Simulation of multibunch motion with the Headtail code and application to the CERN SPS and LHC

Multibunch instabilities due to beam-coupling impedance can be a critical limitation for synchrotrons operating with many bunches. It is particularly true for the LHC under nominal conditions, where according to theoretical predictions the 2808 bunches rely entirely on the performance of the transverse feedback system to remain stable. To study these instabilities, the HEADTAIL code has been extended to simulate the motion of many bunches under the action of wake fields. All the features already present in the single-bunch version of the code, such as synchrotron motion, chromaticity, amplitude detuning due to octupoles and the ability to load any kind of wake fields through tables, have remained available. This new code has been then parallelized in order to track thousands of bunches in a reasonable amount of time. The code was benchmarked against theory and exhibited a good agreement. We also show results for bunch trains in the LHC and compare them with beam-based measurements.