Abstract
The measurement of the betatron tunes in a circular accelerator is of paramount importance due to their impact on beam dynamics. The resolution of the these measurements, when using turn by turn (TbT) data from beam position monitors (BPMs), is greatly limited by the available number of turns in the signal. Due to decoherence from finite chromaticity and/or amplitude detuning, the transverse betatron oscillations appear to be damped in the TbT signal. On the other hand, an adequate number of samples is needed, if precise and accurate tune measurements are desired. In this paper, a method is presented that allows for very precise tune measurements within a very small number of turns. The theoretical foundation of this method is presented with results from numerical and tracking simulations but also from experimental TbT data which are recorded at electron and proton circular accelerators.
Highlights
Betatron tune measurements [1] are used as a reliable diagnostic of transverse beam dynamics
Numerical simulations are performed with PyNAFF [22], in order to qualitatively investigate the theoretical derivations of the mixed beam position monitor (BPM) method
The method has been proven to be extremely efficient for precise tune measurements with a very small number of turns
Summary
Betatron tune measurements [1] are used as a reliable diagnostic of transverse beam dynamics. The measurement of the working point of a circular accelerator is an essential procedure in order to optimize performance and reduce particle losses In such an accelerator, each beam position monitor (BPM) records the betatron oscillations of the centroid in the transverse plane for many turns. For the case of a simple fast Fourier transform (FFT) algorithm [5], the exponent l in Eq (1) is l 1⁄4 1, which is inadequate for a precise determination of the betatron tunes in a circular accelerator To overcome such limitations, refined frequency analysis (RFA) methods have been developed [2,6,7] which offer a substantially improved resolution in tune estimations, with respect to a plain FFT. The resolution has been analytically calculated from Laskar to have the asymptotic approximation for N → ∞ [14]:
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