Utilizing the $N$ beam position monitor method for turn-by-turn optics measurements

The $N$ beam position monitor method ($N$-BPM) which was recently developed for the LHC has significantly improved the precision of optics measurements that are based on BPM turn-by-turn data. The main improvement is due to the consideration of correlations for statistical and systematic error sources, as well as increasing the amount of BPM combinations which are used to derive the $\beta$-function at one location. We present how this technique can be applied at light sources like ALBA, and compare the results with other methods.

Figure 1

Phase advances of consecutive BPMs in the nominal model. Many phase advances close to 0° impair the calculation of $\beta$-functions when using only neighboring BPMs.

Figure 2

In the $N$-BPM method, $N$ BPMs at position $s_1$ to $s_N$ are used to derive the $\beta$-function at a probed BPM at position $s_p$. The probed BPM is usually set at the center of the $N$ BPMs, as optics errors decrease the gain of using further BPMs in both directions.

Figure 3

Contribution of the uncertainties from Table 1 to the total variance of the derived $\beta$-function. The average value over all BPMs is shown for the case of probing the middle BPM of neighboring BPMs, as it is the combination which has the smallest systematic error. The top bar is for the horizontal plane (H) and the bottom one for the vertical plane (V). Quadrupolar errors are shown in blue and misalignment uncertainties in red.

Figure 4

Precision of the derived horizontal $\beta$-functions from simulations for different ranges of BPMs and different amount of BPM combinations.

Figure 5

Accuracy of the derived horizontal $\beta$-functions from simulations for different ranges of BPMs and different amount of BPM combinations.

Figure 6

Turn-by-turn oscillations at BPMs where $\beta =12.7\mathrm{m}$.

Figure 7

Frequency spectrum of the horizontal (H) and vertical (V) turn-by-turn oscillations. The two peaks correspond to the tunes $Q_x=18.15$ and $Q_y=8.36$.

Figure 8

Comparison of $\beta$-beating as derived from BPM turn-by-turn data using the phase of the betatron oscillation ($N$-BPM method with an 11-BPM range) to the $\beta$-beating from LOCO.

Figure 9

Comparison of $\beta$-beating as derived from BPM turn-by-turn data using either the amplitude information or phase of the betatron oscillation ($N$-BPM method).