LHC impedance reduction by nonlinear collimation

A nonlinear collimation system can allow larger aperture for mechanical jaws, and it thereby can help to reduce the collimator impedance, which presently limits the LHC beam intensity. Assuming the nominal LHC beam at 7 TeV, we show how a nonlinear betatronic collimation insertion would reduce considerably the LHC coherent tune shift for the most critical coupled-bunch mode as compared with the conventional baseline linear collimation system of Phase-I. In either case, the tune shifts of the most unstable modes are compared with the stability diagrams for Landau damping.