Application of Modified Asymptotic Integration Scheme in Theory of Multiharmonic Two-Stream FELs with Helical Electron Beams

In the framework of method of averaged characteristics we demonstrated the application technique of modified asymptotic integration scheme. The technique was shown on the example of multiharmonic two-stream superheterodyne free-electron laser (TSFEL) with helical electron beam non-linear theory. We obtained the system of shortened differential equations for the amplitudes of interacting waves. This system considers diverse types of plural parametric interactions. We demonstrated that investigated multiharmonic TSFEL with helical relativistic electron beams (REBs) are characterized by higher electromagnetic waves amplification rates compared with TSFELs based on straight beams. It allows to reduce the longitudinal dimensions of the devices. We found out that width of electromagnetic signal frequency spectrum forming in multiharmonic TSFELs with helical REBs is bigger compared with frequency spectrum width in similar TSFELs using straight REBs.