Synchrotron radiation from a charge circulating around a cylinder with negative permittivity

We investigate the radiation from a charged particle rotating around a dielectric cylinder with a negative real part of dielectric permittivity. For the general case of frequency dispersion in dielectric permittivity, expressions are derived for the electric and magnetic fields and for the angular density of the radiation intensity on a given harmonic. Compared with the case of a cylinder with positive real part of the permittivity, new interesting features arise in the nonrelativistic limit and for the radiation at small angles with respect to the cylinder axis. Another feature is the appearance of sharp narrow peaks in the angular density of the radiation intensity for large harmonics. We analytically estimate the height, width and the location of these peaks. The influence of the imaginary part of dielectric permittivity on the characteristics of the peaks is discussed. The analytical results are illustrated by numerical examples. We show that the radiation intensity on a given harmonic, integrated over the angles, can be essentially amplified by the presence of the cylinder.