Impact of resistive-wall wake fields generated by low-gap chambers on the beam at the ESRF

The observation and analysis of betatron tune shifts with current mode at the ESRF are presented. The concerned tune shifts are supposed to arise from the mean quadrupolar wake field induced by the resistive low-gap chambers, which are distributed around the ring for insertion devices. By employing the scheme developed by K. Yokoya (1993), fields are computed for the actual low-gap chambers of the ESRF machine. Effective focusing strengths are then deduced to compute the tune shifts of individual bunches in an arbitrary filling. It is found that the multi-turn effect plays a key role in reproducing the observed tune shift in multibunch fillings. Tune shifts are also expected to be significant in single bunch due to the strong short-range resistive-wall wake field. Experimental evidence of the numerical finding is pursued. The impact to the coherent single bunch tune shifts and hence to the modelling of the broadband impedance is also discussed