Study on the longitudinal instability of relativistic electron rings

The work is an extension of a series of works devoted to the study of longitudinal instability of electron rings injected into resonator prior to injecting into the accelerating system. The numerical simulation method is used to study the possibility of nonlinear stabilization of the ring. The plots present the calculated characteristics and parameters of the beam and their variations as functions of the beam impedance and the resonator quality. The main conclusion of the study are: in some cases the results of the numerical examination of the electron ring instability in resonator in terms of the thin ring model agree with experiment; a better agreement may be obtained if a greater number of harmonics (in particular incoherent harmonics) and the ''resonance motion'' effect are taken into account