Beam instabilities that arise in the compression zone of a gyrotron
oscillator can degrade the beam quality and hence adversely affect the
operating characteristics of the device. This paper investigates a class of space-charge instabilities that are related to unstable Bernstein modes. These are
investigated both by simulations with a 2½-dimensional fully electromagnetic
particle-in-cell code and by solving the linear dispersion equation (obtained
with kinetic theory). Use of the code makes it possible to study effects that
cannot be taken into account in the linear dispersion relation, such as the effect
of static self-fields. The simulation strongly suggests that the instability is
convective. The dependence of growth rate and frequency spectrum on beam
parameters is calculated both with simulation and the analytical method, and
the results show good agreement. A detailed analysis of the electromagnetic
fields calculated in the simulation shows that the unstable waves are not (as has
frequently been assumed in the past) purely electrostatic.