Measurement of the average local energy spread of electron beam via coherent harmonic generation

The local energy spread of electron beam is a very important parameter for high-gain free-electron lasers (FELs), especially the seeded FELs. Highly accurate measurement of the extremely small local energy spread is rather challenging. In this paper, a simple method to accurately measure the average local energy spread based on the coherent harmonic generation is proposed. A one-dimensional analytical estimation is given to show the principle of this method, and three-dimensional simulation codes have been used to verify the theory. This method has been demonstrated on the Shanghai deep ultraviolet FEL, and the results show that the average local energy spread is about only 1.2 keV at the exit of the 136 MeV linac, which agrees well with the numerical simulations.