Record low $\beta$ beating in the LHC

The LHC is currently operating with a proton energy of 4 TeV and ${\beta }^{*}$ functions at the ATLAS and CMS interaction points of 0.6 m. This is close to the design value at 7 TeV (${\beta }^{*}=0.55\mathrm{m}$) and represented a challenge for various aspects of the machine operation. In particular, a huge effort was put into the optics commissioning and an unprecedented peak $\beta$ beating of around 7% was achieved in a high energy hadron collider.

Figure 1

Layout of the main interaction region (top) and $\beta$ functions (bottom) versus longitudinal location from the IP for ${\beta }^{*}=0.6\mathrm{m}$.

Figure 2

Measured peak $\beta$ beating (top) and rms orbit (bottom) at injection for beam 2 versus time.

Figure 3

Beam 1 (top) and beam 2 (bottom) $\beta$ beating at three IP1 and IP5 ${\beta }^{*}$ values during the squeeze of the virgin machine.

Figure 4

$\beta$ beating of the virgin machine along the squeeze. Beam 1 (left) and beam 2 (right), horizontal (top) and vertical (bottom) plots showing the peak and rms $\beta$-beating values versus ${\beta }^{*}$.

Figure 5

Normalized dispersion beating for beam 1 (top) and beam 2 (bottom) for the virgin machine at ${\beta }^{*}=0.6\mathrm{m}$.

Figure 6

Illustration of the segment-by-segment technique applied to IR5 simultaneously to the two beams and three different ${\beta }^{*}$. The black lines show the reconstructed error model.

Figure 7

Beam 1 $\beta$ beating and normalized dispersion beating after global correction at ${\beta }^{*}=0.6\mathrm{m}$.

Figure 8

Beam 2 $\beta$ beating and normalized dispersion beating after global correction at ${\beta }^{*}=0.6\mathrm{m}$.

Figure 9

$\beta$ beating after global correction for ${\beta }^{*}\le 0.7\mathrm{m}$ and after local correction for ${\beta }^{*}\ge 0.8\mathrm{m}$. Beam 1 (left) and beam 2 (right), horizontal (top) and vertical (bottom) plots showing the peak and rms $\beta$-beating values versus ${\beta }^{*}$.

Figure 10

$\beta$ beating from $K$ modulation at the first quadrupoles by IP1 and IP5.

Figure 11

Beam 1 horizontal (upper) and vertical (middle) Montague functions as defined in Eq. (3). The model function is shown in red, and the measurement in blue. The relative error of the measurements is shown in the lower plot. The figure shows the case for 0.6 m ${\beta }^{*}$ optics at 4 TeV beam energy, before corrections.

Figure 12

Beam 1 horizontal (upper) and vertical (middle) Montague functions as defined in Eq. (3). The model function is shown in red, and the measurement in blue. The relative error of the measurements is shown in the lower plot. The figure shows the case for 0.6 m ${\beta }^{*}$ optics at 4 TeV beam energy, after corrections.