Improvements of the undulator spectral performance by compensating the backing beam deflection

This study thoroughly examines how the backing beam deflection affects the undulator spectral performance. Reduction of the undulator spectral intensity owing to backing beam deflection is analytically evaluated based on plane-wave approximation. The results reveal that the amplitude and the slope of the backing beam deflection affect the undulator spectral performance. Provided is a novel figure-of-merit, rms of the regressed accumulated gap deviation, to determine the backing beam deflection budget. An example of a 3.9 m undulator supporting carriage mounted with 50-mm period length undulator magnet (U5) under a maximum magnetic loading of 5 metric tons at a minimum operating gap of 14 mm, is provided. Its mechanical features are first examined via 3D commercial finite element code ANSYS that concludes the backing beam deflection is influenced heavily by the rigidity of the undulator support frames. Examining the corresponding spectral performance shows that significantly diminishing the undulator spectral degradation by backing beam deflection is attainable by compensating the deflection at the undulator minimum operating gap properly. The numerical results agree well with those deduced from the measured magnetic field of the as-built undulator.