Analytical and experimental analysis of the undulator radiation at finite distance as a function of the e-beam parameters

The radiation emitted by the linear undulator installed on a straight section of the ADONE storage ring is studied both experimentally and theoretically. In particular, expressions are provided for the field at finite distance, based on the complex Fresnel integral. In addition, several expressions are derived for the average intensity pattern as a function of the electron beam divergence and energy spread. These formulae are used for analyzing the spectral and angular patterns of the radiation measured from a distance of 20 m from the undulator origin. The excellent quality of the undulator and the negligible influence on the pattern of the electron beam divergence are confirmed by the satisfactory agreement of the measured radiation field with the computer-generated one.