The increase in the number of chambers of irregular shape in the machine, in particular transitions to vessels of small vertical aperture, has had detrimental effects on the beam. The machine's performance is suffering (along with other effects) from the strong detuning of the working point with increasing current resulting in low values of the current, thresholds of longitudinal and transverse instabilities [1]. The underlying effect is characterised by a deformation of the self-field of the beam (wake field) which leads to an inhomogeneous deceleration and acceleration of the individual bunches in the longitudinal as well as in the transverse direction. The effect is formally expressed in the quantities known as longitudinal and transverse machine impedance.

Determination of the machine impedance requires the calculation of the geometrical wakefield produced by each piece of the vacuum chamber of the ring. The computation is made in three dimensions with a dedicated program [2] which requires significant computer resources. This task was initiated in 2000 and is advancing. So far it has been restricted to the vertical plane. The main purpose consists in understanding the detuning of the single bunch as a function of current. The vertical transverse impedance of all tapers (including in-vacuum undulators), cavities, scrapers, RF-fingers and pumping slots have already been calculated. The contribution from each element is weighted by its local vertical beta-function. Simulations show that the contribution from some components located at a spot where the vertical beta-function is high plays a much more important role than originally expected. This is true in particular for the RF-fingers (located inside the bellows) whose change in cross-section from one extremity to the other is found to produce the dominant contribution of the total transverse impedance, even assuming perfect electrical contact of the fingers.

At present, the simulations can account for one half of the measured detuning. The study will be continued to identify the other elements having an important vertical transverse impedance contribution. It will also be extended to the horizontal plane. Such studies allow the ab initio computation of the impedance contributions generated by each new piece of vacuum chamber and can therefore be used to find a satisfactory engineering solution minimising the impact on beam stability.

[1] J.L. Revol, R. Nagaoka, P. Kernel, L. Tosi, E. Karantzoulis, EPAC 2000 Vienna.
[2] W. Bruns, GdfidL: A Finite Difference Program with Reduced Memory and CPU Usage, PAC 97,Vancouver, p. 2651.
[3] ESRF Highlights 2000.