Transverse beam instabilities and linear coupling in the LHC

Transverse beam instabilities had been observed in the LHC when the tunes were moving closer together (Laslett tune shift at injection) or when the coupling was known to be large (the beam measurement of the closest tune approach, |C-| showed an increase to approximately the tune separation). This knowledge, in addition to the examples of transverse beam instabilities seen during the energy ramp at the HERA proton ring, hinted at a link between linear coupling and transverse stability. Linear coupling had been used in the Proton Synchrotron (PS) at CERN to stabilise a strong horizontal instability by coupling into the vertical plane. This was possible due to a sharing of the instability rise times between the two planes. These two sets of observations are seemingly in contradiction to each other. This provided the motivation for a study into how linear coupling plays a role in transverse beam stability in the LHC.