Beam Measurements of the LHC Impedance and Validation of the Impedance Model

Abstract

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 Ω, 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. MOTIVATION During the design phase of the LHC, significant efforts were made to reduce its impedance in order to minimize the impact of collective effects on the accelerator performance. Thanks to that, no longitudinal instabilities have been observed for operational parameters so far. However, as anticipated, controlled longitudinal emittance blow-up during the acceleration is required for stability. Future LHC operation with higher intensity beams relies on an improved impedance model verified by measurements. According to the LHC Design Report [1] and the current LHC impedance model [2], the LHC reactive impedance Im Z/n is 0.08 Ω. This value is very small compared to other CERN proton accelerators, e.g. 4 Ω in the SPS and 20 Ω in the PS. Therefore, beam measurements of the LHC impedance with usual methods are very challenging. A first attempt to measure the resistive part of the longitudinal impedance from synchronous phase measurements was presented in [3]. In this paper, beam measurements of the reactive part of the longitudinal impedance are described together with simulations based on the LHC impedance model. An estimate of Im Z/n from the synchrotron frequency shift is given therein. Also, observations of the loss of Landau damping are compared with simulations. In the LHC, injection and acceleration need more time than in other accelerators. In addition, the time dedicated to Machine Development (MD) is very limited and highly demanded, so only a few sessions devoted to this subject took place during the LHC Run1 and the results are discussed here.