  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.
