Dynamics of electron beam in ion undulator

A dynamics of relativistic high-current electron beam in ion undulator is investigated. The problem of an excitation the electron radial oscillations by eans of ion Coulomb forces is under consideration. Self-consistent fields of electron beam are taken into account by using the long-wavelength stationary approximation. Two different regimes are examined. First one is the short-pulse regime when the ion background may be treated as immobile. In the second, long-pulse, case the dynamics of ions is included in consideration. The main process preventing to the excitation the large-amplitude oscillations is found. It is the phase mixing of particle´s radial oscillations caused by the nonuniform radial forces. The conditions of beams injection are found when practically nondamping vibrations of electron beam occur even in long-pulse regime. This is in the case when an equilibrium injection of the ion beam takes place.