Stabilizing effect of the electron-beam self-fields on the phase-space trajectory in a self-amplified spontaneous emission free-electron laser operating in ultraviolet and x-ray spectral ranges

A detailed treatment is introduced to measure the dynamic stability of the relativistic electrons in a self-amplified spontaneous emission free-electron laser (FEL) system, which includes the numerical approach of the Kolmogorov entropy (entropy-like quantity), the general equations of motion for a charged particle and the method of monitoring the simulation accuracy. Numerical experiments reveal a new phenomenon that there exists the possibility of the transition from chaotic to non-chaotic phase-space trajectories of the strongly relativistic electrons due to the effect of their self-fields. The adiabatic magnetic field of a one-dimensional wiggler may have a slight influence on the electron transportation in the absence of the FEL fields, but substantially affects the dynamic stability of the electrons in the process of the FEL interaction. Moreover, the laser fields diminish the dynamic stability of the electrons as the FEL interaction grows exponentially.