The dispersion relation for electromagnetic waves in a magnetized plasma with weakly inhomogeneous magnetic field is investigated within the framework of a WKB approximation. A dispersion function useful for the case of plasma particles described by a generalized loss-cone distribution is introduced, valid for waves propagating in weakly relativistic plasmas, for any direction relative to the ambient magnetic field and to the inhomogeneity. This dispersion function is in some particular cases related to other plasma dispersion functions well known from the study of homogeneous plasmas. An application is made for the case of ordinary mode waves propagating perpendicularly to the magnetic field in inhomogeneous loss-cone plasmas.

We investigate the dispersion relation for a magnetized plasma with weak magnetic Geld gradients perpendicular to the ambient magnetic Geld. An explicit expression for the efFective dielectric tensor is derived, incorporating the relevant contributions due to the inhomogeneity, which include corrections to all orders in the small parameter e, where e = K1/Bs)(dBO/dz)]. It is shown that this effective dielectric tensor satisGes the required symmetry conditions and is the tensor which should be utilized in the dispersion relation, in order to describe correctly wave-particle interactions in media with inhomogeneous magnetic field. The case of high frequency oscillations propagating perpendicularly to the magnetic field in a Maxwellian plasma is considered as an example and the effect of inhomogeneities in the magnetic Geld upon the absorption coefIicient and the optical depth of ordinary mode waves is discussed. A region of negative absorption coefBcient is predicted near the electron cyclotron frequency for sufficiently high inhomogeneity. Moreover, it is shown that significant difFerences may exist between the absorption coeKcient evaluated with the present formulation and results from other approaches found in the literature which do not exhibit correct symmetry properties.

In this work, we make use of a Hamiltonian formalism to analyze the wave-particle dynamical interaction that takes place in cyclotronic systems. It is shown that the usual model of test particles moving in externally given wave 6elds is good only when the amplitude of the radiation is large enough; otherwise, wave dynamics must be considered and the dynamics mentioned undergoes some considerable changes. In this regard, the appearance of new Axed points and the saturation of the autoresonance process are both analyzed as functions of the dispersion relation of the laser field.

We present results obtained in recent years for wave propagation in a magnetized dusty plasma, including variable charge of the dust particles, and using a kinetic approach. Two forms of the dielectric tensor are obtained, which can be used depending on the application to be done. This dielectric tensor is used in some applications, in order to study the importance and influence of the variable charge on dust particles in the wave propagation characteristics. We first consider the magnetosonic wave and show that the variable charge of the dust gives the possibility of absorption. We also analyze the spatial absorption of this wave, including effects up to second order in the Larmor radius. Finally, we analyze Alfvén waves behavior in such dusty plasmas. The dispersion relation and damping rates of this mode are obtained.Index Terms-Alfvén waves, kinetic theory, magnetized dusty plasmas, variable dust charge, wave propagation.

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.