly and then saturate

Angular Velocity

Cluster Radius

The mean cluster radius , decreases as magnetic field strength increases

The mean cluster radius is generally larger as the number of particles increases in the cluster

Total Angular Momentum

Total angular momentum L remains approximately constant with increasing N

L is summed over all particles, that is:

L= mr2

R (10-4m)

(10-1rad/s)

L (10-20Nms)

Planar-8

where r is the distance of the particles away from the cluster geometrical center

N

i = 1

Ion drag force FI in the azimuthal direction is a possible mechanism for rotation*

FI is given by the formula:

Friction Force & Ion Drag

The driven 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:

* Source: Morfill et al. Phys. Rev. E, 61(2), Feb 2000

Calculated values of FD and FI

Assuming ion drag force is responsible for cluster rotation, then:

FI+FF = FI –FD = 0

FI =FD

The calculated value of the driven force FD (using the equation for the neutral friction force FN) is ~ 2 x 10-16 N

The calculated value of the azimuthal ion drag force FI is ~ 5 x 10-20 NSo the magnitude of the ion drag is 4 order less than the actual driven force of rotationSo there must be some other mechanism which drives the cluster rotation other than ion drag.

Radial Electric Field Profile

Assuming ion drag model, we can equate FI and FF and obtain that:

EConfinement ~ v

So the linear velocity of the cluster v, with different cluster radius (i.e. at different radial position r) can inform us about the radial electric field profile.Electric field increases as the magnetic field strength increases

We attempted to model the previously shown vs B plot by assuming:

= Bk

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/N4(8.27/N3/2)

Theoretical Model of vs B

The above vs B plot shows how the graph change as the number of particles in the cluster N increases

= Bk

Data Verification of vs B

Our approximation model shows the linear variation for planar-3, 4 and 5, yet logarithmic nature for planar-6 up to planar-12

Our approximation model also fits quite accurately to the actual experimental data

Theoretical Model of vs N

Using our approximation model again but from a different point of view, we can plot vs N with increasing magnetic field strengthThe plot seems to behave differently for single ring and double ring clusters

This is probably because

multiple rings clusters have a bigger cluster radius hence the particles experience different electric field at different region

Experimental Trend of vs N

Our approximation model also agrees with our experimental data from the vs N plot

From the plot, in general, increases as the number of particle N increases. And the rate of change becomes constant for double ring clusters.

Conclusion

It was demonstrated that rotation of small dust coulomb clusters is possible with the application of an axial magnetic field

Clusters maintain their stable structure during rotation. And the direction of the rotation is left-handed to the direction of the magnetic field

The cluster rotation is dependent on N and its structural configuration . It is easier to initiate the rotation of the clusters with larger N than smaller N

at very low magnetic field strength

Thus BThreshold decreases as N increases and can be expressed by

BThreshold =200/N2

increases while decreases as the magnetic field strength increases. L is conserved when the magnetic field strength increases.

From experimental data, we obtained the relationship

We were able to measure the radial electric field from the linear velocity of the cluster rotation

= e(-22.83/N) x B -4/N4(8.27/N3/2)

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Dust Plasma Clusters in an Axial Magnetic Field