Nonlinear stabilization of beam plasma interactions by parametric effects

The nonlinear stabilization of the kinetic stage of electron beam plasma instabilities by parametric effects is investigated. It is found that within a definite range of plasma parameters parametric instatilities induced by the beam generated waves can stabilize the system at a level of wave energy density substantially lower than expected by quasi-linear theory. This occurs because at a certain level of beam-generated plasma waves, the transfer rate of wave energy outside the spectral region in resonance with the beam exceeds the beam plasma instability growth rate. A model of a quasi-steady state for the case of continuous beam injection is proposed. The possibility of utilizing ultrarelativistic electron beams for achieving ignition temperatures in a tokamak is discussed.