Effect of Emittance and rms Phase Error on Angular Flux Density and Pinhole Flux. A Simulation Study of Two Undulaters at 10.5mm Gap Incuding Very High Harmonics.
There is a trade-off between how much effort should go into the tuning of insertion devices to reduce their rms phase errors and the actual benefits achieved in spectral quality when the real APS beam emittance and beam energy spread are taken into account. In the magnetic measurement laboratory, the measured magnetic fields are analyzed in terms of the rms phase error and the angular flux density, which is calculated from the measured fields for an ideal electron beam, i.e., a zero-emittance beam. In this study, we go beyond the case of an ideal beam to study the effect of the APS beam emittance and beam energy spread on the angular flux density and the pinhole flux (for a typical pinhole size that covers most of the central cone of the radiation) for real-field insertion devices to get an estimate of how low an rms phase error is reasonable to attain. The results presented here are directly applicable to the APS 'canted' undulators of type A (planar permanent-magnet hybrid insertion devices 2.1 m long and 3.3 cm period length) but also to the standard undulators A (which have a similar design with the same period length but are 0.3 m longer) unless otherwise noted, e.g., the asymptotic ratios of the real-to- ideal intensity at very high harmonic numbers differ.
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