Symplectic map tracking for the LHC

Tracking simulations remain the essential tool for evaluating how multipolar imperfections in ring magnets restrict the domain of stable phase-space motion. In the LHC, particles circulate at the injection energy, when multipole errors are most significant, for more than 10 million turns, but systematic tracking studies are limited to a small fraction of this total time-even on modern computers. A considerable speed-up is expected by replacing element-by-element tracking with the use of a symplectified one-turn map. We have applied this method to the realistic LHC lattice, version 6, and report here our results for various map orders, with special emphasis on precision and speed.