Three-dimensional Simulation of a Harmonic Lasing Free-electron Laser Amplifier

Three-dimensional simulation of harmonic lasing Freeelectron laser is represented in the steady-state regime. Here, the third harmonic of the first wiggler is adjusted at the fundamental resonance of the second wiggler by reducing the magnetic field strength of the second wiggler. The hyperbolic wave equations can be transformed into parabolic diffusion equations by using the slowly varying envelope approximation. A set of coupled nonlinear first-order differential equations describing the nonlinear evolution of the system is solved numerically by CYRUS3D code. This set of equations describes self-consistently the longitudinal spatial dependence of the radiation waists, curvatures, and amplitudes together with the evaluation of the electron beam. Thermal effects in the form of longitudinal velocity spread are also investigated.