Stability of the Electron Motion in a Free-electron Laser with Tapered Wiggler

One of the methods in enhancing the efficiency and output of a free-electron laser is the use of a tapered wiggler for postponement of the beam-wave interaction saturation. In this paper, the electron motion stability in a free-electron laser with tapered wiggler is studied by means of the Kolmogorov entropy (K-entropy). It is shown that values of K-entropy of the equilibrium electron oscillate around zero when the wiggler is un-tapered, whereas values of K-entropy end to the negative value when the wiggler is tapered and consequently the motion stability is improved. It is found that the laser fields exponentially growing by extracting the kinetic energy of the electron beam cause heavy fluctuation of the K-entropy, and instead of a positive taper, a negative taper should be employed so as to improve the stability of the electron motion.