Linear dispersion relation of backward-wave oscillators with finite-strength axial magnetic field

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.