Field evolution of harmonic radiation in an HGHG FEL

As a natural character of high gain free electron laser (FEL), harmonic radiation is regarded as the natural extenstons to short wavelengths. In high gain harmonic generation (HGHG) scheme, harmonic evolution may be attributed to the initial harmonic bunching, self amplification of the harmonic radiation, electron beam strongly bunched by the fundamental radiation, the faster longitudinal dynamics and the fundamental synchrotron oscillation. It is more complex than harmonic evolution in other FEL schemes. In this paper, via theoretical analyses and three dimensional simulations, a general description of different aspects of harmonic evolution in the HGHG process is presented.