Transverse instabilties in the ESRF storage ring: simulation, experimental results and impedance modelling

Transverse coherent single bunch motions are studied theoretically and experimentally for the ESRF machine. Starting from the mode-merging instability observed at low chromaticities, the head-tail mode frequencies and current thresholds are measured systematically in the vertical plane as functions of chromaticity, beam current, RF voltage and optics. Measurement of damping and growth rates of the dipolar mode is also attempted as a function of chromaticity to characterise the machine impedance empirically. Theoretical analysis is made in parallel to investigate the dynamics and to fit the model impedance to best reproduce the observations. Two numerical methods are employed: multi-particle tracking and solution of an extended Sacherer´s equation with the program MOSES. It is found that the machine impedance can be well represented by a simple BBR (broad band resonator) impedance, the parameters of which are quasi uniquely be determined from the fit of the mode-merging instability. It is experimentally shown that the low gap vacuum chamber sections contribute largely to the machine impedance. The resultant model is found to describe the observed thresholds at higher chromaticities as well, the dynamics of which is analysed to consist of higher-order head-tail instabilities