Simulations of Sextupolar Contribution to Amplitude Detuning in the LHC

Nonlinear dynamics can impact circular machines’ performance and stability. A measurement of the machine nonlinearities can be obtained by characterizing the amplitude detuning: the dependency of the tune as a function of the amplitude of particle oscillations. It has been shown that the direct amplitude detuning coming from octupoles changes by a factor 2 depending on the nature of the betatron oscillations (free or forced oscillations). This study aims to investigate the hypothesis of the sextupolar amplitude detuning exhibiting similar behavior to that of octupolar amplitude detuning. To test this hypothesis, numerical simulations for LHC were performed with MAD-X, both for an AC dipole driving the beam and for free oscillations. Analysis of the tracking data confirmed the expected behavior.