Effect of finite V⊥ on Cerenkov FEL in adielectric loaded waveguide

Allowance for finite V_⊥ of an annular electron beam propagating through a dielectric-loaded waveguide immersed in an axial magnetic field opens up the possibility of excitation of TE modes. The interaction is observed using Cerenkov and cyclotron resonances. On approximating the field distribution at the electron orbits to some suitable form, an analytical solution to the Vlasov equation is obtained, leading to a comprehensive dispersion relation for azimuthally symmetric TE_0n modes. In the special case where all the guiding centres lie on the axis, a fluid treatment for the arbitrary azimuthal-mode number is applicable. In these cases the growth rate increases with V_⊥