Small signal gain for crossed-field devices

Summary form only given. The stimulated microwave emission from electrons undergoing E/sub Ospl times/B/sub O/ motion inside slow wave cavities (magnetrons, crossed field amplifiers) is analyzed. A guiding center approach is applied to single mode evolution in cross-field devices. The cyclotron motion contribution to the instability ensemble averages to zero to all orders in Larmor radius if relativistic bunching effects are negligible. The small signal gain is found by expansion in powers of the RF amplitude. It is found that (i) the lowest order contribution comes from the self-field of the rippled beam and is independent of the detuning between the phase and the drift velocity (ii) higher order contributions, due to the bunching of the GC orbits in space and the modifications of the RF profile from the vacuum profile, are symmetric relative to resonance, and (iii) the growth rate goes over to the diocotron growth when all the impedance comes from the rippled beam (i.e., smooth anode at infinite distance). The theory thus explains the experimentally observed symmetric growth relative to the detuning.