Electrostatic modes in dense dusty plasmas with high fugacity: Numerical results

Abstract

The existence of ultra low-frequency wave modes in dusty plasmas has been investigated over a wide range of dust fugacity [defined by f≡4πnd0λD2R, where nd0 is the dust number density, λD is the plasma Debye length, and R is the grain size (radius)] and the grain charging frequency (ω1) by numerically solving the dispersion relation obtained from the kinetic (Vlasov) theory. A detailed comparison between the numerical and the analytical results applicable for the tenuous (low fugacity, f≪1), the dilute (medium fugacity, f∼1), and the dense (high fugacity, f≫1) regimes has been carried out. In the long wavelength limit and for frequencies ω≪ω1, the dispersion curves obtained from the numerical solutions of the real as well as the complex (kinetic) dispersion relations agree, both qualitatively and quantitatively, with the analytical expressions derived from the fluid and the kinetic theories, and are thus identified with the ultra low-frequency electrostatic dust modes, namely, the dust-acoustic wave (DAW), the dust charge-density wave (DCDW) and the dust-Coulomb wave (DCW) discussed earlier [N. N. Rao, Phys. Plasmas 6, 4414 (1999); 7, 795 (2000)]. In particular, the analytical scaling between the phase speeds of the DCWs and the DAWs predicted from theoretical considerations, namely, (ω/k)DCW=(ω/k)DAW/fδ (where δ is the ratio of the charging frequencies) is in excellent agreement with the numerical results. A simple physical picture of the DCWs has been proposed by defining an effective pressure called “Coulomb pressure” as PC≡nd0qd02/R, where qd0 is the grain surface charge. Accordingly, the DCW dispersion relation is given, in the lowest order, by (ω/k)DCW=PC/ρdδ, where ρd≡nd0md is the dust mass density. Thus, the DCWs which are driven by the Coulomb pressure can be considered as the electrostatic analogue of the hydromagnetic (Alfvén or magnetoacoustic) waves which are driven by the magnetic field pressure. For the frequency regime ω≫ω1, the numerical results confirm the existence of only the DAWs, while the DCWs are absent as predicted by the fluid and the kinetic theories. The wave damping rates due to the charge fluctuations as well as the wave–particle interactions (Landau type) have been numerically computed and compared with the analytical results. For the tenuous as well as the dilute regimes, there is good agreement between the numerical and the analytical results at small wave numbers. However, at larger wave numbers and for the dense regime, the damping rates are underestimated by the theoretical expressions obtained under suitable approximations. Some comments on the sources for these differences have also been presented.