Saddle point analysis of a high power backward wave oscillator near cyclotron absorption

Summary form only given. The absolute and convective instabilities of high power backward wave oscillator (BWO) driven by an intense relativistic electron beam are analyzed through saddle point analysis assuming finite strength axial magnetic field within the scope of linear analysis. Using a dielectric tensor including the effect of finite strength magnetic field, we formulate and analyze numerically the dispersion relation of the TM(01) mode in a BWO with infinitely long slow wave structure and columnar electron beam on the axis. To identify the root corresponding to BWO operation among various roots in the relation, we reduce the imaginary part of frequency from a large positive value (initial state) to zero (steady state) keeping the real part unchanged; the loci of the roots are depicted on the complex wavenumber plane. If the locus crosses the real axis, the root corresponds to a convective instability, while if the root merges with another root before it reaches the steady state, the double roots (saddle point) correspond to an absolute instability, as found in a BWO. We assume the parameters in the previous experiments at the University of Maryland. We calculate the loci of roots for the condition near cyclotron absorption. As an example, near a magnetic field of 1.02 T, the absolute instability disappears and the root becomes a convective instability for a range of magnetic field. The cessation of backward wave oscillations near cyclotron absorption was observed in the experiments and can be explained by the present analysis. In the dielectric tensor in our analysis, perpendicular component can be included in addition to the parallel component of the beam velocity. No enhancement in spatial nor temporal growth rates of the TM(01) mode is obtained with increase in perpendicular velocity component for a given beam energy.