The small-signal theory of the cyclotron maser and other gyrotron-type devices

The simplified cyclotron maser model presented by Lau (ibid., vol.ED-29, p.320-35, 1982) is analyzed under small-signal conditions with an exact analytical solution to the proper boundary condition taken across a thin, hollow rotating beam. Not only is the transverse electric field discontinuous but so are the axial and radial magnetic field components. The simultaneous presence of TE and TM modes are considered, leading to modifications in the dispersion relationships. The simultaneous inclusion of both modes and space charge leads to the main contribution to the theory: TE-TM coupling, off-resonance behavior, and subcutoff operation in the drift spaces of klystron-type devices. Also, since radial displacement of the beam is taken into account, the theory predicts a peniotron interaction in the cyclotron maser. Examples are presented of gyrotron or peniotron interactions in either the TE and TM modes as well as off-resonance and subcutoff