Optics of a two-stage collimation system

Abstract

We derive the exact specification that a two-stage betatronic collimation insertion must satisfy to cut the halo of a proton beam down to its ultimate limit which is the aperture of the secondary collimators. Our result is a set of correlated phase advances between primary and secondary collimators. We then determine the number of jaws needed to reach a given level of performance. We also specify the optic of a momentum collimation insertion.