Error Analysis and Field Correction Methods in Superconducting Undulators

In Free Electron Lasers (FEL), the electron trajectory through the undulator must meet stringent requirements in terms of trajectory wander and phase variation. This paper analyzes the feasibility of using line current pairs as correctors for superconducting undulators given a set of expected fabrication errors. A tolerance study has first been performed to investigate the impact of geometrical errors on the field quality. These errors are corrected with line currents that increase or decrease the magnetic field locally. Once the uncorrected trajectory is known, an algorithm finds the minimum number of correctors required to fulfill the trajectory specifications, and gives the corrector locations. All the correctors can be powered with the same current, greatly simplifying the implementation. The current then offers a degree of freedom to correct the trajectory and can be tuned dynamically as a function of the magnetic deflection.