Tune shifts of eccentric beams in elliptic vacuum chambers

The incoherent image coefficients of thin beams in elliptic chambers have been expressed in closed form, and are summarized in two graphs, including the limiting cases of circular and parallel plate geometries. Several cases of beams of finite widths are also shown graphically, as well as the contribution due to direct space-charge. For circular chambers, which are usually proposed for future superconducting machines, it can be seen that the image coefficients can become quite large for eccentric beams, and should not be neglected. As an example, the geometric coefficients are used to calculate the tune shifts of substacks on a dynamically compensated working-line in the ISR. (6 refs).