On a mechanism of resonance amplification of a slow Langmuir wave in a relativistic electron beam

The interaction of relativistic electron beam (REB) with an electromagnetic wave of finite initial amplitude excited with an external source in a slowing-down structure is considered. Under resonance conditions when external wave parameters satisfy dispersion relation for a slow Langmuir mode, effective amplification of Langmuir mode occurs: amplitude of wave longitudinal electric field in the beam-structure system increases linearly in time and along system axis. Two methods of description of resonance interaction including that making allowance for nonlinear regime are developed. Parameters of this mechanism are evaluated. These estimates indicate that the resonance interaction is a rather effective mechanism for creating a large space modulation of REB density and an electromagnetic wave amplitude higher than 100 kV/cm and a small phase velocity