PRECISE MEASUREMENT OF THE BETATRON TUNE

In circular accelerators, sophisticated algorithms for frequency analy sis can provide very precise estimates of the betatron tune from a rel atively short sequence of turn-by-turn measurements of the beam positi on. They rely either on analytical interpolations of the Fast Fourier Transform, or on the numerical estimate of the Continuous Fourier Tran sform. In this paper we review these methods, and the analytical estim ates of the frequency error as a function of the sample size. Furtherm ore, we evaluate numerically the influence of noise in the determinati on of the tune. Finally, we present experimental applications to the L EP machine: they provide an accurate estimate of the detuning with amp litude due to the chromaticity sextupoles.