A kinetic approach to the problem of wave propagation in dusty plasmas, which takes into account the variation of the charge of the dust particles due to inelastic collisions with electrons and ions, is utilized as a starting point for the development of a new formulation, which writes the components of the dielectric tensor in terms of a finite and an infinite series, containing all effects of harmonics and Larmor radius. The formulation is quite general and valid for the whole range of frequencies above the plasma frequency of the dust particles, which were assumed motionless. The formulation is employed to the study of electrostatic waves propagating along the direction of the ambient magnetic field, in the case for which ions and electrons are described by Maxwellian distributions. The results obtained in a numerical analysis corroborate previous analysis, about the important role played by the inelastic collisions between electrons and ions and the dust particles, particularly on the imaginary part of the dispersion relation. The numerical analysis also show that additional terms in the components of the dielectric tensor, which are entirely due these inelastic collisions, play a very minor role in the case of electrostatic waves, under the conditions considered in the present analysis.

A kinetic formulation developed to analyze wave propagation in dusty plasmas, which takes into account the variation of the charge of the dust particles due to inelastic collisions with electrons and ions, is utilized to study the propagation and damping of electrostatic waves with wave number exactly parallel to the external magnetic field and Maxwellian distributions for the electrons and ions in the equilibrium. It is shown that, due to the presence of the dust, the damping of Langmuir waves in the region of large wavelengths is increased as compared to conventional Landau damping. Langmuir waves in the occurrence of collisional charging of dust particles also feature weak damping for small wavelengths, which vanishes if the effect of collisional charging of the dust particles is neglected in the dispersion relation. It is also shown that the damping of ion-acoustic waves is modified by the presence of the dust, and that some damping effect due to the dust particles remains even if the effect of collisional charging of dust particles is neglected in the dispersion relation.

The preservation of Onsager symmetry for the effective dielectric tensor is discussed for a homogeneous plasma immersed in a inhomogeneous magnetic field, using the unperturbed orbits correct up to order kB, which is the scalelength of the field inhomogeneity. General features of the calculation of the components of the tensor are discussed and detailed calculations are developed for the zz component, which is shown to satisfy the conditions for Onsager symmetry, in agreement with previous results obtained using less precise expressions for the unperturbed orbits.

We compare and discuss several approximations to the dispersion relation for electrostatic waves in inhomogeneous plasmas, either obtained directly from Poisson's equation, or from the dielectric constant obtained using a dielectric tensor derived using the plane wave approximation, or from the dielectric constant derived using the effective dielectric tensor.

We present a detailed derivation of the effective dielectric constant to be used in the dispersion relation for electrostatic waves in the case of a plasma immersed in a inhomogeneous magnetic field, with inhomogeneity perpendicular to the direction of the magnetic field.

The procedures used to obtain general expressions for the components of the effective dielectric tensor for electromagnetic waves in inhomogeneous magnetized plasmas are briefly reviewed, and the relationship between these expressions and their counterparts which can be obtained assuming electrostatic fluctuations is discussed. It is argued that a general formulation formerly available in the literature, which do not satisfy Onsager symmetry in the case of electrostatic fluctuations, is not the suitable form for description of dielectric properties in the electrostatic case, which require a dielectric constant. A general expression for an effective dielectric constant is therefore provided, obtained from the effective dielectric tensor, which satisfy Onsager symmetry.