Nonlinear single particle issues for the LHC at CERN

One of the critical design issues of the LHC is the field quality of the super-conduting dipole and quadrupole magnets, in particular at injection energy. In close collaboration with the magnet designers the field quality is optimised with respect to required dynamic aperture and technological and financial limitations. The main tool is still brute force tracking simulations. The simulation codes are simple, easily adaptable to new requirements and highly optimised for the use on modern computer architectures. To perform the massive tracking studies needed to do this field quality optimisation, a cluster of 20 DEC alpha workstations has been purchased. On the other hand one has to analyse these tracking results with tools that can evaluate the highly nonlinear content of the accelerator structure. In the last decade the Normal Form Tool and more recently the Frequency Map Analysis have been introduced to our field which allow for such an analysis. A number of programs have been developed that are based on these methods and their usefulness will be demonstrated for the special case of the LHC.