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

Two High Luminosity Large Hadron Collider (LHC) type crab-cavities have been installed in the CERN SPS for testing purposes. An attempt to characterize the skew-sextupolar component of the radio frequency field of the crab-cavity ($a_3$) has been carried out by means of beam-based techniques using turn-by-turn monitoring of the betatron motion. The skew nature of $a_3$ couples the horizontal and vertical betatron motions through a non-linear term. Therefore by exciting the horizontal betatron motion it was possible to observe a spectral line in the vertical beam motion driven by the non-linear coupling at the characteristic frequency $2Q_x$. A measurement of the magnitude of $a_3$ was thus obtained by characterizing amplitude and phase of such line. The results of the measurements are discussed here.