Electron beam properties and impedance characterization for storage rings used for free electron lasers

Good electron beam qualities and stability are the crucial features of Storage Rings dedicated to synchrotron radiation sources or to Free Electron Laser. Most of these characteristics depend on the coupling of the e-beam with the machine environment, which can be in turn modelled in terms of a characteristic impedance, whose absolute value and structure can be used to specify both the stability (longitudinal and transverse) of the beam and its qualities (energy spread, bunch length, peak current, etc.). In this paper we consider two specific examples of Storage Rings used for FEL operation and analyze their performances by means of semianalytical and numerical methods. The analysis is aimed at clarifying the dependence of beam energy spread and bunch length on beam current and at providing a set of parameters useful for the optimization of Free Electron Laser or synchrotron radiation sources.