A fast tracking method using resonance basis Hamiltonians

A resonance basis map is an important way of analyzing lattice properties in circular accelerators. A method is developed to do tracking with resonance basis maps. The speed of this method is faster than other map tracking methods, and can be dramatically increased by dropping insignificant resonance terms. This mapping method enables us to simulate and study the interplay between lattice nonlinearities and other effects such as the beam-beam interaction.