Dispersion relation of a sheet beam driven backward wave oscillator

Summary form only given, as follows. Backward wave oscillators (BWOs) driven by high current relativistic electron beams produce high power coherent radiations in a wide frequency range. The device consists of a periodic metallic structure into which a high current relativistic electron beam is injected. The slow wave structure reduces the phase velocity of electromagnetic waves below the vacuum speed of light so that Cerenkov synchronism is satisfied. This allows the electrons to give up energy to one of the eigenmodes of the slow wave structure. High power radiation output necessitates high beam power. To obtain this capability without invoking high current density, we propose the use of a sheet or a ribbon electron beam. Such beams are especially suited to stable and well focused transport. We consider a modified version of a relativistic backward wave oscillator whose walls are the two parallel surface of a rectangular waveguide. A sheet beam having thickness t and width w is being injected through the rippled wall waveguide. The dispersion relation of such a configuration is obtained and stability of the system is discussed.