Dusty plasma cavities: Probe-induced and natural

A comprehensive exploration of regional dust evacuation in complex plasma crystals is presented. Voids created in three-dimensional crystals on the International Space Station have provided a rich foundation for experiments, but cavities in dust crystals formed in ground-based experiments have not received as much attention. Inside a modified Gaseous Electronics Conference rf cell, a powered vertical probe was used to clear the central area of a dust crystal, producing a cavity with high cylindrical symmetry. Cavities generated by three mechanisms are examined. First, repulsion of micrometer-sized particles by a negatively charged probe is investigated. A model of this effect developed for a dc plasma is modified and applied to explain experimental data in rf plasma. Second, the formation of natural cavities is surveyed; a radial ion drag proposed to occur due to a curved sheath is considered in conjunction with thermophoresis and a flattened confinement potential above the center of the electrode. Finally, cavity formation upon increasing the probe potential above the plasma floating potential is justified by a combination of ion drag and sheath edge modification. The cavities produced by these methods appear similar, but each is shown to be facilitated by fundamentally different processes.

Figure 1

Dust particle positions in a planar dust crystal with an open central cavity created by a negatively biased vertical probe located at the center of the cavity. The rf peak-to-peak voltage was 90 V for a neutral gas pressure of 100 mTorr, providing a probe potential of $-30$ V. A 1-in.-diam circular cutout with depth of 1 mm was used for horizontal confinement.

Figure 2

Probe potential-induced cavity size (blue squares) as a function of probe bias with respect to the ground. The system parameters are the same as those in Fig. 1. The probe current (green circles) is superimposed, showing the significant difference between negative- and positive-probe biases.

Figure 3

Cavity radii versus probe bias. (a)–(c) System pressure is fixed as indicated, for $50V_{pp}$ (blue), $70V_{pp}$ (gray), and $90V_{pp}$ (red). (d)–(f) Results are shown for a constant $V_{pp}$ as indicated, with the circles denoting a pressure of 50 mTorr, the squares 100 mTorr, and diamonds 300 mTorr. Lines represent linear fits to the data.

Figure 4

Electron density at the dust levitation height as a function of probe potential. The data shown were determined by fixing the cavity radius to that measured experimentally and adjusting the electron density until the model-predicted potential at the probe matched the experimentally imposed value. As shown, the change in electron density causes a change in the plasma screening length (green circles). The lines represent linear fits.

Figure 5

Natural cavity radius versus pressure for $90V_{pp}$. The (blue) squares and (black) circles indicate cavity radii found using a 1-mm lower electrode cutout at both natural bias and a fixed dc bias of $-50$ V, respectively. Using the fixed bias did not permit plasma ignition at 200 mTorr. The (red) triangles represent cavities produced using a 3-mm lower electrode cutout for horizontal confinement, as in Ref. [15]. At pressures greater than 400 mTorr, the dust levitated within the 3-mm cutout, preventing it from being illuminated by the horizontal laser.

Figure 6

Natural cavity radius versus $V_{pp}$ for various fixed pressures. The (blue) circles represent cavities found using the 1-mm-deep lower electrode cutout depression at 750 mTorr, whereas the (black) squares and (red) triangles represent cavities found using the 3-mm-deep electrode cutout, which was also used in Ref. [15], at 350 and 250 mTorr, respectively.

Figure 7

Distance from the lower electrode as a function of pressure. The experimentally determined sheath edge (squares with a dashed fit) decreases nonlinearly with increasing pressure, whereas the dust levitation height (circles with a solid fit) decreases linearly. A theoretical collisional sheath width (diamonds with a dotted fit) also decreases with pressure, as well as coinciding with the experimental sheath width (edge), showing the applicability of the collisional regime. The average areal density of the dust (green triangles with a dash-dotted fit), which was found by taking the particle number and dividing by the area of the dust annulus, increases as the pressure is increased.

Figure 8

Average areal dust density as a function of the radial position, where the radial distance of dust particles is binned and the interparticle distance averaged. The dust density increases as a function of the radius until it reaches a maximum near the outer edge of the annulus.

Figure 9

Curvature of the sheath edge as viewed from a cross section through the lower electrode (accentuated). The sheath widths in the center and at the cutout edge are defined as $\mathrm{\Delta }{S}_0$ and $\mathrm{\Delta }{S}_e$, respectively. The difference in sheath edge position between the plasma center and cutout edge changes the equilibrium levitation height of a dust particle.

Figure 10

Side-view plasma temperature (in kelvin) between the electrodes at system pressures of (a) 300 mTorr, (b) 500 mTorr, and (c) 700 mTorr.

Figure 11

Potential energy of the average particle in a dust crystal having a naturally formed cavity, shown for various pressures. The (black) vertical lines show the average annular radii, which coincide with the minima of the total potential energy (black triangles). Contributions to the total potential energy include the potential energy of thermophoresis (green diamonds), radial ion drag (red circles), and horizontal confinement (blue squares).

Figure 12

Initial ion speed as a function of positive-probe-potential normalized to the Bohm speed. The line is a quadratic fit. The values are found by fitting the minimum of the total potential energy to match the average radial dust position.

Figure 13

Potential energy plot for positive-probe-potential-induced cavities. The (black) triangles indicate the total potential energy, with contributions from the repulsive energy due to the raised sheath edge (green circles), outward ion drag (red diamonds), and horizontal confinement (blue squares). The vertical lines indicate the minimum in the total potential energy, which coincides with the average experimental radial position of the dust.