Radiation from a moving bunch of particles with a variable charge

We study the electromagnetic radiation of a charged particle bunch with small size moving at a constant velocity and having a variable charge. The environment medium is considered to be isotropic and homogeneous, and it may have frequency dispersion, but not spatial dispersion. The general solution of the problem is obtained. The main attention is paid to the case when the bunch charge, starting from a certain moment, decreases exponentially with time. The saddle point method is used to obtain the approximate expressions for the field components that are valid in the wave zone. The energy characteristics of the excited spherical wave are studied and compared with the case of a decelerating charge. In the case of excitation of Vavilov–Cherenkov radiation, we obtain the asymptotics which are valid in the entire wave zone, including the region in which the field cannot be divided into the spherical and cylindrical waves.