Unsteady processes during stimulated emission from a relativistic electron beam in a quasi-longitudinal electrostatic pump field

The problem of stimulated emission from a relativistic electron beam in an external electrostatic pump field is studied. A set of nonlinear time-dependent equations for the spatiotemporal dynamics of the undulator radiation amplitude and the amplitude of the beam space charge field is derived. The beam electrons are described by a modified version of the macroparticle method. The regimes of the single-particle and collective Cherenkov effects during convective and absolute instabilities are considered. The nonlinear dynamics of radiation pulses emitted during the instabilities of the beam in its interaction with the forward and backward electromagnetic waves is investigated.