Review of linear optics measurement and correction for charged particle accelerators

Measurement and correction of charged particle beam optics have been a major concern since the advent of strong focusing synchrotron accelerators. Traditionally, particle colliders have led the development of optics control based on turn-by-turn beam centroid measurements, while lepton storage rings have focused on closed-orbit-response matrix techniques. Recently, considerable efforts are being invested in comparing these techniques at different synchrotron radiation sources and colliders. An emerging class of less invasive techniques based on the optimization of performance-related observables is demonstrating a great potential. In this paper, a review of existing techniques is presented highlighting comparisons, relative merits and limitations.

Figure 1

Measured or inferred $\beta$-beating versus time for many circular accelerators as found in the bibliography of this paper. Three stages are differentiated: (i) commissioning, when magnet powering mistakes are expected, (ii) after fixing these mistakes but before careful optics corrections and (iii) after final optics corrections.

Figure 2

Coupling evolution versus time for many circular accelerators as found in the bibliography of this paper. The closest tune approach in hadron machines and the emittance ratio ${\epsilon }_y/{\epsilon }_x$ in lepton rings are used as figures of merit for the coupling.

Figure 3

Tune jitter measurement at ALBA. In a single acquisition, the rms tune spread over the 120 BPMs (in red) is only $2\times {10}^{-6}$, but this increases to ${10}^{-4}$ when the measurement is extended over 100 acquisitions due to the power supplies noise [48].

Figure 4

Comparison between the vertical beam response (top) to a single kick in the LHC at injection energy, and to an ac dipole excitation (bottom) [61].

Figure 5

Singular U-vectors derived from free betatron oscillation data in the SLC. The top four singular vectors represent the betatron oscillations while the singular vectors 5 and 6 show uncorrelated signals originating from malfunctioning BPMs. Reprinted from [72], copyright 1999 by the American Physical Society.

Figure 6

Comparison between the 3-BPM (also called neighboring BPM) and N-BPM methods in the LHC [91]. The average error bar of the experimentally measured beta function for different optics configuration at 4 TeV, except for injection at 0.45 TeV.

Figure 7

Example of closest tune approach applied to the CERN PS after powering a strong skew quadrupole [95]. Top: The model betatron tunes programmed to cross the difference resonance. Bottom: Corresponding measured tune values. $\mathrm{\Delta }{Q}_{\min }$ is inferred from the closest approach between the tunes at the crossover point.

Figure 8

Vertical beam size evolution after applying the random walk optimization at SLS [138].