Decoherence of a longitudinally kicked beam with chromaticity

In this report a method to measure the machine chromaticity is presented. This method consists in applying a longitudinal kick to the beam and computing the Fourier transform of the transverse turn-by-turn position. Analytical expressions for the Fourier transform are derived, which show how the chromaticity can be inferred from the synchrotron sidebands. Multiparticle simulations are also performed to validate the analytical expressions.