Improving the precision of linear optics measurements based on turn-by-turn beam position monitor data after a pulsed excitation in lepton storage rings

Beam optics control is of critical importance for machine performance and protection. Nowadays, turn-by-turn (TbT) beam position monitor (BPM) data are increasingly exploited as they allow for fast and simultaneous measurement of various optics quantities. Nevertheless, so far the best documented uncertainty of measured $\beta$-functions is of about 10‰ rms. In this paper we compare the $\beta$-functions of the ESRF storage ring measured from two different TbT techniques—the N-BPM and the Amplitude methods—with the ones inferred from a measurement of the orbit response matrix (ORM). We show how to improve the precision of TbT techniques by refining the Fourier transform of TbT data with properly chosen excitation amplitude. The precision of the N-BPM method is further improved by refining the phase advance measurement. This represents a step forward compared to standard TbT measurements. First experimental results showing the precision of $\beta$-functions pushed down to 4‰ both in TbT and ORM techniques are reported and commented.

Figure 1

The lattice $\beta$-functions along the ESRF storage ring. The markers refer to BPM positions.

Figure 2

Simulated rms phase-advance error computed from single-particle simulations of the ESRF storage ring lattice as a function of the number of turns used for the analysis in two cases where the betatron tune is calculated from a single BPMs or averaged over the set of all BPMs (realistic noise has been added to BPM TbT data). The initial displacement of 0.55 mm (horizontal) and 0.15 mm (vertical) at ${\beta }_x=38\mathrm{m}$ and ${\beta }_y=2.9\mathrm{m}$ (initial actions: $J_{x0}=4.0\times {10}^{-9}\mathrm{m}$ and $J_{y0}=3.9\times {10}^{-9}\mathrm{m}$).

Figure 3

Simulated rms of artificial $\beta$-beating computed by N-BPM from the same single-particle simulations of Fig. 2.

Figure 4

Simulated artificial $\beta$-beating computed by N-BPM from single-particle simulations of the ESRF storage ring lattice at different initial displacements (${\beta }_x=38\mathrm{m}$ and ${\beta }_y=2.9\mathrm{m}$) corresponding to actions from $\sim 5\times {10}^{-9}\mathrm{m}$ to $\sim 2.5\times {10}^{-7}\mathrm{m}$.

Figure 5

Simulated rms of artificial $\beta$-beating computed by N-BPM and Amplitude methods from the same single-particle simulations with different diagonal initial displacement as in Fig. 4. The error bars refer to the mean (single-BPM) error bars averaged over all BPMs.

Figure 6

Measured $\beta$-beating when analyzing the TbT data delayed by different number of turns.

Figure 7

TbT BPM position readings with estimated exponential envelope.

Figure 8

Average $\beta$-beating vs rms $\beta$-beating (binned) of perturbed simulated lattices with respect to the unperturbed model of the ESRF storage ring (simulations).

Figure 9

Measured $\beta$-beating with respect to the ORM model.

Figure 10

Measured phase advance beating between neighboring BPMs with respect to the ORM model.

Figure 11

Difference between measured normalized dispersion obtained from TbT data and from ORM.