Nonlinear theory for the excitation of monochromatic waves in a dielectric medium by an unmagnetized relativistic electron beam

In an analysis of the nonlinear interaction of an unmagnetized, relativistic, monoenergetic electron beam with a transparent medium having a dielectric constant epsilon/sub 0/(..omega..) it is shown that, if the waves excited by the beam are almost purely electrostaic (this is the case if epsilon/sub 0/(..omega..) less than 1 for all frequencies), the amplitude saturation results from trapping of beam electrons in the potential field of the wave. If, on the other hand, the wave excited by the beam is almost purely electromagnetic (this is the case if epsilon/sub 0/(..omega..) greater than 1 and if there is spatial modulation of the beam) the amplitude increase is limited by deceleration of the beam electrons by the transverse field of the excited wave. These conditions are used to find the amplitudes of the steady-state waves and the efficiency at which beam energy is transferred to the waves.