Interaction between an electron beam of periodically varying diameter and EM waves in a cylindrical guide

A simple theory is presented of forward and backward wave interaction between a fast wave in a guide and an electron beam injected into a magnetic field and rippling at the cyclotron frequency. Experiments on a tube at Q band seem to confirm the theory but show that there are other effects as well. An RF output of 36 kW in the forward wave mode indicates a possible traveling wave amplifier at millimeter wavelengths.