Temperature dependence of peak field errors and phase error tuning of cryogenic permanent magnet undulators at HEPS

Cryogenic permanent magnet undulators (CPMUs) with high magnetic field are the most advantageous type of insertion sections (IDs), and are widely used in 4-generation light sources, such as the High Energy Photon Source (HEPS). The RMS phase error, which is highly related to the ID radiation brightness and flux, is a key indicator for evaluating the ID performance. For CPMUs, the phase error at low temperature (LT) is higher than that at room temperature (RT) in some cases. The main reason is that the trajectory error and local phase error are greater at LT than that at RT. All of them are affected by the first integral of the magnetic field over half a period. Since the errors in period length caused by cryogenic contraction can be ignored, the peak field is the prominent factor to investigate the reason for the change in phase error between LT and RT. To clarify the root causes, this study firstly discusses and analyses the changes in peak field before and after temperature reduction of pure permanent magnet and hybrid permanent magnet arrays. Secondly, the phase error tuning is continually carried out for 4 CPMUs in the first phase of HEPS. Through the reasonable adjustment of the tuning scheme, all of them are adjusted to within 3° meeting the requirements for high-order harmonic radiation brightness.