Tune Determination of Strongly Coupled Betatron Oscillations in a Fast-Ramping Synchrotron

Abstract: Tune identification - i.e. attribution of the spectral peak to a particular normal mode of oscillations - can present a significant difficulty in the presence of strong transverse coupling when the normal mode with a lower damping rate dominates spectra of Turn-by-Turn oscillations in both planes. The introduced earlier phased sum algorithm helped to recover the weaker normal mode signal from the noise, but by itself proved to be insufficient for automatic peak identification in the case of close phase advance distribution in both planes. To resolve this difficulty we modified the algorithm by taking and analyzing Turn-by-Turn data for two different ramps with the beam oscillation excited in each plane in turn. Comparison of the relative amplitudes of Fourier components allows for automatic correct tune identification. The proposed algorithm was implemented in the Fermilab Booster B38 console application and successfully used in tune, coupling and chromaticity measurements.