Dust-Coulomb and dust-acoustic wave propagation in dense dusty plasmas with high fugacity

Abstract

A detailed investigation of electrostatic dust wave modes in unmagnetized dusty plasmas consisting of electrons, ions and dust grains has been carried out over a wide range of dust fugacity and wave frequency by using fluid as well as kinetic (Vlasov) theories. The dust fugacity parameter is defined by f≡4πnd0λD2R∼ND R/λD where nd0, λD and R are respectively the dust number density, the plasma Debye length and the grain size (radius), and ND=4πnd0λD3/3 is the dust plasma parameter. Dusty plasmas are considered to be tenuous, dilute or dense according as f≪1, ∼1, or ≫1. In particular, attention is focused on the “dust–acoustic waves” (DAWs) and the “dust–Coulomb waves” (DCWs) which exist in the tenuous (low fugacity) and the dense (high fugacity) regimes, respectively, when the wave frequency is much smaller than the grain charging frequency. Unlike the DAWs, which exist even with constant grain charge, the DCWs [N. N. Rao, Phys. Plasmas 6, 4414 (1999)] are the normal modes associated with grain charge fluctuations, and exist in dense dusty plasmas. In the long wavelength limit, the DCW phase speed scales as ∼CDA/f where CDA is the DAW phase speed. In the dilute (medium fugacity) regime, the two modes merge into a single mode, which may be called the “dust charge–density wave” (DCDW) since the latter involves contributions arising from both the DAW and the DCW. On the other hand, for frequencies much larger than the charging frequency, DAWs are shown to exist also in the dilute regime. The real frequency as well as the damping rate in each case are explicitly calculated from both the fluid as well the kinetic theories, and a comparison between the two has been carried out. In the allowed fugacity regimes (tenuous, dilute or dense), all the three waves are weakly damped and, hence, can propagate as normal modes. The present analysis of wave propagation in dusty plasmas over different fugacity regimes suggests the introduction of a new length scale defined by λR≡dWSdWS/3Rδ, where dWS is the Wigner–Seitz radius and δ is a parameter related to the charging frequencies. This length scale which governs the dispersive properties of the DCW modes is most useful in the dense regime, and plays a role which is very similar to that of the Debye length in the tenuous regime. The ratio of λR to λD is a measure of the dust fugacity, and is given through fδ=λD2/λR2. The very recent experimental observation [S. Nunomura et al., Phys. Rev. Lett. 83, 1970 (1999)] on a self-excited instability associated with grain charge fluctuations may be an indication of DCWs in the strong coupling regime. The possibility of the existence of a dust thermal wave (DTW) in the super-dense regime has been pointed out. A heuristic, but simple, derivation of DCWs based on grain dynamics but supplemented by physical inputs from the plasma response has also been presented.