Dust Cluster Rotation - 3-D Phase Diagram

Dust clusters from two to twelve particles in a plane were formed and rotated in the experiment using magnetic field (see figure 1). At the same magnetic field strength setting, clusters with smaller number of particles appears to exhibit "Periodic Pause" more so than the clusters with higher number of particles. In the following chapter, the phase diagram obtained for these clusters will be shown.

Figure 1 - Dust cluster configurations formed in our cluster rotation experiment. The particles were rotated using an axial magnetic field. The clusters with smaller number of particles exhibit "Periodic Pause" even at low magnetic field strength setting.

## Phase Diagram

Here we examine the angular velocity vs. angular position of the particles in the dust cluster in 3-D (see figure 2). Such plot is called a phase diagram and it is a typical method in studying oscillatory motion. The hue color scale in the vertical direction was used to indicate the different magnetic field strength settings (blue = 15G through to red = 90G). An animation was produced by revolving the camera along the phi angle so that structure of the 3-D phase diagram can be examined in details.

 Planar-2 (910kb) (GIF) or Planar-2 (1,325kb) (MOV) Planar-3 (1,336kb) (GIF) or Planar-3 (2,042kb) (MOV) Planar-4 (1,573kb) (GIF) or Planar-4 (2,447kb) (MOV) Planar-6 (2,062kb) (GIF) or Planar-6 (3,165kb) (MOV) Planar-7 (1,746kb) (GIF) or Planar-7 (2,595kb) (MOV) Planar-8 (GIF) or Planar-8 (MOV) Planar-10 (1,729kb) (GIF) or Planar-10 (2,523kb) (MOV) Planar-11 (GIF) or Planar-11 (MOV) Planar-12 (GIF) or Planar-12 (MOV)

To see animation of the phase diagram for the different cluster configuration, please click on the link underneath the image.

To see animation of ALL phase diagram simultaneously (will take a long time to download), please click here.

Figure 2 -
Phase diagram of dust clusters from two to twelve particles. The angular velocity has actually been scaled up 1000 times the actual value (except Planar-2).
The advantage of using such phase diagram is that the occurrence of "Periodic Pause" becomes apparent. For if the dust particles in the cluster undergo uniform angular motion, a circular phase diagram is expected. If the particles exhibit "Periodic Pause", then the phase diagram would be deformed. And if the particles oscillate about a particular angle, then a straight line would be obtained.

## Phase Surface

Here we extend the previous visualization of phase diagram into phase surface in 3-D (see figure 3). Such plot is will show how the "Periodic Pause" disappears as the magnetic field strength increases. An animation was produced by revolving the camera along the phi angle so that structure of the 3-D phase diagram can be examined in details.

 Planar-2 Planar-3 Planar-4 Planar-6 Planar-7 Planar-8 Planar-10 Planar-11 Planar-12

To see plot of the phase surface for the different cluster configuration, please click on the link underneath the image.

Figure 3 - Phase surface of dust clusters from two to twelve particles. The angular velocity has actually been scaled up 1000 times the actual value (except Planar-2).

The advantage of plotting a phase surface is that we get to visualize how angular velocity varies with magnetic field strength as a continuous function. In some of these phase surface, we see that angular velocity actually saturates even though the magnetic field was increased. This is indicated by the cylindrical shape of the phase surface at high magnetic field strength settings.

## Asymmetrical Potential Well

The rotation of the dust cluster is not uniform especially when the magnetic field strength is low and the number of particles is small. The reason why such periodic motion occurs is still unknown. One reason could be that the particles in the dust clusters normally go under uniform rotation (see figure 4). However, it is highly probable that the potential well which was used to confined the particles might not be perfectly circular.

Figure 4 - For an ideal electric potential, the particles in dust cluster should go under uniform rotation. In this visualization, the particles on the outer ring in planar-7 are going under uniform rotation. This visualization is drawn using Maya Unlimited 4.0 and Ulead PhotoImpact 7.
And if we have a hill in the potential well, then the particles will decelerate (see figure 5). This potential irregularity could be due to the asymmetry in the apparatus setup. As a matter of fact, if the particles are unable to overcome this potential hill, then the cluster will not be able to initiate rotation. This coincides with the phase diagrams we obtained in figure 2.1.1. At low magnetic field, because the particles does not have enough driving force to push it over the potential hill, oscillatory motion at a particular angle was observed. And if we look at the phase diagram for planar-2, we see that the angle at which the particles oscillate about increase gradually as magnetic field strength increases. This would coincide with the theory of asymmetric potential well.

Figure 5 - However, if there is a potential hill in the electric potential well, then the particles in a dust cluster must overcome the potential hill during its rotation. As a result, the angular velocity of the cluster would decelerate. In this visualization, the particles on the outer ring of a planar-7 cluster went under deceleration because of the defect in the potential well . This defect could be due to the asymmetry in the experimental setup. This visualization is drawn using Maya Unlimited 4.0 and Ulead PhotoImpact 7.