Ultra Compact Symplectic Scheme for Fast Multi-Particle Tracking

A versatile symplectic integration scheme has been developed in order to produce simplified versions of non linear lattices, preserving fundamental non-linear properties such as the detuning with amplitude and energy, in addition to the linear transport. The method has been applied to the LHC and benchmarked against tracking simulations with Sixtrack. This reduced lattice is made available as a refined replacement of the simple rotation matrix often used in multi-particle studies requiring a fast beam transport routine.