Optimization of Collimator Jaw Locations for the LHC

A highly effective collimation scheme is required in the LHC to limit heating of the vacuum chamber and superconducting magnets by protons either uncaptured at injection or scattered by non-linear phenomena. The proposed system would consist of one set of primary collimators followed by three sets of secondary collimators downstream to clean up protons scattered from the primaries. Each set of collimators would consist of four pairs of jaws horizontal, vertical, and 45 and 135 skew. A study is reported of the optimization of the longitudinal positions of these jaws with the aim of minimizing the maximum betatron amplitudes of protons surviving the collimation system. This is performed using an analytical representation of the action of the jaws and is confirmed by tracking. Significant improvement can be obtained by omitting inactive jaws and adding skew jaws.