Instability of relativistic electron beam-dielectric system for backward microwave amplification

The linear wave dispersion relation of relativistic electron beam propagating along the negative direction of a constant guiding magnetic field in a slow wave structure has been presented by cold fluid limit. The instability occurs when the velocity of beam electrons exceeds the phase velocity of the wave. The numerical simulations of microwave amplification due to the instability indicate that the maximum interaction efficiency achieves about 16%. The maximum transverse drifting distance of the beam electrons calculated from single particle theory is about 0.02 cm and this result is also verified by Particle-In-Cell simulations