• B. Maraghechi, M. Olumi, M.H. Rouhani
  AUT, Tehran

The relativistic cold fluid model is used to study the propagation of the nonlinear traveling wave in a free electron laser (FEL) with electromagnetic wiggler. It is convenient to transform the relevant equations to the frame of reference rotating with the wiggler. The traveling-wave ansatz is employed to obtain three coupled, nonlinear ordinary differential equations that describe the nonlinear propagation of the coupled wave. Saturation and solitary waves in FELs with electromagnetic wiggler may be investigated using these equations. In the small signal limit, the wave equations are linearized and the dispersion relation for the traveling wave is obtained. The numerical solution of the traveling-wave dispersion relation reveals the range of parameters for its unstable solutions. Instability curves with two peaks are found, for which the phase velocity is smaller and larger than the beam velocity.