Influence of two-stream relativistic electron beam parameters on the space-charge wave with broad frequency spectrum formation

We developed a cubic non-linear theory describing the dynamics of the multiharmonic space-charge wave (SCW), with harmonics frequencies smaller than the two-stream instability critical frequency, with different relativistic electron beam (REB) parameters. The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation. This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect. Different REB parameters such as the input angle with respect to focusing magnetic field, the average relativistic factor value, difference of partial relativistic factors, and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels. We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers, with the main purpose of forming a powerful multiharmonic electromagnetic wave.