Exact Solutions for the Longitudinal and Transverse Impedances of an off-Centered Beam in a Rectangular Beampipe

摘要

In storage rings and accumulators, some sections of the beampipe may be rectangular in cross section and the beam may not be at the center of the beampipe. In this note, through conformal mapping, we try to compute exactly the longitudinal, vertical and horizontal transverse impedances for the beam under these circumstances. For simplicity, we restrict the beam to the horizontal symmetry axis of the beampipe. Both the effects due to the resistivity of the beampipe's wall and space-charge are considered. (ERA citation 09:008360)