Nonsingular linear theory for stimulated microwave emission in crossed-field devices

Abstract

The small signal stability of crossed‐field devices fed by a thin electron beam is analyzed. The situation differs from diocotron modes in that the interaction cavity supports slow wave eigenmodes in vacuum. The rippling of the beam causes a modification of the vacuum dispersion relation and mode profiles. The growth rate is found by equating the rate of change of the power flux with the fast scale averaged wave–particle energy exchange rate. The radio frequency (rf) power flow including the energy circulating in the anode structure is related to the wave amplitude via the interaction impedance. The singularities at resonance, the trademark of any linear theory, are avoided by following the particle guiding center (GC) orbits in reference frame with the wave synchronous. The small signal gain is found by expansion in powers of the rf amplitude. A finite linear growth results, even for symmetric particle excursions, due to the self‐field of the rippled beam. Near resonance the growth rate is independent of...