Linear analysis of cyclotron-cherenkov and cherenkov instabilities in dielectric-loaded coaxial waveguides

We present, based on the cold fluid theory, linear analysis of the Cherenkov and cyclotron-Cherenkov instabilities which are driven when a linear electron beam is injected into a dielectric-loaded waveguide immersed in an axial magnetic field. In the analysis we consider azimuthally symmetric TM_0n modes. We derive dispersion relations for three types of waveguide, and compare computationally obtained linear growth rates of both instabilities. For the type A, which consists of a metallic cylinder with dielectric liner on its inner surface, the growth rate of the Cherenkov instability is larger than that of the cyclotron-Cherenkov instability. For the type B, which consists of a dielectric core and an outer metallic cylinder, both growth rates are comparable. And for the type C, which consists of a metallic core with dielectric liner on its surface and an outer metallic cylinder, the growth rate of the latter instability is higher than that of the former instability. Finally, for the type C, obtained are dependences of the oscillation frequency and the growth rates of both instabilities on the following parameters: the beam energy, the beam current, the axial magnetic field, the dielectric constant, and the thickness of the dielectric.