The effect of the tapered wiggler in a free-electron laser

We study the effects of the tapered wiggler in a free-electron laser by using the two wave model which describes the nonlinear interaction between the two resonant waves by a set of partial differential equations. By solving a system of the nonlinear coupled wave equations, we investigate the field amplitude, the spectrum of the emitted radiation, and its Fourier transform. The sideband instability which is triggered by the shot noise in the electron beam is also examined by the numerical simulation. The results with the tapered wiggler are compared to those of the untapered and the linear tapering cases.