CERN Large Hadron Collider optics model, measurements, and corrections

Optics stability during all phases of operation is crucial for the LHC. Tools and procedures have been developed for rapid checks of beta beating, dispersion, and linear coupling, as well as for prompt optics corrections. Important optics errors during the different phases of the beam commissioning were observed and locally corrected using the segment-by-segment technique. The most relevant corrections at injection have been corroborated with dedicated magnetic measurements.

Figure 1

Measured peak $\beta$ beating (top) and rms orbit (bottom) at injection for beam 2 versus the number of days of LHC operation after circulating beam was established in 2008. Relevant events affecting the LHC optics are also displayed. LSA stands for LHC Software Architecture [38].

Figure 2

Measured $\beta$ beating (top) and IPs ${\beta }^{*}$ (bottom) versus the number of days of LHC operation during the ${\beta }^{*}$ squeeze commissioning at 3.5 TeV.

Figure 3

Example of the extended SBST applied to the correction of the IR5 normal and skew optics errors for beam 1 at 3.5 TeV. The IR quadrupoles (top), the vertical phase advance error (middle plot), and the difference resonance term $f_{1001}$ (bottom) are shown. The lines represent the matched model with normal and skew errors located in the triplets.

Figure 4

Measured and simulated horizontal beam excursions with the AC dipole ramping up on the tune resonance.

Figure 5

$\beta$ beating for beam 1 before and after corrections at injection energy.

Figure 6

Illustration of the local optics correction in IR3 for beam 2 at injection.

Figure 7

Beam 2 $\beta$ beating at injection before and after updating the MQW magnetic calibrations, showing a comparable performance.

Figure 8

Beam 1 horizontal (top) and vertical (bottom) phase beat before and after the dipole ${\mathrm{b}}_2$ component correction.

Figure 9

Beam 1 horizontal (top) and vertical (bottom) $\beta$ beating before and after correction with all IPs at ${\beta }^{*}=2\mathrm{m}$ at 3.5 TeV.

Figure 10

Illustration of the two-beam $\beta$ beating correction using the IR5 triplets.

Figure 11

Local Beam 1 IR8 correction increasing by 5% the fifth quadrupole to the right of IP8.

Figure 12

Measured and propagated horizontal and vertical dispersions across the IR8. No significant error is observed from the dispersion functions.

Figure 13

Difference of the beam 1 vertical $\beta$ beating between two measurements at ${\beta }^{*}=2\mathrm{m}$ separated by 5 days.

Figure 14

Skew quadrupole current along the squeeze. kqsx3.r5 is one of the IR5 triplet skew quadrupole correctors. kqs.a78b2 is one of the skew quadrupole families involved in the global coupling correction.

Figure 15

Extrapolation of the 3.5 TeV identified optics errors to 7 TeV with nominal optics.