Effect of two-stream instability on the saturation mechanism of a two-stream free-electron laser with a helical wiggler pump

In this paper we will investigate the effect of two-stream instability on saturation mechanism in Two-Stream Free Electron Laser (TSFEL) with a helical wiggler pump. A two-velocity relativistic electron beam propagates through the helical wiggler field. The relativistic electron stream is assumed to be cold. The slippage of the electromagnetic wave with respect to the electron beam is ignored. Self-consistent evolution of an electromagnetic wave in the presence of two-velocity electron beam is described by a set of coupled nonlinear differential equations in 1D approximation. Slowly varying envelope approximation is used and by the Runge–Kutta method algorithm is solved numerically. The power versus the axial distance has been plotted. It has been found that the TSFEL reaches the saturation regime in a shorter axial distance in comparison with the conventional FEL.