Beam-based measurements of the skew-sextupolar component of the radio frequency field of a HL-LHC-type crab-cavity

Two High Luminosity Large Hadron Collider (LHC) crab-cavity types have been installed in 2018 in the CERN SPS for testing purposes. An attempt to characterize the skew-sextupolar component (a3) of the radio frequency field of the crab-cavity through beam-based techniques has been carried out. By monitoring with turn-by-turn beam position monitors the betatron motion, it was possible to study the non-linear coupling between the transverse planes resulting from the skew nature of the a3 component of the crab-cavity. A measurement of the magnitude of a3 was thus obtained by characterizing amplitude and phase of some of the spectral lines induced by such non-linear coupling. Particular attention was required to disentangle the a3 contribution of the crab-cavity from the SPS optics non-linearities, that unexpectedly was found to play a dominant role over the faint signal induced by the crab-cavity skew-sextupolar component. A detailed description of the measurements, analysis and the results are here presented.