Effect Analyses of Thermal Deformation on Magnetic Performance of the CPMU Prototype in SSRF

A cryogenic permanent magnet undulator (CPMU) prototype cooled by sub-cooled liquid nitrogen was developed in Shanghai Synchrotron Radiation Facility (SSRF) in 2016. The CPMU prototype mainly consist of NdFeB based hybrid magnet arrays with a period of 20 mm and a magnetic length of 1.6 m, a pair of girders to support the magnetic arrays, parallel SLN2 cooling loops attached to the girders, thermal spacers connecting the girders and the copper LN2 tubes, electric heaters to heat the girders and regulate the magnet working temperature at around 120 K, and stems made of stainless steel to support the girders. During the first magnetic field measurement, the RMS phase error of the CPMU prototype changed from 3.2 degree at room temperature to 4.5 degree at 135 K. By shimming the magnetic field, its RMS phase error is reduced to 3.5 at low temperature finally. This paper presents detailed analyses of temperature distribution and thermal deformation along the CPMU girder during cool down process. By comparison with test results, the deterioration of the RMS phase error is well explained. The analyses can provide guidance for magnetic field shimming and avoid or reduce the deterioration of the RMS phase error at low temperature.