Relativistic free-electron wave generator with finite axial magnetic field

An analysis of the parametric excitation of fast and slow space‐charge waves in a cylindrical metallic waveguide filled with relativistic beam electrons is presented. The pump wave in the laboratory reference frame consists of a static, spatially periodic axial electric field. Formulas are derived for the temporal growth rate and frequency of the backscattered fast space‐charge wave in both the laboratory and beam frames. The effects of a uniform axial magnetic field of arbitrary magnitude on the amplitude gain and frequency enhancement are studied.