Radiation instability of a relativistic electron beam moving in a split resonator

In this paper, we considered the radiation instability in a split asymmetric resonator for the relativistic case assuming the space charge of the beam. In the small-signal approximation,  expressions for the energy loss by a particle passing through the resonator and for the beam current modulation are obtained. Based on analytical and numerical calculations, it is shown that the symmetric configuration provides the highest growth rate of instability. It is found that with the increase of the initial electron energy, the modulation of the beam current as well as the efficiency of the energy transfer from particles to the electromagnetic field decrease. The increase of the beam density has a positive effect on the radiation instability. The results obtained have to be taken into account when developing generators of electromagnetic radiation or a system for modulating the beam current based on a split resonator.