Free-electron laser model without the slowly-varying envelope approximation

Free-electron laser is studied without the slowly-varying envelope approximation (SVEA). Electron-Laser-Facility-like parameters in the strong pump regime are adopted for the analysis. Commonly used set of equations of the profiles of the electron energy, the synchrotron phase of the electrons and the electric field of the laser is solved by the numerical simulation through the one-dimensional time-dependent code. Since the cooperation length is much smaller than the electron beam length, the steady-state solution is found to exist. Comparisons are made with the earlier results with the SVEA. It turns out that the SVEA makes a sizable difference when the electron beam and the wiggler are long for the amplifier configuration. It can be concluded that the application of the SVEA in the strong-pump regime is appropriate when the electron beam is short.