Self-similar amplification and self-compression of short microwave pulses during Cherenkov-type interaction with relativistic electron beams

This paper reports the results of studies of super-radiance pulse amplification in the case of Cherenkov interaction of a relativistic electron beam with a traveling electromagnetic wave. 1D Nonstationary (time-domain) nonlinear models of a Cherenkov traveling-wave-tube amplifier are considered in two approximations, namely, in the cases of small variation of electron velocity and small variation of electron energy. For both cases, self-similar solutions, which describe the pulse amplification and compression, are derived and limiting transition between them is discussed. The results of numerical simulation of amplification of a seed pulse are presented showing that the main characteristics of the pulse (peak amplitude, pulse width, etc.) behave in time and space in good agreement with the self-similar solutions.