Numerical modeling of tapered undulators

Abstract

Tapered-undulator radiation will be used in at least one of the third generation synchrotron sources. While the spectral and angular characteristics of the radiation have been calculated for some specific configurations, the effects of tapering on the spectrum are still not well characterized. In this paper we have used an FFT-based method to calculate the spectral and angular distributions of the radiation from a tapered undulator with vertically-polarized magnetic field. The effect of tapering on the horizontal symmetry of the angular distribution of the radiation is investigated. A simple expression for the presence or absence of horizontal reflection symmetry as a function of the undulator parameters is derived. We have shown that for APS-type undulators and energies as high as 25 keV the radiation may be expected to exhibit horizontal reflection symmetry for observation angles up to 200 μrad. Our calculations are in agreement with recent measurements of the on-axis brightness of the prototype APS-CHESS undulator operated in the tapered configuration, and with results from well-established non-FFT programs.