Design formulas for short-wavelength FELs
  Simple formulas for optimization of VUV and X-ray SASE FELs are presented. The FEL gain length and the optimal beta-function are explicitly expressed in terms of the electron beam and undulator parameters. The FEL saturation length is estimated taking into account quantum diffusion in the undulator. Examples of the FEL optimization are given. Parameters of a SASE FEL, operating at the Compton wavelength, are suggested. 
E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov