Evolution of the Langmuir Solitary Pulses in a Nonlinear Plasma with a Kinetic REB

The instability of a modulated ultrarelativistic electron beam in a dense plasma is investigated under conditions when the phase oscillations in the beam are suppressed by the relativistic increase of the electron mass, and the nonlinear mechanism of saturation of the oscillation amplitude can be described by the dependence of the plasma permittivity on the field amplitude. It is shown that external modulation of the beam may be an efficient mean of controlling the instability process and impedes the transition of the system to a turbulent regime as for a certain relation between the modulation frequency and Langmuir frequency the field energy can return to the beam. The unsynchronism of the electrons oscillation leads to irreversible heating of the beam so that a kinetic solutions deviates from a hydrodynamic solitary pulse type solutions. However the solutions, closed to solution solutions, are existing in the approximate limit of the ultrarelativistic energies.