Harmonic operation of high gain harmonic generation free electron laser

In high gain harmonic generation(HGHG)free electron laser(FEL),with the right choice of parameters of the modulator undulator,the dispersive section and the seed laser,one may make the spatial bunching of the electron beam density distribution correspond to one of the harmonic frequencies of the radiator radiation,instead of the fundamental frequency of the radiator radiation in conventional HGHG,thus the radiator undulator is in harmonic operation(HO)mode.In this paper,we investigate HO of HGHG FEL. Theoretical analyses with universal method are derived and numerical simulations in ultraviolet and deep ultraviolet spectral regions are given.It shows that the power of the 3rd harmonic radiation in the HO of HGHG may be as high as 18.5% of the fundamental power level.Thus HO of HGHG FEL may obtain short wavelength by using lower beam energy.