Collective and single-particle Cherenkov effects in a spatially bounded system near the nontransparency band

Abstract

Using the linear approximation, we consider beam instabilities like a collective and a singleparticle stimulated Cherenkov effect developing in a longitudinally bounded electrodynamic system near its nontransparency band, i.e., when the electromagnetic wave excited by the beam has a zero group velocity. A dispersion equation is obtained which determines instability development increments with allowance for the exit of the radiation from the electrodynamic system. Solutions to the dispersion equation for various parameters of the electron beam and the electrodynamic system are investigated.