Electrostatic waves in dense dusty plasmas with high fugacity

Abstract

Propagation of electrostatic dust modes has been reviewed in the light of the concept of dust fugacity defined by f ≡ 4πnd0 λD2 R, where nd0 and R are the dust number density and the grain size (radius) while the plasma Debye length (λD) is given through λD-2 = λDe-2 + λDi-2. Dusty plasmas are defined to be tenuous, dilute or dense when f ≪ 1, ∼1, or ≫ 1, respectively. Attention is focused on “Dust–Acoustic Waves” (DAWs) and “Dust–Coulomb Waves” (DCWs) which exist in the tenuous (f ≪ 1) and the dense (f ≫ 1) regimes, respectively. A simple physical picture of the DCWs has been proposed in terms of an effective pressure called “Coulomb Pressure defined by PC ≡ nd0qd02/R, where qd0 is the grain charge. In the lowest order, the DCW phase speed is given by ω/k = (PC/ρdδ)1/2, where ρd ≡ nd0md is the dust mass density and δ ≡ ω2/ω1 is the ratio of charging frequencies. Thus, DCWs which are driven by the Coulomb pressure can be considered as the electrostatic analogue of hydromagnetic (Alfvén or magnetoacoustic) modes which are driven by magnetic field pressure. In the dilute regime, the two waves loose their identities and merge into a single mode, which may be called “Dust Charge–Density Wave” (DCDW). When the grains are closest, DCW dispersion relation is identical with that of “Dust–Lattice Waves” (DLWs). Dense dusty plasmas are governed by a new scale-length defined by λR ≡ 1/(4πnd0Rδ)1/2, which characterizes the effective shielding length due to grain collective interactions. The scale-length λR plays a fundamental role in dense dusty plasmas, which is very similar to that of the Debye length λD in the tenuous regime. The two scale-lengths are related to the fugacity through fδ ≡ λD2/λR2. The frequency spectrum as well as the damping rates for various dust modes have been analytically obtained, and compared with the numerical solutions of the kinetic (Vlasov) dispersion relation.