Alignment tolerances of IR quadrupoles in the LHC

Luminosity in the LHC will depend critically on the alignment of the triplet quadrupoles. These quadrupoles are closest to the interaction points (IPs), have large gradients and the β functions have their largest values within these quadrupoles. Within a triplet, the cold masses of the Q1 and Q3 quadrupoles will be housed in separate cryostats while Q2a and Q2b will be placed in a single cryostat. The absolute alignments of Q1, Q3 and the Q2a/Q2b pair with respect to the desired axes will be determined during installation. The relative alignment of Q2a and Q2b however will be fixed once they are placed in their common cryostat at Fermilab. In this note, we examine the required relative alignment tolerances of Q2a and Q2b. An early study of some alignment tolerances was done by Weisz [1]