Measurement of Resonance Driving Terms from Turn–by–turn Data

It has been shown that the Fourier analysis of recorded turn–by–turn tracking data can be used to derive resonance terms of an accelerator. Beside the resonance driving terms, the non–linear one–turn map can be obtained with all non–linearities arising from magnetic imperfections and correction elements. This could be interesting for the LHC which will be a machine dominated by strong non–linear fields. The method works very well for tracking data and is expected to work equally well for turn–by–turn beam data. The precision to which these terms can be determined relies on the frequency analysis tool. To demonstrate the feasibility of the method, measurements of real accelerators are presented in which the beam is kicked once and the beam oscillations are recorded over several thousand turns. Besides the tune, the strengths of resonance driving terms have been measured and the results are compared with numerical calculations.