  The radiation instability in a split-cavity asymmetric resonator is
considered for the relativistic case. The space charge of an electron beam is
taken into account. In the small-signal approximation, the energy loss by
particles passing through the resonator and the modulation of beam current are
investigated. Based on analytical and numerical calculations, it is shown that
the symmetric configuration of a split-cavity resonator provides the highest
rate of instability growth. It is shown that the beam modulation and the
efficiency of energy transfer from particles to electromagnetic field decrease
with the increase in the initial electron energy. The increase in beam density
has a positive effect on the radiation instability growth. It is important to
take into account the obtained results when developing generators of
electromagnetic radiation and systems for modulating the beam current based on
a split-cavity resonator.
