Self-sustained oscillations in spatially confirmed beam-plasma systems

Summary form only given. This paper is dedicated to stable oscillations that, in our opinion, result from finite dimensions of the beam-plasma system. Both longitudinal restriction and finite radius of the beam create disrupted feedback and supply initial beam bunching. The task has been solved for a self-consistent approach. Neither the travelling nor standing wave is postulated. Non-linear integro-differential equations have been formulated for beam bunching. The equations implicitly include the necessary amplitude and phase relations. The condition of solvability of the equations determines the spectrum of frequencies for possible self-excited oscillations and the solutions give the amplitude of beam bunching wave and its spatial dependence. Also the case of oppositely directed beams in a plasma has been analyzed.