Dust acoustic waves in three-dimensional complex plasmas with a similarity property

Dust acoustic waves in the bulk of a dust cloud in complex plasma of low-pressure gas discharge under microgravity conditions are considered. The complex plasma is assumed to conform to the ionization equation of state (IEOS) developed in our previous study. This equation implies the ionization similarity of plasmas. We find singular points of IEOS that determine the behavior of the sound velocity in different regions of the cloud. The fluid approach is utilized to deduce the wave equation that includes the neutral drag term. It is shown that the sound velocity is fully defined by the particle compressibility, which is calculated on the basis of the used IEOS. The sound velocities and damping rates calculated for different three-dimensional complex plasmas both in ac and dc discharges demonstrate a good correlation with experimental data that are within the limits of validity of the theory. The theory provides interpretation for the observed independence of the sound velocity on the coordinate and for a weak dependence on the particle diameter and gas pressure. Predictive estimates are made for the ongoing PK-4 experiment.

Figure 1

Dimensionless dust particle ($n^{*}$, solid line) and electron number density ($n_e^{*}$, dashed line) as a function of the dimensionless ion number density $n_i^{*}, \theta =\text{0}\text{.0431}$.

Figure 2

Dimensionless quantities at the second singular point as a function of the temperature parameter $\theta$. Solid line indicates the sound velocity $c_s^{*}$; dashed line, the dust particle potential ${\mathrm{\Phi }}_s^{*}$; and dashed-dotted line, the particle number density $n_s^{*}$.

Figure 3

Dependence of the sound velocity on the dimensionless ion number density (solid line), $\theta =\text{0}\text{.0431}$. Dashed lines indicate the boundaries of a band, in which the sound velocity measured at different locations inside the dust cloud are scattered [20], and dotted line points to the location of the second singular point.

Figure 4

Sound velocity in the dust clouds formed by the particles of different diameter in argon RF discharge. Solid line indicates the calculation using (36); dashed line, using the formula in Ref. [25] (37). Dots represent experimental data for different particle diameter (from left to right): $2a_d=1.55$ [19], $2.55$ [20], $6.8$ [11, 12], and $9.55\mu \text{m}$ [11, 14].