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The linear dispersion relation of backward wave oscillators (BWOs) with finite strength axial magnetic field is derived and calculated numerically. Axisymmetric mode radiation in a slow wave structure (SWS) with corrugated metal wall including a column of relativistic electron beam streaming along the lines of a finite strength axial magnetic field is analyzed. Three theoretical achievements [viz. 1) the dielectric tensor derived by Bogdankevich et al., 2) the formulation of EM waves in the beam column that are expressed as a linear combination of extraordinary and ordinary modes elucidated by Antonsen et al., and 3) a consideration of boundary conditions in the beam-SWS system initiated by Swegle et al. ] are combined in our numerical code to be exact and universal under the scope of linear treatment. Our dispersion relation can include effects of interaction between a structure mode and electron cyclotron modes in addition to conventional beam space charge modes. Numerical analysis is carried out using the parameters of a BWO experiment at the University of Maryland. The results show the well-known cyclotron absorption of radiation from the BWO at a particular value of magnetic field that was previously analyzed in various ways different from ours.Index Terms-Absolute instability, backward-wave oscillators (BWOs), dielectric tensor, electron cyclotron mode, high-power microwave, slow-wave structure (SWS).

A unified linear dispersion relation that describes both slow-and fast-wave devices excited by a constrained large gyration orbit (LO) monoenergetic electron beam of infinitely small thickness has been derived and studied numerically. Beam electrons in a sufficiently long sinusoidally corrugated metal slow-wave structure are assumed completely neutralized by the background ions in equilibrium state. An exact dispersion relation of an LO backward-wave oscillator that can reasonably describe instabilities in the slow-wave device region has been obtained. A parameter , defined as a ratio of the transverse to the longitudinal component of the electron velocity, is found to have a critical value above which the excitation of a nonaxisymmetric quasi-TE 11 mode caused by the fast cyclotron instability dominates the conventional Cherenkov instability. However, for an SWS having infinitely small amplitude of corrugation, radiation with in the fast-wave device region is obtained. Here, and are, respectively, microwave angular frequency and relativistic electron cyclotron frequency. The conventional cyclotron resonance maser (CRM) instability with is altogether suppressed; instead, an alternate mechanism, namely, Cherenkov instability in the azimuthal direction with found first in the current paper leads to the excitation of microwaves. This suggests that the radiation from some previous CRM experiments with a high current density electron beam neutralized by ions might have been caused not by CRM instability but by the present Cherenkov instability in the azimuthal direction.Index Terms-Backward-wave oscillator (BWO), Cherenkov instability, cyclotron maser instability, cyclotron resonance maser, fast-wave devices, gyrotron, high-power microwaves, slow-wave devices.

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