Cubic Nonlinear Theory of Superheterodyne Parametric H-ubitron FEL with Section for Amplifying Longitudinal Space Charge Waves

In this paper, an analysis of the wave dynamics of a parametric superheterodyne H-ubitron free-electron laser with a longitudinal wave amplification section is carried out within the cubic nonlinear approximation. A key feature of the studied free-electron laser is the implementation of two interconnected three-wave parametric resonances. The first parametric resonance occurs between the electromagnetic signal and the magnetic field of the H-ubitron pump. The second parametric resonance occurs between the longitudinal field of the electrostatic undulator and the fast and slow space-charge waves. The second parametric resonance pro-vides additional amplification of the slow space-charge wave. The studied model considers the effect of electrostatic pumping field generation, an analysis of the influence of a quasi-electrostatic support field is carried out, and the lengths and saturation levels of such devices are determined. It is demonstrated that, due to the additional amplification of the slow space charge wave in the longitudinal wave amplification section, as well as taking into account the effect of electrostatic pumping field generation, the saturation length of the electromagnetic signal wave is reduced by 18%. To increase the output electromagnetic signal's saturation level, we propose using a quasi-electrostatic support field, in which the electrostatic field strength in-creases linearly starting from a specific coordinate. It is demonstrated that an optimal quasi-electrostatic support field allows us to increase the output saturation level of the electromagnetic signal by more than 130%. Thus, the use of a parametric superheterodyne H-ubitron free-electron laser with a longitudinal space charge wave amplification section and a quasi-electrostatic support field has several advantages compared to a traditional H-ubitron free-electron laser, namely, a reduction in the longitudinal dimensions of the en-tire device and an increase in the power of the output electromagnetic signal.