Induced fields effect on the stability of the electron beam coherent oscillations in a linear accelerator

Influence of the induced electric and magnetic fields upon the lateral motion of the beam undergoing the coherent oscillations in a channel with longitudinal magnetic field is considered. It is shown that the presence of conducting surfaces surrounding the beam causes not only the coherent oscillation frequency shift but also the existance of a finite stability region. It is also shown that the bound lateral oscillation region decreases, going to a point, with the energy increases, if the induction of charges and currents takes place at surfaces of different radii. The magnetic field strength energy dependence is found with which small oscillations do not grow in the acceleration process. It is shown that if the fields are induced on the same surface, then the stability region increases and the small oscillation amplitudes decreases going in the limit to a constant value