LAUSR

The phase error is an important parameter to represent the quality of an undulator, which makes it possible to quickly evaluate the reduction in photon intensity due to magnetic field errors without rigorous numerical calculations. Although the phase error has been used as a standard to evaluate the undulator field errors because of its simplicity, a couple of papers have reported that the phase error actually overestimates the intensity reduction under practical conditions, and thus its tolerance tends to be too tight. In other words, the applicability of the phase error defined in the conventional form is rather limited. To overcome this difficulty, we derive a set of formulas to quickly evaluate the undulator quality based on an analytical approach, which can be used in a more universal manner. Comparisons with rigorous numerical results under various conditions show the validity and universality of the derived formulas. Analytical methods to investigate the effects due to systematic errors in undulators are also presented as one of the important applications of these formulas.