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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. (1981), (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. (1985) 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.