Ricerc@Sapienza

The study of collective effects in circular accelerators can be tackled by solving numerically the Vlasov equation or by using tracking codes. The two methods are obtained with different approaches: Vlasov solvers consider a continuous distribution function and describe the beam with coherent oscillation modes in frequency domain (ending up usually with an eigenvalue system to solve), while tracking codes use macroparticles and wakefields in time domain.

Following the same approach as for the recently developed GALACTIC Vlasov solver in the transverse plane and taking into account the potential-well distortion, a new Vlasov solver, called GALACLIC, was developed for the longitudinal plane. In parallel, a new mode analysis was implemented for the post-processing of the results obtained through macroparticle tracking simulations. The results of the several benchmarks performed between the two methods are presented.

The Future Circular Collider (FCC) study aims at designing different options of a post- LHC collider. The high luminosity electron-positron collider FCC-ee based on the crab waist concept is considered as an intermediate step on the way towards FCC-hh, a 100 TeV hadron collider using the same tunnel of about 100 km. Due to a high intensity of circulating beams the impact of collective effects on FCC-ee performance has to be carefully analyzed.