Period and Field Intensity Errors and their Effects on the Undulator Synchrotron Radiation: an Investigation for the National Synchrotron Undulator

The first prototype Iranian undulator is under design and fabrication. The undulator makes a periodic magnetic field which forces the electrons travelling through it to move along the undulator with a sinusoidal motion and radiate synchrotron radiation with specific properties. In this paper, two classes of errors, which are important to consider in the design and fabrication of undulators, so to speak, the period error and field error are introduced. Additionally, their effects on the radiation harmonics were studied. For this purpose, MATLAB software was used to generate pseudo-random errors for the undulator periods and peak fields. Then, the fields were applied to a pure sinusoidal magnetic field, used for calculation of the final harmonics by the B2E code. It was found that with the increase of the number of harmonics, the effects of errors are enhamced. Also, it was found that the effect of the field error is higher than that of the phase error. Finally, it could be concluded that in order to reach %90 of the ideal intensity at the first and third harmonics, the desired errors at the peak field and the period must be less than %0.1 and 3 degree, respectively. Also, the tolerance for the gap value must be no more than 15±0.2 mm.