The installation of more and more devices of irregular shape in the machine vacuum vessel, in particular transitions to vessels of small vertical aperture, has detrimental effects on the beam. The bunch length, the energy spread, as well as the current thresholds of longitudinal and transverse instabilities are affected. Their deterioration can significantly spoil the performance of the machine operation. The underlying effect is characterised by a deformation of the self-field of the beam (wake field) that leads to an inhomogeneous deceleration and acceleration of the individual bunches in longitudinal as well as in transverse direction. The effect is formally expressed in the quantities known as longitudinal and transverse machine impedance.

During the design phase of the machine, calculations were already carried out to estimate the machine impedances. However, to obtain correct results the description of the input geometry has to be very fine. Furthermore, the available computing power was very limited and so the calculations were only made in two dimensions. However, today, using parallel computing and an adequate programme (GdfidL) [1,2], the electromagnetic interaction of the beam with the vacuum chamber geometry can be studied correctly in detail in three dimensions. This is essential for the impedance evaluation of devices of complex geometry such as a scraper.

So, in parallel to the study of the beam transverse motion described above and to the development of a Machine impedance model based on measurements, a campaign was started to compute the contribution of each vacuum chamber device to the impedance of the machine. The aim is to merge both models to obtain a common view of the impact of the machine impedance on the beam, in particular on the mode detuning and on beam instabilities. The effect of a number of devices, essentially vacuum chamber tapers, has already been calculated. It is intended to cover all devices along the machine circumference. The results will lead to the improved design of certain vacuum chamber elements to reduce their spoiling impact on the beam. Ultimately this will allow an increase of the current thresholds of various beam instabilities and therefore improve the performance of the machine.

[1] W. Bruns, GdfidL: A Finite Difference Programme with Reduced Memory and CPU Usage, PAC 97,Vancouver, p. 2651.
[2] W. Bruns, Improvements in GdfidL, PAC 99, NY.