Studies of transverse single bunch instabilities, which began in 1997 partly as the thesis work of P. Kernel, in collaboration with G. Besnier (Univ. of Rennes), were accomplished during autumn 2000. The mechanism of instabilities that severely limit the maximum single-bunch current in the ESRF machine, unless one sets the chromaticity to a large positive value at the cost of reducing the lifetime, was investigated both experimentally and theoretically. A systematic investigation starting from the characterisation of instabilities at low currents, followed by the modelling of the machine impedance, led to a marked prediction that growth times of the instability at high currents may become even shorter than the synchrotron oscillation period.

The conclusion obtained, however, is not compatible with the classical head-tail theory. A theory beyond the head-tail regime was further formulated to describe what is named as a "post head-tail instability", according to which the instability develops when the coherent tune shift exceeds the width of the energy-dependent betatron tune spread in an electron bunch. The established theory was confirmed which explains the measured instability thresholds well. An equally important finding, obtained numerically through particle tracking (which explains the postponement of the instability until the post head-tail regime) is the stabilisation effect brought about by the synchrotron tune spread. It can therefore be said that high single-bunch currents are reached due to the presence of longitudinal instabilities. 

Multibunch operations at the ESRF are affected by the resistive-wall (RW) instability. Thresholds are raised with positive chromaticities and by adopting a partial filling. To have a better control of the instability, a systematic study was initiated. In parallel, the effectiveness of a transverse feedback was investigated. Measurement of instability thresholds due to a specific coupled-bunch (CB) mode provided an interesting link to the single-bunch studies, enabling a separation of the RW contribution from the rest of the broadband impedance, which was not evident in the former study.

Measurement of the vertical emittance growth with an X-ray pinhole camera proved to be excellent way for an early detection of vertical instabilities which exhibited several interesting results: 1) Partial fillings have a clear threshold at around the same chromaticity. 2) A non-uniform continuous filling has an extra stabilising effect even compared to partial fillings. 3) The uniform filling has a long tail of instability versus chromaticity and has a threshold at a larger chromaticity. The large incoherent tune shift observed in the multibunch filling was identified to be due to a long-range wake field generated by the RW of an asymmetric cross section, and its possible link to 2) is being investigated.

The prototype vertical feedback that makes a mode-by-mode suppression of instability on two independent CB modes successfully suppressed the two strongest RW CB modes, restoring both the vertical emittance and lifetime, in the uniform as well as in a partial filling. Through feedback studies the long tail in 3) revealed it to be due to excitation of modes that do not belong to the RW instability, which raised the question of ion trapping. A series of experiments were performed to pursue the mode evolution against chromaticity, beam current, coupling and particularly, the vacuum level. The ion-electron instability was observed not only in the uniform filling, but also in partial filling when the vacuum level was notably high, such as immediately after work on the vacuum system. While the former is identified to be the classical ion trapping, the latter is considered to be the so-called fast beam-ion blow up, which occurs due to the interaction within a single passage of the train of electron bunches. Further analysis of these ion instabilities is underway.