Beam-based measurement of skew-quadrupole field distribution along the longitudinal direction in a long undulator

The skew-quadrupole field errors in an undulator were determined from the response of the stored beam. This method used was to measure the change of the horizontal closed orbit distortion produced by two types of vertical local bump orbit in the undulator. In this method, the unknown distribution of the skew-quadrupole field along the longitudinal direction in the undulator was expressed quantitatively by the multipole moments. Therefore, the reliable result is obtained. In addition, this method is faster than the global modelling of a ring, which uses the response matrix of the whole ring, and is not sensitive to skew-quadrupole field errors in sections other than the target section. Therefore, this method is suitable for measuring the gap dependence.