Neglecting collisions, we have found an operator for the dielectric permeability tensor of a rarified, inhomogeneous plasma in a magnetic field. The initial set of equations consists of kinetic equations with a self-consistent field for electrons and ions, and Maxwell's equations for an electromagnetic field. Neglecting magnetic-field inhomogeneity, the unperturbed distribution function is chosen as a product of Maxwell's function and the arbitrary function from the position of the center of the Larmor circle described by a particle in a plane perpendicular to the magnetic field. In contrast to the usual setup of the problem, no limitation is imposed on the smallness of unperturbed density gradients, so that the characteristic dimension of inhomogeneity can be compared to the Larmor radii of the particles. The equations obtained for electromagnetic wave distribution in inhomogeneous plasma represent a system of integral equations for the Fourier components of the electric field. These equations are investigated in simple cases. Both an ordinary wave propagating across a magnetic field, and potential perturbations have been examined.
Plasma permittivity of weakly ionized inhomogeneous magnetized plasmas