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The measurement of chromaticity via a head-tail phase shift

The most common method of measuring the chromaticities of a circular machine is to measure the betatron tune as a function of the beam energy and then to calculate the chromaticity from the resulting gradient. Even as a simple difference method between two machine energies this technique does not allow instantaneous measurements, for instance during energy ramping or beta squeezing. In preparation for the LHC, a new approach has been developed which uses the energy spread in the beams for chromaticity measurements. Transverse oscillations are excited with a single kick and the chromaticity is calculated from the phase difference of the individually sampled head and tail motions of a single bunch. Using this method the chromaticity can be calculated using the data from only one synchrotron period (about 15–50 msec in the case of the LHC). This paper describes the theory behind this technique, two different experimental set-ups, and the results of measurements carried out in the SPS.