Electromagnetic processes associated with a charged particle moving in a strong circular magnetic field is considered in cylindrical coordinates. We investigate the relation between the vacuum curvature emission and Cherenkov emission and argue, that for the superluminal motion of a particle in the inhomogeneous magnetic field in a dielectric, the combined effects of magnetic field inhomogeneity and presence of a medium give rise to the synergetic Cherenkov-curvature emission process. We find the conditions when the operator relations between electric field and electric displacement in cylindrical coordinates may be approximated by algebraic relations. For nonresonant electromagnetic wave the interaction with particles streaming along the curved magnetic field may be described in the WKB approximation. For the resonant waves interacting with superluminal particles we find a particular case of plane-wave-like approximation. This allows a fairly simple calculation of the dielectric tensor of a plasma in a weakly inhomogenous magnetic field. We find in this approximation the polarization of normal modes in the plasma, Cherenkov-curvature and Cherenkov-drift emissivities and growth rates.

31 Pages, 5 Figures