Hybrid fast multipole method applied to beam-beam collisions in the strong-strong regime

The strong-strong interactions of two colliding beams are simulated by tracking the motion of a set of macroparticles. The eld generated by each distribution is evaluated using the Fast Multipole Method (FMM) together with some elements of particle-mesh methods. This technique allows us to check the exact frequencies of the coherent modes and the frequencies of oscillations of individual particles in the beam. The agreement between the simulations and analytical calculations is largely improved. Furthermore it is an ecient method to study the coherent modes in the case of separated beams.