TUNE EVALUATION IN SIMULATIONS AND EXPERIMENTS

In circular accelerators, the betatron tune is measured by analysing t he particle coordinates, sampled over N turns. Algorithms based either on the Average Phase Advance method or on the Fast Fourier Transform (FFT) are routinely used to compute the tune. More sophisticated appro aches have recently been proposed. They rely on analytical interpolati ons of the FFT, as suggested by E. Asseo, or on algorithms based on co ntinuous spectral analysis, according to the studies of J. Laskar. In this paper we critically review the various methods of measuring the t une and we present analytical estimates of the error as a function of N. The results are supported by numerical simulations carried out on b oth simple and complicated lattices, including nonlinear magnets. Appl ications to experimental data obtained in the CERN SPS are also shown.