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The effects of a finite beam pipe on resistive wall instabilities

The effect of resistive wall instabilities on beam break-up is investigated for beam pipes with finite and infinite thickness walls. Analytic solutions for the electric field along the beam axis are determined for both finite and infinite thickness walls using complex analysis. The longitudinal and transverse impedances are also determined; variations from the infinite wall case are observed when the wall thickness is of the order of the skin depth of the beam pipe material.