On non-linear theory of instability of a mono-energetic electron beam in plasma

Abstract

The excitation of a monochromatic plasma wave by a 'cold' electron beam is investigated. The solution obtained describes the transition from the exponential growth of the wave amplitude in the linear stage to the amplitude oscillations associated with trapping of the beam in the potential well created by the wave. The maximum amplitude and its oscillation period are found. Both non-relativistic and relativistic beams are investigated.