The measurement of Q' and Q'' in the CERN-SPS by head-tail phase shift analysis

A so-called "Head-Tail" chromaticity measurement system has recently been installed in the CERN-SPS, which allows the chromaticity (Q') to be calculated from several hundred turns of data after transverse excitation. The measurement relies on the periodic dephasing and rephasing that occurs between the head and tail of a single bunch for non-zero chromaticity. By measuring the turn-by-turn position data from two longitudinal positions in a bunch it is possible to extract the relative dephasing of the head and the tail, and so to determine the chromaticity. In addition, by changing the orbit of the circulating beam this technique allows the variation of chromaticity with radial position (Q'') to be measured with a much higher resolution than is currently possible using RF modulation. This paper describes this "Head-Tail" measurement technique and discusses some recent results obtained using prototype LHC beam (25ns spacing) in the CERN-SPS.