Beam lifetime in storage rings and colliders is affected by, among other effects, lattice nonlinearities. Their control is of great benefit to the dynamic aperture of an accelerator, whose enlargement leads in general to more efficient injection and longer lifetime. This article describes a procedure to evaluate and correct unwanted nonlinearities by using turn-by-turn beam position monitor data, which is an evolution of previous works on the resonance driving terms (RDTs). Effective normal and skew sextupole magnetic errors at the ESRF electron storage ring are evaluated and corrected (when possible) by using this technique. For the first time, also octupolar RDTs could be measured and used to define an octupolar model for the main quadrupoles. Most of the deviations from the model observed in the sextupolar RDTs of the ESRF storage ring turned out to be generated by focusing errors rather than by sextupole errors. These results could be achieved thanks to new analytical formulas describing the harmonic content of the nonlinear betatron motion to the second order. For the first time, linear combinations of RDTs have been also used for beam-based calibration of individual sextupole magnets. They also proved to be a powerful tool in predicting faulty magnets and in validating magnetic models. This technique also provides a figure of merit for a self-assessment of the reliability of the data analysis.

• Received 7 February 2014

DOI:https://doi.org/10.1103/PhysRevSTAB.17.074001

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Published by the American Physical Society