Kinetic Theory of a Nonlinear Interaction Noindent Ultrarelativistic Electron Beam with Plasma

The nonlinear interaction of the ultrarelativistic electron beam with cold fixed in magnetic field plasma is investigated analytically and numerically (particle technique). The dependence of the field energy density in plasma is found. In contrast to 'slightly relativistic' (nonrelativistic) beam, when the beam-wave resonance is destroying by means of acceleration or deceleration individual electrons, ultra- relativistic increase in the mass suppresses velocity diffusion and the instability is stabilized by plasma nonlinearity (by decrease of plasma wave velocity).