Magnet strength measurement in circular accelerators from beam position monitor data

Recent measurements of resonance terms suggested the extension of the existing technique to measure magnet strengths from turn-by-turn beam position monitor data. This article describes the algorithm to infer the magnet strength from the variation along the ring of the resonance terms and reports on the first measurement. Both the algorithm and the software written for the analysis of the data can be particularly useful in the commissioning period of an accelerator in order to find magnets with wrong strengths or polarities as well as magnets with large magnetic errors.

Figure 1

RDT $f_{3000}$ along the ring. The vertical lines indicate the location of the seven extraction sextupoles. Error bars correspond to $1\sigma$. Only the values from BPMs providing error bars smaller than 20% are shown.

Figure 2

Measured and expected absolute value of ${\chi }_{3000}$. Error bars correspond to $3\sigma$. Only the values providing error bars smaller than 20% are shown.

Figure 3

Measured and expected absolute value and phase of ${\widehat{h}}_{3000}$ corresponding to the seven excited extraction sextupoles. Error bars correspond to $3\sigma$.

Figure 4

Examples of BPM spectra from single-particle tracking simulation with betatron coupling driven by skew quadrupoles (left plot) and nonlinearities driven by normal sextupoles (right plot). $Q$ and $\nu$ denote the bare tunes and the nonlinear tunes, respectively.

Figure 5

Schematic view of a ring taking into account the distribution of BPMs and multipoles.

Figure 6

Schematic view of a section of the ring when several multipoles are placed between two BPMs.