Interaction of a high-current relativistic electron beam with the higher modes of a dielectric waveguide

The Cerenkov instability is studied for a relativistic electron beam passing at a finite distance from a dielectric layer on a metal substrate. A comparative analysis is made of the growth of the instability at the fundamental and higher modes of the electrodynamic system. The instability growth rates and instability bands for different modes are studied as a function of the electron energy and the surface charge density of the beam. It is demonstrated that the frequency corresponding to the maximum growth rate in the instability spectrum increases with increasing electron energy, and it is found that at high beam densities the transition to higher modes occurs at higher energies. It is shown that a relativistic microwave generator with a higher working mode has a larger output power and a narrower radiation band in comparison with a slightly relativistic device working at the fundamental