Sketch of the setup and of the force balance on the particles levitating in the combined rf and dc plasmas, where Fi is ion drag force, Fg gravity, FDC electric force by dc plasma, and FGF is neutral drag force (due to the gas flow).
Dust structures observed in thepure rf (left panel) and combined rf + 1 mA dc (right panel) discharge with general (a) and side (b) views. Particles are color-coded by their radial distance from the tube axis (the distance is in mm units). The white squares show relatively homogenous regions used for the structural analysis. The lines indicate approximately the local orientations of the (string-like) structures. Considered structures consist of about 105 particles, which is comparable to the biggest complex plasma systems analyzed so far.
Axial cross-sections of the particle cloud levitated in combined rf and dcdischarge with different dc currents (a) 0.1 mA, (b) 0.2 mA, (c) 0.4 mA, and (d) 0.6 mA. It is clearly visible that the global distribution of the particles is systematically effected by the dc current increase, slowly decreasing the number of particles levitating along the center of the tube and gradually forming the void around them. Particles are color coded by the radial position indicated by the color (distances are in mm units).
The typical particle distribution on the plane of bond order parameters q 4 and q 6 (for pure rf plasma). Particles are color-coded by the w 4 value. Rotational invariants were calculated by using 12 nearest neighbors; those for perfect fcc/hcp/ico lattice types are also indicated. The distribution reveals presence of solid-like (hcp-like and fcc-like), weakly disordered (glassy), liquid-like and string-like phases in the cloud. Inset shows the RDF for rf (solid red line) and rf + 1 mA dc (solid green line) plasma. The cumulative distributions (mean number of particles located inside sphere of radius r in mm units) of the RDFs are shown by dashed lines. Both the cumulative distribution and splitting of the first maximum of the RDF indicate the presence of string-like structures.
Typical particle distribution on the plane of the order parameters (calculated by using 6 nearest neighbors). The domains occupied by both the quasi-isotropic and string-like structures (consisting of microparticles) are indicated. The color coding from blue to red corresponds to the increasing probability of finding a particle in a given region of (q 4, q 6) plane.
Observed string-like structures in pure rf (a) and rf + 1 mA dc (b) plasma. Particles are color-coded by the parameter (mm) which is the distance to the nearest neighbor. Inset shows corresponding probability distribution functions. The cumulative distribution (green line) is also plotted. The PDF reveal shoulder-like behavior at distances r far less than the averaged interparticle distance, indicating the presence of string-like structures in the system.
Probability distribution function in an rf (solid red line) and rf + rf + 1 mA dc (solid green line) plasmas. Similar PDFs are also plotted for isotropic liquid-like (the data set is taken from Ref. 7 , solid blue line) and solid-like (the data set is taken from Ref. 15 , solid orange line) 3D complex plasmas. Corresponding cumulative distributions are also plotted by dashed lines of the same color. The inset shows the distribution of the string-like structures over the number of particles they contain for rf (solid red line) and rf + 1 mA dc (solid green line) complex plasmas.
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