Abstract
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.
Highlights
AND MOTIVATIONMany factors make the implementation of a magnetic optics in a circular accelerator different from the nominal one, among which are: deviations from the magnet calibration curves and from the ideal magnetic lengths, displacements from the reference position and axis, and unknown multipole components
The optics model in this case is necessary for the evaluation of the ð8 · NBPMÞ × 1 matrix M only, whereas the left-hand side contains two combined RDTs (CRDTs) vectors measured with two different sextupole strengths, i.e., 074001-6
The first natural preliminary step is to verify the synchronization of all 224 beam position monitors (BPMs) installed along the ESRF storage ring and to ensure that both kickers are synchronized so as to have the bunch train on their flattop: The measured invariants and CRDTs would be corrupted if the beam experiences the kicker pulse rise and/or fall
Summary
Many factors make the implementation of a magnetic optics in a circular accelerator different from the nominal one, among which are: deviations from the magnet calibration curves and from the ideal magnetic lengths, displacements from the reference position and axis, and unknown multipole components. While an artillery of different methods and algorithms has been developed and successfully implemented in routine operation for the evaluation and correction of focusing errors (linear optics) and betatron coupling, their extension to the nonlinear modeling and correction remains difficult because they are either time-consuming or require diagnostic tools unavailable a decade ago. In most cases, such as at the ESRF storage ring, the correction of the nonlinear optics is done by trial and error seeking heuristically longer lifetime. Mathematical derivations are summarized in separate appendices (complete proofs may be found in Ref. [12])
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call