Transverse Feedback Parameter Extraction from Excitation Data

In this paper we present a simple and fast approach to extract essential parameters of a transverse feedback system such as phase advances between pick-ups and kickers, fractional tune, kicker delay, or per-bunch transverse activity from discrete-time samples of position signals. In this approach the beam is excited and subsequent beam oscillations are recorded. Given that any number of pick-ups can be evaluated at once with only a marginal increase of transverse beam size this method is suitable for regular health checks of a transverse feedback system, e.g., for every injection. The fundamental idea relies on the reconstruction of the transverse phase space by means of digital filters. We sketch a simple mathematical model to illustrate the underlying method. Examples are given together with a set of filter kernels for the fractional tunes of the LHC transverse feedback system.