Calculations of safe collimator settings and β* 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 β*. 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 β*. In this paper, we present calculations to determine safe collimator settings and the resulting limit on β*, 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 β* 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.