Theory of a cavity around a large floating sphere in complex (dusty) plasma

In the last experiment with the PK-3 Plus laboratory onboard the International Space Station, interactions of millimeter-size metallic spheres with a complex plasma were studied [M. Schwabe et al., New J. Phys. 19, 103019 (2017)]. Among the phenomena observed was the formation of cavities (regions free of microparticles forming a complex plasma) surrounding the spheres. The size of the cavity is governed by the balance of forces experienced by the microparticles at the cavity edge. In this article we develop a detailed theoretical model describing the cavity size and demonstrate that it agrees well with sizes measured experimentally. The model is based on a simple practical expression for the ion drag force, which is constructed to take into account simultaneously the effects of nonlinear ion-particle coupling and ion-neutral collisions. The developed model can be useful for describing interactions between a massive body and surrounding complex plasma in a rather wide parameter regime.

Figure 1

Sketch of the PK-3 Plus discharge chamber. Adapted from Ref. [18].

Figure 2

Experimental video images showing a metallic sphere surrounded by complex plasma in an argon discharge. In (a) the pressure is 17.5 Pa, the particles interacting with the sphere have a diameter of $1.55\mu \mathrm{m}$, the diameter of the cavity is $\simeq 4.2$ mm; in (b) the pressure is 30.4 Pa, the complex plasma interacting with the sphere consists mostly of agglomerate particles, and the diameter of the cavity is $\simeq 4.8$ mm.

Figure 3

Dependence of the cavity diameter on the neutral gas pressure. Circles are experimental measurements (symbol's size is comparable to experimental uncertainty), the solid curve corresponds to the theoretical calculation.

Figure 4

Reduced drift velocity of ${\mathrm{Ar}}^{+}$ ions in Ar gas at $T=300$ K as a function of $E/N$—the ratio of electric field strength to the neutral gas density. The latter is measured in Townsend (Td) units; 1 Td = ${10}^{-17}$ V ${\mathrm{cm}}^2$. Symbols correspond to the experimental data [58]. The curve is calculated using Eqs. (7) and (12).