<title>Field dynamics under overlimiting electron beam instability development in microwave sources</title>

Abstract

The evolution of initial perturbations in a plasma-filled system with a high current relativistic electron beam is considered. The beam current is assumed to be comparable or higher than the limiting vacuum current. The approach is based on equation for slowly varying amplitude of the induced waveform, which enable us to separate out the most intrinsic peculiarities of the overlimiting electron beam instabilities. An equation for slowly varying amplitude is derived and solved. An analytical expression describing space structure and development dynamics of the fields is obtained and analyzed. The well-known maximal growth rate of beam instability is actually the growth rate in the peak of induced wave train. Results are valid both for instability due to aperiodic modulation of the beam density in medium with negative dielectric constant and for instability due to excitation of beam wave with negative energy. Comparison with the case of a sublimiting beam is carried out.