Time structure of undulator radiation

Abstract

A numerical method has been presented to compute the time structure of the radiation emitted from a relativistic electron moving inside an undulator, which plays important roles in the cutting-edge synchrotron radiation applications. The method is based on the Lienard-Wiechert potential in conjunction with the Lorentz equation to calculate the electron motion in retarded time. In this method, we used the Fourier transformation to calculate the spectral structure of the radiation and cut off high harmonic components, which do not propagate in the optical components in the experiment. Then, by using inverse Fourier transformation the time structure of the fundamental radiation has been obtained. We show some numerical examples under some experimental conditions. An interesting finding is that, by applying an external uniform magnetic field and deflecting the electron orbit, the waveform is chirped which may be interesting for some applications.