Symplectic Map Tracking for the LHC

Tracking simulation is the essential tool to evaluate how multipolar imperfections of the magnets limit the regime of stable particle motion in phase space. In the LHC, for instance, particles have to remain at injection energy, where the multipolar errors are at their maximum, for more than 10 million turns. Systematic tracking studies have to be limited to a small fraction of this total time even on modern computer systems. A considerable speed-up is expected when a symplectified one-turn map can be used instead of the element-by-element tracking. In this report we have applied this method for various map orders to the realistic case of the LHC lattice version 6 with special emphasis on precision and gain in speed