An experimental determination of particle charge in a bulk dc discharge plasma covering a wide range of neutral gas pressures, was recently reported [S. Ratynskaia, Phys. Rev. Lett. 93, 085001 (2004)]. The charges obtained were several times smaller than the predictions of collisionless orbital motion limited theory. This discrepancy was attributed to the effect of ion-neutral collisions. In the present paper a more detailed description of this experiment is provided and additional experimental results obtained with particles of different sizes are reported. The measurements are compared with molecular dynamics simulations of particle charging for conditions similar to those of the experiment, with other available experimental data on particle charge in the bulk of gas discharges, and with a simple analytical model accounting for ion-neutral collisions. All the considered evidence indicates that ion-neutral collisions represent a very important factor, which significantly affects (reduces) the particle charge under typical discharge conditions.

The effect of the polarization force acting on the grains in a nonuniform plasma background on the propagation of low-frequency waves in complex (dusty) plasmas is analyzed. It is shown that polarization interaction leads to a renormalization (decrease) of the dust acoustic phase velocity. The effect becomes more pronounced as the grain size increases. Finally, there is a critical grain size above which the dust acoustic waves cannot propagate, but aperiodic (nonpropagating) perturbations form instead.

The charge of dust particles is determined experimentally in a bulk dc discharge plasma in the pressure range 20-100 Pa. The charge is obtained by two independent methods: one based on an analysis of the particle motion in a stable particle flow and another on an analysis of the transition of the flow to an unstable regime. Molecular-dynamics simulations of the particle charging for conditions similar to those of the experiment are also performed. The results of both experimental methods and the simulations demonstrate good agreement. The charge obtained is several times smaller than predicted by the collisionless orbital motion theory, and thus the results serve as an experimental indication that ion-neutral collisions significantly affect particle charging.

|0⟩ |1⟩ |2⟩ 4 J J J J P P 5 C J C P C U L Figure 1: Topolectrical circuit model. a, Artistic view of two-photon excitations in the array of microresonators with tunneling couplings. The depicted state isâ † 1â † 3 |0 . b, Extended version of Bose-Hubbard model considered in the present article. Single-photon tunnelings J are shown by blue solid lines, direct two-photon tunnelings P are indicated by purple wavy lines. c, Top view of the equivalent two-dimensional topolectrical circuit with a voltage at the site (m, n) corresponding to probability amplitude βmn for one photon to be located at the m th resonator of the array with another one located at the n th resonator [cf. Eq. (2)]. Colored regions show characteristic voltage patterns for two-photon scattering states (green), doublons (red), and doublon edge state (blue). External voltage source applied for the system excitation and voltmeter are shown to the right. Side view of the diagonal (lower inset) and off-diagonal (upper inset) sites of the topolectrical circuit, where grounding elements are shown. d, The photograph of experimental setup having the size of 15 × 15 nodes. Inset shows the enlarged fragment of the circuit which includes two unit cells. d c b a J J P J P J J P J

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