Analysis of the head tail damping and growth time for the estimation of the ESRF machine impedance

A theoretical and experimental characterisation of transverse damping mechanisms was initiated within the framework of the single bunch transverse instability studies. An attempt is made to estimate the machine impedance through the measurement of the head tail damping time as a function of the chromaticity. The presence of strong sextupole fields used for chromaticity compensation however induces large momentum and amplitude dependent tune shifts. A systematic study of the different damping mechanisms was therefore performed in order to quantify the different contributions, which for the ESRF storage ring are in the same range. Numerical simulations and record of the beam response to a kick were performed. The transverse signal decay after the excitation was observed on the tune monitor system used in zero span mode. The tune amplitude dependence which depends on the kick amplitude is discussed first. Then the modulation induced by chromaticity overcompensation which could blind the observation is described. The measurement of the head tail damping and growing time, under precise operating conditions, with positive and negative chromaticity, is presented. Finally, a model for the machine impedance is discussed