Dispersion function for plasmas with loss-cone distributions in an inhomogeneous magnetic field

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.