Fluid approach to evaluate sound velocity in Yukawa systems and complex plasmas

The conventional fluid description of multicomponent plasma, supplemented by an appropriate equation of state for the macroparticle component, is used to evaluate the longitudinal sound velocity of Yukawa fluids. The obtained results are in very good agreement with those obtained earlier employing the quasilocalized charge approximation and molecular dynamics simulations in a rather broad parameter regime. Thus, a simple yet accurate tool to estimate the sound velocity across coupling regimes is proposed, which can be particularly helpful in estimating the dust-acoustic velocity in strongly coupled dusty (complex) plasmas. It is shown that, within the present approach, the sound velocity is completely determined by particle-particle correlations and the neutralizing medium (plasma), apart from providing screening of the Coulomb interaction, has no other effect on the sound propagation. The ratio of the actual sound velocity to its “ideal gas” (weak coupling) scale only weakly depends on the coupling strength in the fluid regime but exhibits a pronounced decrease with the increase of the screening strength. The limitations of the present approach in applications to real complex plasmas are briefly discussed.

Figure 1

Adiabatic index $\gamma =c_{\mathrm{p}}/c_{\mathrm{v}}$ as a function of the coupling parameter $\Gamma$ for four values of the screening parameter: $\kappa =1.0$ (red solid curve), $\kappa =2.0$ (blue dashed curve), $\kappa =3.0$ (black dotted curve), and $\kappa =4.0$ (green solid curve). The discontinuity in $\gamma$ is the consequence of plasma-related contribution to the thermodynamic quantities.

Figure 2

Reduced sound velocity of Yukawa fluids, $c_{\mathrm{s}}/{\omega }_{\mathrm{p}}a$, as a function of the screening parameter $\kappa$. The solid curves correspond to the results of the simple fluid approach of this paper for $\Gamma =10$ (blue curve) and $\Gamma =100$ (red curve). The dashed curve is plotted using QLCA result of Ref. [28], given by Eqs. (21) and (22).

Figure 3

Long-wavelength dispersion of the longitudinal waves in Yukawa fluids near freezing, plotted in the $(q,\omega /{\omega }_{\mathrm{p}})$ plane, where $q=ka$ is the reduced wavenumber. Symbols correspond to the results from numerical simulations of Ref. [35] for $\kappa =1.0$ (red circles), $\kappa =2.0$ (blue triangles), and $\kappa =3.0$ (olive rhombuses). The corresponding dashed lines correspond to the acoustic asymptotes $\omega =k{c}_{\mathrm{s}}$ with the sound velocity $c_{\mathrm{s}}$ calculated using the fluid approach described in the present paper [Eq. (20)].

Figure 4

Contour plot of the reduced sound velocity $c_{\mathrm{s}}/c_0$ of Yukawa fluids in the plane $(\kappa ,\Gamma /{\Gamma }_{\mathrm{m}})$. Calculations are made using the fluid model described in this paper.

Figure 5

The reduced sound velocity $c_{\mathrm{s}}/c_0$ of Yukawa fluids versus the reduced coupling parameter $\Gamma /{\Gamma }_{\mathrm{m}}$. The curves (from top to bottom) correspond to $\kappa =1.0,\kappa =2.0,\kappa =3.0$, and $\kappa =4.0$, respectively. Calculations are made using the fluid model described in this paper. The equation of state used in these calculations may not be very accurate at $\Gamma /{\Gamma }_{\mathrm{m}}\lesssim 0.1$.