On universal dispersion of the acoustic modes in dusty plasma

A model of the universal/scale-invariant dispersion of acoustic modes in dusty plasma is presented. It is shown that (a) the acoustic modes exist over the entire range of the dust density 0≤P≤∞ where P is the Havnes parameter, (b) the dispersion properties of the acoustic spectrum are described solely by a few dimensionless quantities, namely, the mass ratio μ=mime mi, me are the masses of ions and electrons, the plasma temperature ratio τ=Te/Ti (Te and Ti are the electron and the ion temperatures, respectively) and P. Thus, the dispersion data from widely diverse dusty plasma sources with similar values of these parameters are expected to fall on unique dispersion curves and can be compared. The conditions for the weak coupling of the dust particles are established. The dispersion properties are studied using two models of dust charging: (i) the model by Havnes et al. applicable to astrophysical scenarios, (ii) the Constant ion density model (CIM) applicable to laboratory dusty plasmas.