Storage ring lattice calibration using resonant spin depolarization

This paper presents measurements of the GeV-scale electron beam energy for the storage rings at the synchrotron light source facilities Australian Synchrotron (AS) and SPEAR3 at SLAC. Resonant spin depolarization was employed in the beam energy measurement, since it is presently the highest precision technique and an uncertainty of order 10(-6) was achieved at SPEAR3 and AS. Using the resonant depolarization technique, the beam energy was measured at various rf frequencies to measure the linear momentum compaction factor. This measured linear momentum compaction factor was used to evaluate models of the beam trajectory through combined-function bending magnets. The main bending magnets of both lattices are rectangular, horizontally defocusing gradient bending magnets. Four modeling approaches are compared for the beam trajectory through the bending magnet: a circular trajectory, linear and nonlinear hyperbolic cosine trajectories, and numerical evaluation of the trajectory through the measured magnetic field map. Within the uncertainty of the measurement the momentum compaction factor is shown to agree with the numerical model of the trajectory within the bending magnet, and disagree with the hyperbolic cosine approximation