Non-linear theory of Cherenkov excitation of a plasma by a modulated charged-particle beam

The authors consider the non-linear problem of the excitation of a plasma resonator by the Cherenkov emission of a density-modulated, injected beam of charged particles. It is assumed that the beam current and the resonator length are small and that the particle energy is large, so that the transit time is small compared with the characteristic field rise time. The modulation frequency is assumed to be equal to one of the natural frequencie s of the resonator. The main non-linear effect is considered to be the reciprocal influence of the excited field on the motion of the beam particles; the plasma is assumed to be linear. The authors derive two non-linear equations of first order which determine in this approximation the time-dependence of the amplitude and phase of the field in the resonator.The maximum field amplitude and the corresponding phase value are found, and estimates are made of the pulse duration necessary to reach the maximum and of the average beam particle energy losses per pulse.