This paper describes an analytical approach to consideration of the tradeof
f between the gain and the bandwidth in gyroklystrons and gyrotwystrons wit
h stagger-tuned cavities, This approach is based on the "point-gap" model,
in which short cavities are responsible for electron energy modulation only
, while orbital phase bunching caused by this modulation proceeds in long d
rift sections. The paper contains a review of results of the analysis of st
agger-tuned gyroklystrons and gyrotwystrons obtained previously. It also in
cludes new results of the study of gyroklystrons in which different cavitie
s operate at different cyclotron harmonics.