Electromagnetic processes associated with a charged particle moving in a st
rong circular magnetic field are considered in cylindrical coordinates. We
investigate the relation between the vacuum curvature emission and Cherenko
v emission and argue that, for the superluminal motion of a particle in the
inhomogeneous magnetic field in a dielectric, the combined effects of magn
etic field inhomogeneity and the presence of a medium give rise to the syne
rgetic Cherenkov-curvature emission process. We find the conditions under w
hich the operator relations between electric field and electric displacemen
t in cylindrical coordinates may be approximated by algebraic relations. Fo
r nonresonant electromagnetic waves, the interaction with particles streami
ng along the curved magnetic field may be described in the WKB approximatio
n. For resonant waves interacting with superluminal particles we use a plan
e-wave approximation to compute the local dielectric tensor of a plasma in
a weakly inhomogeneous magnetic field. We find in this approximation the po
larization of normal modes in the plasma, Cherenkov-curvature and Cherenkov
-drift emissivities and growth rates.