Dispersion and interaction of waveguide modes in a relativistic electron beam with ion-channel guiding

A theory for the high-frequency eigenmodes of a cylindrical metallic waveguide partially filled with a relativistic electron beam and guided by an ion channel is presented. Equations that permit calculation of dispersion curves for five families of wave modes are derived. The dependence of the frequencies and the dispersion curves of azimuthally asymmetric modes on the ratio of the beam radius a to the waveguide radius R are studied in detail. The coupling of the dispersion curves of different modes is studied and illustrated for the partially filled waveguide. It was found that, in their course of interaction, HE modes cannot displace the betatron modes in a completely filled waveguide, which is different from the case of a magnetized electron beam. Physical and analytical explanations are presented for this difference.