Density and energy modulations of a gyrotron electron beam in a periodically corrugated beam channel

The equilibrium distribution of an electron beam, under the action of its self and image fields is studied in a periodically corrugated beam channel with dielectric lining of the indentations. The Poisson and beam equations are solved selfconsistently in terms of the Fourier components of the electrostatic potential and the beam density and velocity. The system is solved numerically, to give the amplitude of the density and the energy modulations for each harmonic. It is found that the relative amplitudes of the dominant first harmonic of the potential/density modulations exhibit their maximum/minimum value at low currents and the inverse at currents approaching the limiting current. The results are extended to a weakly non-uniform system, to assess the behaviour in a gyrotron beam channel.