Rotation of a strongly coupled dust cluster in plasma by the torque of an electron beam

A 1-mm-size cluster composed of 10 dust particles immersed in plasma is rotated by the torque of a pulsed electron beam with energy in the range 8–12 keV. The dust particles are electrically charged spheres with radius 5.9 $\mu \mathrm{m}$ and are levitated in the plasma sheath, forming a round, planar, Coulomb-coupled cluster. The electron beam irradiates the dust cluster passing slightly off its center, and sets the particles in motion by the action of the electron drag force. The total torque at 12 keV is $4.9\pm 0.2\times {10}^{-11}$ Nm at an angular speed $1.41\pm 0.05$ rad ${\mathrm{s}}^{-1}$. The main dynamical features of the cluster such as intershell rotation and itinerancy of the dust particles inside the cluster are simulated by using a molecular dynamics code.

Figure 1

A strongly coupled planar dust cluster is irradiated by an EB while it is levitated in the RF plasma sheath. A metallic ring with an inner diameter of 10 mm placed on the RF electrode confines the cluster to its center. A sheath of light obtained from a laser diode and a cylindrical lens is used to illuminate the cluster. The cluster dynamics is monitored from the top with a Photron CCD camera operating at 60 fps equipped with a Micro Nikkor 40 mm f/2.8 objective and two teleconverters ($\times 2$ and $\times 3$).

Figure 2

(a) Top view of the pulsed EB inside Ar at $100\times {10}^{-3}$ Torr, above the RF electrode (the image has been processed by increasing its brightness). The cluster (indicated with a small yellow circle) is positioned at the center (marked with a cross) of the circular cut in the ring, near the EB axis. The diameter of the confining region is 10 mm, while the diameter of the cluster is $\approx 1$ mm. The EB central axis is slightly displaced relative to the center of the dust cluster; (b) Top view of the dust cluster levitated in the plasma sheath at the center of the confining region, with no EB; (c) Cross section of the EB imaged on a scintillating screen; (d) Measured EB profile (continuous line) along the diameter of the cross section shown in (c) with a FWHM of $4.5\pm 0.5$ mm, fitted with a Gaussian function (dotted line). For reference, the cluster is drawn in yellow in order to indicate its location and diameter relative to the beam cross section and the difference in the intensity of the beam on both sides of the cluster.

Figure 3

(a) Cluster rotation in the horizontal plane and direction of the EB at 11 keV: (a) initial position when the EB is turned on; (b) rotation induced by the EB torque; outer dust particles labeled 1 to 5 are tracked in time; (c) rotation with angle $\approx \pi$ around the cluster center, and (d) itinerancy towards the cluster center of dust particle 2.

Figure 4

(a) Measured dust trajectories induced by the pulsed EB with energy 11 keV around the center of rotation (marked with $+$); (b) Evolution in time of the unwrapped rotational angle $\varphi$ of each dust particle. Dust particles itinerancy between inner and outer trajectories (with dashed and dotted lines) at $t\approx 9.5$ s is shown with arrows.

Figure 5

(a) Simulated dust trajectories for a continuous EB with energy 0.75 keV; the inset shows the initial position of the cluster, while the arrow shows the width of the EB. The cluster center is in the origin of axes; (b) Simulated evolution in time of the unwrapped rotational angle $\varphi$ of all dust particles. Itinerancy between the inner and outer trajectories (with magenta and blue line) is seen at $t\approx 40$ s, marked by arrows.

Figure 6

(a) Measured torque ${\tau }_{EB}$ (squares) exerted by the pulsed EB on the whole cluster and average angular speed of rotation $\omega$ (diamonds) of the outer cluster ring; (b) Simulated total torque ${\tau }_{EB}$ (squares) exerted by the continuous EB and average angular speed ${\tau }_{EB}$ (diamonds).