Measurement of the APS storage ring electron beam energy spread using undulator spectra

The angle-integrated flux spectrum of an undulator has sharp dropoffs at harmonic photon energies. Its derivative therefore shows pronounced peaks with RMS width Δω/ω ~ 0.4/nN, where ω is the photon energy, n is the harmonic number, and N is the number of undulator periods. For the fundamental photon energy of the Advanced Photon Source diagnostics undulator, the derivative of the angle integrated flux spectrum is a peak with rms width of ~0.2%. By using this feature, we have successfully developed techniques to measure the energy centroid, spread, and momentum compaction factor of the APS storage ring beam. In this paper, we present analytical and numerical analyses of the undulator spectrum derivative and examine the sources of experimental errors of this technique