Linear dispersion relation of a beam loaded slow wave structure in finite strength axial magnetic fields

Summary form only given. A linear dispersion relation of beam loaded slow wave structure (SWS) with finite strength guiding axial magnetic field is derived and analyzed numerically. In most theoretical analyses of high power backward wave oscillators (BWO´s), the axial magnetic field to guide electron beam in the SWS has been assumed to be infinitely large. In the present paper, we derive an exact linear dispersion relation for a finite magnetic field in which space charge modes, cyclotron modes and the structure modes can interact resonantly. We consider an axisymmetric mode in an infinitely long SWS with sinusoidally corrugated metal wall in the axial direction. A solid cylindrical beam is present on the axis. The dielectric tensor in the beam region has 9 non-zero components. Coupled ordinary and extra-ordinary modes must exist to satisfy boundary conditions at the beam and metal surfaces. We assume practical size and beam parameters that have been studied in the University of Maryland and Niigata University.