Undulator radiation as ane-beam diagnostic tool

Summary

We discuss the possibility of exploiting the undulator radiation as a diagnostic tool for the emitting e-beam itself. We suggest, indeed, a method to infer the radiating e-beam emittance from the integrated brightness. We evaluate numerically the Lienard-Wiechert radiation integral and calculate the undulator brightness, including the betatron motion effects. We consider linearly polarized undulators and cylindricale-beams. We analyse the details of the spectrum emitted in the region of the first three harmonics. We prove that the brightness integrated on a suitable solid-angle portion and frequency interval around the second harmonic, can be parametrized by using two characteristic parameters only. It is also shown that this measurable, in principle, quantity is a linear function of thee-beam emittance.