The sinusoid as the longitudinal profile in backward-wave oscillators of large cross sectional area

High-power generation in backward-wave oscillators (BWO) of large section requires that the beam electrons flowing close to the corrugated wall interact efficiently with surface waves supported by a periodic structure. Such waves are described by the superposition of slow-wave space harmonics of the operating mode. The present paper reports on design tools for BWOs operating in symmetric TM modes since these modes are able to perturb the axial velocity and electron density on rectilinear beams confined by an external magnetic field in slow-wave systems. Here we investigate whether a cylindrical guide with sinusoidally rippled wall can provide strong coupling between the guide surface waves and mildly relativistic (~ 500 keV) electron beams in the 8-9 GHz frequency range for BWOs of large diameter (D ~ 3lambda). For this purpose, the characteristic equation of a sinusoidally corrugated structure is derived on the basis of the Rayleigh-Fourier method, whereby the field solution is represented by a single expansion of TM eigenmodes. From the dispersion diagrams thus obtained we infer the appropriate periodic length and ripple amplitude of the guiding structure that optimize the beam-wave interaction