Strong-Strong Simulations of β$^∗$-Levelling for Flat and Round Beams

Simulations of β$^∗$ luminosity levelling using the strongstrong beam-beam code COMBI are undertaken. Simulations for both flat and round beam profiles are discussed and analysed with respect to the coherent spectra. It is shown that bunches with a round beam profile will have a beambeam parameter that is independent of β$^∗$ over the levelling steps. Flat bunches however will have a beam-beam parameter that is dependent on β$^∗$ over the levelling steps since the beam aspect ratio will change. This will change the tune of the π-mode as the β$^∗$ is levelled, which could lead to a resonance crossing.