Beam measurements of the LHC impedance and validation of the impedance model

Different measurements of the longitudinal impedance of the LHC done with single bunches with various intensities and longitudinal emittances during measurement sessions in 2011-2012 are compared with particle simulations based on the existing LHC impedance model. The very low reactive impedance of the LHC, with Im Z=n = 0.08, is not easy to measure. The most sensitive observation is the loss of Landau damping, which shows at which energy bunches become unstable depending on their parameters. In addition, the synchrotron frequency shift due to the reactive impedance was estimated following two methods. Firstly, it was obtained from the peak-detected Schottky spectrum. Secondly, a sine modulation in the RF phase was applied to the bunches of different intensities and the modulation frequency was scanned. In both cases, the synchrotron frequency shift was of the order of the measurement precision.