The influence of fringe fields on particle dynamics in the Large Hadron Collider

The need of maximizing luminosity in the Large Hadron Collider requires the use of High-Gradient Quadrupoles in the interaction region. These quadrupoles combine relatively short length, large aperture, and short focal length with a rather peculiar configuration of the return coils, all of which enhances the relevance of their fringe field effects. The influence of resulting nonlinearities on the dynamics is analyzed via high-order maps determined with Differential Algebraic (DA) techniques and the code COSY INFINITY. Normal form methods are utilized to determine amplitude-dependent tune shifts as well as resonance strengths. An analysis based on a detailed description of the fringe field of the superconducting quadrupoles reveals that the strength of resonances increases by more than one order of magnitude, and that amplitude-dependent tune shifts are enhanced substantially.