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 method 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 a chromaticity measurement. 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.