Calculations of safe collimator settings and ${\beta }^{*}$ at the CERN Large Hadron Collider

The first run of the Large Hadron Collider (LHC) at CERN was very successful and resulted in important physics discoveries. One way of increasing the luminosity in a collider, which gave a very significant contribution to the LHC performance in the first run and can be used even if the beam intensity cannot be increased, is to decrease the transverse beam size at the interaction points by reducing the optical function ${\beta }^{*}$. However, when doing so, the beam becomes larger in the final focusing system, which could expose its aperture to beam losses. For the LHC, which is designed to store beams with a total energy of 362 MJ, this is critical, since the loss of even a small fraction of the beam could cause a magnet quench or even damage. Therefore, the machine aperture has to be protected by the collimation system. The settings of the collimators constrain the maximum beam size that can be tolerated and therefore impose a lower limit on ${\beta }^{*}$. In this paper, we present calculations to determine safe collimator settings and the resulting limit on ${\beta }^{*}$, based on available aperture and operational stability of the machine. Our model was used to determine the LHC configurations in 2011 and 2012 and it was found that ${\beta }^{*}$ could be decreased significantly compared to the conservative model used in 2010. The gain in luminosity resulting from the decreased margins between collimators was more than a factor 2, and a further contribution from the use of realistic aperture estimates based on measurements was almost as large. This has played an essential role in the rapid and successful accumulation of experimental data in the LHC.

Figure 1

The $\beta$-functions around the ATLAS experiment in the LHC for the clockwise rotating beam (B1), calculated with mad-x [7], shown together with the layout of dipoles (MB, main bend), horizontally focusing (QF) and defocusing (QD) quadrupoles, and tungsten collimators (TCTs) for protection of the aperture bottleneck. This optics [6] with ${\beta }^{*}=60\mathrm{cm}$ was used in the 2012 physics run. The IP is located at $s=0$ and the beam direction is from left to right, meaning that the incoming beam passes the TCTs before the inner triplets and the IP. The optics is identical in CMS except that the horizontal and vertical planes are switched.

Figure 2

The schematic layout of the LHC (the separation of the two rings is exaggerated). The two beams are brought into collision at the four experiments ATLAS, ALICE, CMS, and LHCb. Adapted from Ref. [17].

Figure 3

Schematic illustration (not to scale) of the collimator settings and the minimum aperture that can be protected during the physics runs in 2010 (3.5 TeV), 2011 (3.5 TeV), and 2012 (4 TeV), together with the nominal settings (7 TeV). The resulting values of ${\beta }^{*}$ are also indicated.

Figure 4

Measured drifts of the horizontal B2 orbit at a BPM close to the TCTH in IR5 during the first part of the 2011 run with ${\beta }^{*}=1.5\mathrm{m}$ (top) and during the second part with ${\beta }^{*}=1.0\mathrm{m}$ (bottom). The orbits were sampled every 10 s.

Figure 5

Calculated triplet aperture, for 4 TeV proton beams with $3.5\mu \mathrm{m}$ in the LHC, as a function of ${\beta }^{*}$ for different values of the beam-beam separation $d$, where $d=9.3{\sigma }_r$ with the assumption of ${\epsilon }_n=2.5\mu \mathrm{m}$, was used in LHC operation during the last part of Run I. The calculation was carried out based on Eq. (13) and the measured aperture in 2011. The crossing angle varies along the curves.

Figure 6

Example of the on-momentum integration regions defined by Eq. (15) for the dump protection collimators (TCS6 and TCDQ) and all TCTs in B1 (left) and B2 (right) for a setting of $7.1\sigma$ for the TCS6 and the TCTs, while the TCDQ is positioned at $7.6\sigma$. The normalized kick $\theta$ is also at $7.1\sigma$ and a perfect machine is assumed. The circles represent lines of constant phase space density at every $\sigma$. The TCDQ is the first collimator seen by the beam, followed by the TCS6 and the TCTs. A perfect optics and ${\beta }^{*}=60\mathrm{cm}$ was assumed.

Figure 7

The simulated losses during a single-module prefire, from PSI and SixTrack (ST), on TCTs in different IRs and beams for 4 TeV 50 ns operation with ${\beta }^{*}=60\mathrm{cm}$ optics. Losses are summed over all bunches in a train and shown as a function of the TCT setting. The results are shown together with estimates of the TCT damage limits from Ref. [28].

Figure 8

The simulated losses during a single-module prefire from PSI on the TCT in IR1, B1, when all IR7 collimators are retracted, as a function of TCT setting. The solid red curve shows the result for a perfect optics, while the color scale shows, for each TCT setting, the probability distribution of losses under the influence of random phase errors compatible with the LHC optics correction. The results are shown together with the TCT damage limits given in Ref. [28].

Figure 9

A schematic view of a collimator protecting an aperture illustrating the variables introduced in Appendix pp2. The collimator is initially centered around the reference orbit, which is present during the collimation setup. At a later time, the orbit can be slightly perturbed.

Figure 10

Change of margin due to orbit movements between the horizontal TCT in IR5 B2 and the aperture bottleneck in triplet (bottom) as calculated by Eq. (b4). All running periods from 2011 with stable beams and ${\beta }^{*}=1\mathrm{m}$ were accounted for, except where large luminosity scans were performed. The orbits were sampled every 10 s.