Exact solutions for the longitudinal and transverse impedances of an off-centred beam in a rectangular beampipe

The longitudinal and transverse impedances of an off-centered beam in a rectangular beampipe are solved exactly using conformal mapping. The results are represented in each case by the product of the corresponding impedance due to a circular beampipe with the beam at the center and a form factor that takes into account that the beampipe is rectangular in shape and that the beam is off center. When the width to height ratio of the beampipe is large, the form factor is found to stay flat for a wide range of beam displacement. Both effects due to the resistivity of the beampipe wall and to space charge are considered. (author)