LHC optics commissioning: A journey towards 1% optics control

Since 2015 the LHC has been operating at 6.5 TeV. In 2016 the $\beta$-functions at the interaction points of ATLAS and CMS were squeezed to 0.4 m. This is below the design ${\beta }^{*}=0.55\mathrm{m}$ at 7 TeV, and has been instrumental to surpass the design luminosity of $10^{34}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. Achieving a lower than nominal ${\beta }^{*}$ has been possible thanks to the extraordinary performance of the LHC, in which the control of the optics has played a fundamental role. Even though the $\beta$-beating for the virgin machine was above 100%, corrections reduced the rms $\beta$-beating below 1% at the two main experiments and below 2% rms around the ring. This guarantees a safe operation as well as providing equal amount of luminosity for the two experiments. In this article we describe the recent improvements to the measurement, correction algorithms and technical equipment which allowed this unprecedented control of the optics for a high-energy hadron collider.

Figure 1

Measured deviation of the AC dipole horizontal beam 1 tune when 2000 turns out of 6600 were analyzed, starting from different turn numbers. The plot shows six different measurements at a ${\beta }^{*}$ of 80 cm. This bump was not visible for the other plane or beam and has been fixed by replacing the amplifier of the beam 1 AC dipole.

Figure 2

Average precision of the measured phase advance for different number of turns used in the analysis for beam 1. The fit function is $\alpha /\sqrt{x}$, and for the horizontal plane only the first five data points were used for the fit.

Figure 3

Uncertainties of the measured betatron phase advances for both beams for optics with ${\beta }^{*}=60\mathrm{cm}$ (2012) and ${\beta }^{*}=80\mathrm{cm}$ (2015). The y-axis shows the frequency for each level of uncertainty. The total area under each line is normalized to 1.

Figure 4

The conceptual layout and nomenclature for the parameters close to the IP. The read line represents the $\beta$-function. The figure is taken from [26].

Figure 5

Horizontal and vertical tune measurements of beam 2 during the gradient modulation of the first quadrupole right of IP1.

Figure 6

Linear fit of horizontal tune data for beam 2 with an illustration of the data cleaning process. The rejected data is shown in blue. An online tool is used to specify the domain of acceptance shown in green.

Figure 7

A comparison between how the 2016 and 2015 corrections would correct the phase error (on top) and the local $\beta$-beating (bottom). The red line shows the 2015 correction, the green 2016 and the blue show the measurement. Note that both the lines and points show the deviation from the ideal model.

Figure 8

$\beta$-beating at 40 cm ${\beta }^{*}$ for beam 1 (upper) and beam 2 (lower) plot.

Figure 9

The average shift of the waist of the $\beta$-function at IP1 and IP5 for the ${\beta }^{*}=40\mathrm{cm}$ optics.

Figure 10

Comparison of dispersion beating at ${\beta }^{*}$ of 40 cm between 2015 and 2016.

Figure 11

The rms $\beta$-beating when calculating a correction at a certain ${\beta }^{*}$ and applying it at a different. The blue points are based on simulations while the green and orange are based on measurements.