Accurate crab cavity modeling for the high luminosity Large Hadron Collider

As part of the Large Hadron Collider high luminosity upgrade it is proposed to include crab cavities in the lattice in order to enhance the luminosity. For one proposed cavity design the dynamics of the cavity is considered in terms of its impact upon the dynamic aperture of the machine. Taylor maps of the cavity are created and used to perform this analysis with a full assessment of their validity. Furthermore from these Taylor maps, symplectic methods are developed further, guided by the knowledge gained in the study of the physics contained in them