Waveguide modes in a relativistic electron beam with an axial magnetic field

Dispersion relations (DRs) for the azimuthally symmetric waves in a cylindrical metallic waveguide completely filled with a magnetized relativistic electron beam are investigated within the framework of cold-fluid description. The defocusing effect of self-fields is counteracted by considering a rotating electron beam. Both electrostatic and electromagnetic waves are investigated by a general electromagnetic analysis. As an approximation, waves are separated into transverse magnetic (TM) and transverse electric (TE) waves with the field components taken as the field components of waves in an empty waveguide. The DRs are solved numerically to study the wave-mode properties. The justification for separating the waves into TM and TE modes is presented and errors that are so introduced are given. It is shown that the TE DR gives only one legitimate high frequency electromagnetic TE mode and the other two are not physically acceptable modes.