Information from Beam Response to Longitudinal and Transverse Excitation

The response of a beam to small longitudinal or transverse excitation defines its "beam transfer function" (BTF). The BTF is the inverse of the stability diagram and is affected by phenomena such as Landau damping, the chamber wall impedance, active feedback systems, and non-linear resonances. The contribution of each phenomenon is extracted from the BTF. Measurement of the working line in the presence of a stack and the monitoring of instabilities is performed by suitable processing of the BTF. These measurements have a completely negligible effect on the beam quality and may therefore even be performed during periods of "stable beams". The BTF technique has been implemented in the transverse plane in a set-up involving a dual-channel fast Fourier transform (FFT) spectrum analyser. This set-up allows fast measurement of the BTF from white noise excitation of the beam. Typical examples of actual measurements are given.