Beam-based studies at the LHC injection energy showed that compensation of the strongly driven sextupolar resonance, Qx+2Qy, improved both the dynamic aperture and lifetime of the beam, even when far from the working point and on the far side of the 3Qy resonance. Thus, a reduction of other strong normal sextupolar resonance sources was of interest. In 2024, the first measurements of resonance driving terms with long-range beam-beam (LRBB) interactions were performed. These showed that LRBB was driving the same Qx+2Qy resonance strongly when colliding, in agreement with model predictions. A correction was found for the strongest normal sextupole resonances using the existing sextupole corrector magnets in the LHC, obeying the constraints on the chromatic coupling and the maximum magnet powering. Beam-based tests to validate the response of this correction with non-colliding beams have been performed along with the testing of the LRBB resonance correction during LHC commissioning.

During operation for luminosity production, the LHC runs with very strong Landau octupoles to ensure the collective stability of the beams. A disadvantage of this is that these octupoles can drive resonances which can be detrimental to beam lifetime. Recently, a special optics configuration has been utilised to reduce the impact of the main octupoles on lifetime. This design relies on correctly modelling the resonance driving term (RDT) response to changes in these magnetic circuits. This paper presents beam-based studies comparing the RDT response to simulations where large discrepancies were found. To try and understand the source of this, several approaches were taken. Various methods including individual circuit measurements, studies of other circuits, and tests at different energy were employed but it remained challenging to localise the source of the discrepancy around the ring. This paper presents an attempt to apply and extend a segment-by-segment method, that has been very effective at identifying local linear optics errors, to non-linear errors through analysis of RDTs.