HIGH CURRENT SINGLE BUNCH TRANSVERSE INSTABILITIES AT THE ESRF: A NEW APPROACH

Abstract

Single bunch operation at the ESRF is severely limited by vertical coherent instabilities. The user requirement (15 mA) is much above the mode-coupling instability threshold (0.7 mA), observed at a low chromaticity. The nominal current is reached by increasing the vertical chromaticity to a large positive value, and by lengthening the bunch with a reduction of the RF voltage. The transverse feedback implemented and tested at various chromaticities is not quite as efficient. Although the classical head-tail theory could be applied below the threshold, it does not explain the hard edged and higher threshold observed. The measured fast growth of the instability invalidates the notion of synchrotron motion and in consequence the notion of head-tail modes. The idea of a post-head-tail mechanism is introduced. The theory, simulation results and experimental verifications are presented. A model of the machine impedance is also discussed. Initially efforts were concentrated towards the classical head-tail theory in order to understand the ESRF vertical instability threshold. The discrepancies between the predictions of the head-tail theory and the observations realised at the ESRF led us to imagine that the ESRF does not evolve in the head-tail regime in the vicinity of the threshold at positive chromaticity. Measurements and tracking simulations confirmed that the implied instability in the threshold mechanism is much faster than the synchrotron motion. The head-tail theory, which deals with collective modes based on the synchrotron motion, is not appropriate to describe such a phenomenon. A post-headtail theory that considers instabilities faster than the synchrotron motion is proposed in this paper. The theoretical post-head-tail intensity threshold is consistent with the measured one at the ESRF.