“…Coherence of the generated radiation arises due to bunching of electrons in phase with respect to the electromagnetic wave. For values of the beam and waveguide parameters relevant to this experiment, the force exerted on the electrons by the waveguide mode was dominated by the resonant space-charge force, so the maser operated in a Raman-type regime, with strongest amplification of the waveguide mode expected when it was resonant with the slow space-charge wave of the beam, i.e., when the angular frequency and the axial wavenumber of the waveguide mode satisfy (1) where is the axial electron velocity, is the relativistic factor, is the plasma frequency, is the electron density, , is the relative velocity, is the total electron velocity, is the speed of light, and and are the electronic charge and rest mass, respectively. and must also, of course, satisfy the characteristic equation for a dielectric-lined cylindrical waveguide, which for a mode is as in [7].…”