A simple model based magnet sorting algorithm for planar hybrid undulators

Various magnet sorting strategies have been used to optimize undulator performance, ranging from intuitive pairing of high- and low-strength magnets, to full 3D FEM simulation with 3-axis Helmholtz coil magnet data. In the extreme, swapping magnets in a full field model to minimize trajectory wander and rms phase error can be time consuming. This paper presents a simpler approach, extending the field error signature concept to obtain trajectory displacement, kick angle and phase error signatures for each component of magnetization error from a Radia model of a short hybrid-PM undulator. We demonstrate that steering errors and phase errors are essentially decoupled and scalable from measured X, Y and Z components of magnetization. Then, for any given sequence of magnets, rms trajectory and phase errors are obtained from simple cumulative sums of the scaled displacements and phase errors. The cost function (a weighted sum of these errors) is then minimized by swapping magnets, using one's favorite optimization algorithm. This approach was applied recently at NSLS to a short in-vacuum undulator, which required no subsequent trajectory or phase shimming. Trajectory and phase signatures are also obtained for some mechanical errors, to guide 'virtual shimming' and specifying mechanical tolerances. Some simple inhomogeneities are modeled to assess their error contributions.