Analytical solution of phase space evolution of electrons in a SASE FEL

Nishimori, Nobuyuki

Proceedings of 26th International Free Electron Laser Conference (FEL 2004) and 11th FEL Users Workshop (CD-ROM), p.41 - 44, 2004/00

The phase space evolution of electrons in a self-amplified spontaneous emission (SASE) FEL operating in the linear regime before saturation is solved analytically from the one dimensional (1D) FEL equaiton. The analytical solution agrees well with a time-dependent numerical simulation which solves the 1D FEL equation in an exact manner and includes a shot-noise effect. The radiation field reaches saturation when the optimum bunching of the electrons is formed on the scale of the resonant wavelength. The optimum bunching leads to the well known saturation condition Nw 1.