The axial velocity spread acceptance of free electron lasers and its application to X-ray FEL design

We present various criteria for the definition of axial velocity spread acceptance of free electron lasers (FEL), and provide analytical approximations, numerical calculations and design curves for this parameter in the low, high, and intermediate gain regimes. This parameter is used to calculate the energy spread acceptance, emittance acceptance and other e-beam quality parameters. A special emphasis is put on the design considerations of short wavelength (X-ray) FELs. For this reason, the parameter calculation in this work is limited to the tenuous beam regimes only, and parameters are calculated for intermediate and moderately high gain regimes, which correspond to the low quality factor of X-ray resonators in the present state of the art.