Conditions on the grazing function g for efficient collimation

The grazing function g is introduced – a synchrobetatron optical quantity that parametrizes the rate of change of total angle with respect to synchrotron amplitude for particles grazing a collimator or aperture. The grazing function is particularly important for crystal collimators, which have limited acceptance angles. The implications for RHIC, SPS, Tevatron and LHC crystal implementations are discussed. An analytic approximation is derived for the maximum value of g in a matched FODO cell, and is shown to be in good agreement with a realistic numerical example. The grazing function scales linearly with FODO cell bend angle, but to is independent of FODO cell length.