Cherenkov radiation from a relativistic annular electron beam propagating through a dielectric loaded waveguide

Stability properties of the free-streaming mode (space-charge wave) in a relativistic annular electron beam with radius R0 propagating through a dielectric loaded waveguide is investigated, in connection with the Cherenkov radiation. The stability analysis is carried out within the framework of the linearized Vlasov-Maxwell equations for an electron distribution function, in which all electrons have a Lorentzian distribution in the axial canonical momentum. One of the most important features of the analysis is that, for some ranges of physical parameters, a strong mode coupling between the vacuum dielectric waveguide and free streaming modes occurs, exhibiting possibilities of a Cherenkov radiation. The typical maximum growth rate of instability is a few percent of c/R0, where c is the speed of light in vacuo. However, the growth rate and bandwidth of instability are substantially reduced by increasing the axial momentum spread.