Influence of magnetic focusing fields and transverse electron motion on starting conditions for spurious oscillations in 0-type backward-wave oscillators

The ratio of the starting current for the first spurious mode of oscillation, in 0-type backward-wave oscillators, to the starting current for the main oscillation has been computed, taking into account the magnetic fields used for beam focusing as well as the transverse components of RF circuit fields. The results show an appreciable influence of both parameters on this ratio and partially explain the suppression of spurious outputs in backward-wave oscillators which can be achieved by deliberate misalignment of the tube in the magnetic field. For higher losses uniformly distributed over the RF circuit length, the ratio I´s/I´odecreases; i.e., the tendency toward spurious oscillations increases. This effect may be understood from the coupled-mode theory, since for higher losses the interaction between the circuit wave and the slow space-charge wave decreases much more rapidly for the main mode than for the spurious one.