Cherenkov radiation generated by an electron bunch in a rectangular dielectric waveguide filled with a transversely isotropic medium

Dielectric waveguides are being intensively studied as accelerating structures excited by an electron bunch. Rectangular dielectric structures are used both to test the principles of new accelerating schemes and to study the electric properties of filling materials. Several dielectric materials used as fillers of waveguides have anisotropic properties (sapphire, ceramic films). Anisotropy can have a significant effect on the wakefields generated by an electron bunch in a structure. The paper presents an analytical calculation of Vavilov–Cherenkov radiation generated by a relativistic electron bunch in a rectangular waveguide filled with a transversely inhomogeneous transversely isotropic dielectric. A method for constructing an orthogonal basis of the transverse operator with its subsequent use to find the wakefield is presented. A dispersion relation for the structure and expressions for the wakefield created by a point electron bunch in a transversely isotropic rectangular dielectric structure are obtained. Based on the formalism presented, parameters of an accelerating structure based on sapphire, allowing the generation of fields above 100 MV/m, are calculated.