# Refined betatron tune measurements by mixing beam position data

## TL;DR

This paper introduces a new method for highly precise betatron tune measurements in circular accelerators using limited turn-by-turn data, overcoming decoherence effects and improving measurement resolution.

## Contribution

The paper presents a novel technique that enhances betatron tune measurement accuracy with fewer turns, supported by theoretical, simulation, and experimental validation.

## Key findings

- Achieves high-precision tune measurements with fewer turns
- Validates method with simulations and real accelerator data
- Reduces impact of decoherence on tune measurement accuracy

## 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.