A new design for a multistage High-Gain Harmonic Generation (HGHG) scheme is proposed. The main difference with previous HGHG schemes is that in our scheme the HGHG technique can be applied more than once in a HGHG chain (single bunch scheme). This is consequence of the fact that the growth of the energy spread due to the HGHG process in our case is much less than initial energy spread, and exponential growth rate in the main undulator is practically the same as without stage sequence. Problems

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... relating to X-ray HGHG FEL are discussed. Our studies have shown that the frequency multiplication process produces a noise degradation proportional to at least the square of the multiplication ratio. This prevents operation of HGHG FEL at a very short wavelength range. The results presented in this paper have demonstrated that the HGHG FEL approach is quite adequate for the VUV coherent source, but not scalable to X-ray devices.