Three-dimensional numerical investigations of the laser-beam interactions in an undulator

Laser-beam interaction in an undulator is commonly suggested in the development of free electron laser (FEL) schemes. In this paper, a three-dimensional algorithm is developed to assist in laser-beam interaction simulation in an undulator, which is built on the basis of the fundamentals of electrodynamics, i.e. the electron's behavior is determined by the magnetic field and the laser electric field in the time domain. On the basis of the algorithm, the detuning effect in a laser heater, the carrier envelope phase effect of a few-cycle laser in attosecond X-ray FEL schemes and output wavelength tuning in a high gain harmonic generation FEL are numerically discussed.