Nonlinear dynamics of electron bunches in the presence of dissipative effects

The transition phase between two nonlinear regimes of electron-beam-wave in teraction depending on the amplitude and the nature of the effective dissip ation is investigated with the help of numerical simulations. Effective dis sipation due to wave escaping to infinity out of the beam-wave interaction region as well as to collisions in the background plasma is considered. If the dissipation is strong enough, the evolution of the electron beam procee ds in a general way, independently of the type of dissipation and of the na ture of the considered waves: structures of strongly concentrated electron bunches are formed. These bunches are not trapped in the wave, and decelera te continuously owing to friction on waves: in the presence of dissipation, the usual quasiperiodic exchange of energy between the wave and the trappe d particles, which prevents the wave from collapsing, does not occur. Consi dering beam interaction with a finite number of waves (modulated wave packe t), it is shown that, if the dissipation is strong enough, the structure of electron bunches is dynamically stable in a range of times exceeding sever al characteristic times of their formation.