Computational studies of collective effects in particle beams in the Future Circular Collider

The conceptual design report (CDR) for the Future Circular Collider - hadron hadron (FCC-hh) is in its final stage to be presented to the European Strategy for Particle Physics Update in 2019. There are still open questions. One of these questions is whether the current stabilization program is sufficient to stabilize the beam. In this study, the stabilization effect of this scheme has been audited for the latest impedance model of the FCC-hh with two computational Vlasov solvers: Discrete-Expansion-Over-LaguerrePolynomials-and-Head-Tail-Modes (DELPHI) and Nested Head-Tail (NHT). After introducing basic concepts to analyze the beam stability, a theoretical background for these two Vlasov solvers will be described. Then a sufficient transverse feedback setting is proposed for injection and top energy. A bottleneck in the impedance of the FCC-hh and a destabilizing effect of strong resistive transverse feedback at top energy is also revealed. In addition, a comparison to an analytical approach (Sacherer formalism) is given, and it is exposed why this equation cannot be applied for the FCC-hh parameters. Keywords: FCC-hh, Beam instabilities, CDR, Collective effects, Octupoles, Transverse feedback, Wake fields, Impedance, TMCI, Destabilizing of strong resistive transverse feedback, Sacherer formalis