Study of the Non-linear Behaviour of the LHC using Normal Forms

Normal form tools are used in view of understanding the causes of dynamic aperture limitations in the LHC optics versions 4 and 5. To this end, maps up to 11th order have been produced and analysed by means of Lie algebraic methods, for all models and 60 different realisations of the accelerator, at injection energy. The resonances up to 12th order are systematically analysed and correlated with the dynamic aperture. It has been of particular interest to establish the link between the individual multipole coeffcients and the higher order contributions to a specific resonance