Beam Transfer Function Measurements and Transverse Stability in presence of Beam-Beam

Instability thresholds are explored at the Large Hadron Collider (LHC) by means of the computation of the Landau Stability Diagram (SD). In the presence of diffusive mechanisms, caused by resonance excitations or noise, the SD can be reduced due to the modification of the particle distribution inside the beam. This effect can lead to a possible lack of Landau damping of the coherent modes previously damped by lying within the unperturbed SD area. The limitations deriving from coherent instabilities in the LHC is crucial in view of future projects that aim to increase the performance of the LHC such as the High-Luminosity upgrade (HL-LHC) or Future Circular Collider (FCC). Simulation tools for the computation of the SD have been extended in order to take into account the incoherent effects from long particle tracking through the detailed model of the accelerator machine. The model include among others beam-beam interactions and octupoles and the interplay between both is addressed. Finally the simulation results are compared to the Beam Transfer Function (BTF) measurements in the LHC.