Theoretical analysis of iron-bore superconducting undulators

The unavoidable undulator field errors due to machining tolerances of the yokes lead to a reduction of the gain in comparison to the case computed with an ideally perfect undulator. We describe a mathematical model of errors in iron-dominated micro-undulators introduced by manufacturing tolerances. Explicit expressions for the perturbation fields are derived. We use these fields to calculate the first, second and phase integrals describing the effects on the electron trajectory. We conclude that the intrinsic tolerances achievable with wire electric discharge machining do not significantly affect the performance of the Accelerator Test Facility free-electron laser.